Category: 1st PUC

Students can Download 1st PUC Chemistry Model Question Paper 4 with Answers, Karnataka 1st PUC Chemistry Model Question Papers with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

Karnataka 1st PUC Chemistry Model Question Paper 4 with Answers

Time: 3.15 Hours
Max Marks: 70

Instruction:

1. The questions paper has five parts A, B, C, D and E. All parts are compulsory.
2. Write balanced chemical equations and draw labeled diagram wherever allowed.
3. Use log tables and simple calculations f necessary (use of scientific calculations is not allowed).

Part – A

I. Answer ALL of the following (each question carries one mark): ( 10 × 1 = 10 )

Question 1.
Give an example for a homogeneous mixture.
Answer:
Air, Gasoline, Sea water, etc.

Question 2.
Write the ideal gas equation for ‘n’ moles of a gas.
Answer:

Question 3.
What is hydronium ion?
Answer:
H₃O⁺ is called hydronium ion

Question 4.
Write the IUPAC name of an element with atomic number 107.
Answer:
Ununnillium.

Question 5.
Identify the element in the compound K₂Cr₂O₇ showing negative oxidation number.
Answer:
Oxygen.

Question 6.
Name the gas liberated when a piece of sodium metal is added into the water.
Answer:
Hydrogen (H₂).

Question 7.
What is Zeolite?
Answer:
Zeolites are alumino silicates having a three-dimensional cage like structure with a general
formula Mⁿ⁺_x/n [(AlO₂)_x(SiO₂)_y]H₂O, where M is a cation ion like K⁺Na⁺,Ca²⁺.
These are obtained by replacing some of the silicon atoms by aluminium atoms. The aluminosilicate thus formed acquires negative charge and it is balanced by the cations like
Na⁺,K⁺ or Ca²⁺

Question 8.
Give the composition of water gas.
Answer:
Water gas [CO + H₂] is a mixture of carbon monoxide and hydrogen.

Question 9.
Write the bond line formula for 3-chloro octane.
Answer:

Question 10.
Alkanes are not soluble in water. Give reason.
Answer:
Non-polar and saturated.

Part – B

II. Answer any FIVE of the following questions carrying TWO marks: (5 x 2 = 10 )

Question 11.
Calculate the molarity of NaOH in the solution, prepared by dissolving lOg in enough water to form 500mL of the solution. Molar mass of NaOH is 40 g mol^-1
Answer:

Question 12.
Give any two differences between ideal and non-ideal (real) gas.
Answer:
Ideal Gas

1. Obeys ideal gas equation PV = nRT.
2. Ideal gas does not exist in nature.

Real Gas:

1. Does not obeys the ideal gas equation but obeys van der Waals equation.
2. All gases which exist in nature are real gases.

Question 13.
Mention any two conditions for the combination of atomic orbitals.
Answer:
The conditions for the combination of atomic orbitals are:
(a) The combining atomic orbitals should have comparable energy.
1s orbital can combine with another Is orbital but not with 2s orbital.

(b) The combining atomic orbitals should have the same symmetry about the molecular axis. For example: 2p orbital can combine with 2s orbital or another 2p_z orbital but not with 2p_x or 2p_y.
2s cannot combine with 2p_x or 2p_y .
(c) The combining atomic orbitals must overlap to the maximum extent.

Question 14.
Complete the following equations:
(i) 4Li + O₂ → _____
Answer:

(ii) 2Na + O₂ → _____
Answer:
2Na + O₂ → Na₂O₂ (Sodium peroxide)

Question 15.
(a) What is dry ice?
Answer:
Solid CO₂ is called dry ice. It is called dry ice because it directly changes into gaseous state without becoming liquid.

(b) Write the formula of basic structural unit of silicates.
Answer:
Silicates are the compounds in which the anions are present as either discrete SiO^- tetrahedral or a number of such units joined together through comers.

Silicates are basically made up SiO⁴_4- tetrahedra (as shown in the figure) in which silicon atom is bonded to four oxygen atoms in a tetrahedral manner. In the figure, big circles indicate oxygen atoms and small circle indicates silicon atoms.

Question 16.
Explain Wurtz reaction with a suitable example.
Answer:
When alkyl halides are heated with sodium metal in ether medium higher alkanes are formed. This reaction is known as Wurtz reaction and employed for the synthesis of higher alkanes containing even number of carbon atoms.

Question 17.
What are benzenoids? Give an example.
Answer:
Aromatic compounds with palanar structure and delocalized n e A above and below the plane of the ring, eg: Benzene, Toluene.

Question 18.
How ozone is formed in the atmosphere? Give equations.
Answer:
The UV radiations of very short wavelength (< 250 nm) have sufficient energy to cause photo – dissociation of oxygen molecules into oxygen atoms. Highly reactive oxygen atoms combine with oxygen molecules to form ozon

Part – C

III. Answer any FIVE of the following questions carrying THREE marks: (5 x 3 = 15 )

Question 19.
(a) Write the general electronic configuration of p-block elements.
Answer:
General electronic configuration of p-block elements is ns² np^1_6.
Both s and p block together is called representative or normal elements.

(b) How does ionisation enthalpy varies along a period and down the group?
Answer:
The amount of energy required to remove the most loosely bound electron from an isolated gaseous atom. Ionization energy increases along the period and decreases down the group.

Question 20.
Define the terms (a) Bond angle (b) Bond order (c) Co-valent radius.
Answer:
(a) Bond angle: It is defined as the “angle between the oribitals containing bonding electron pairs around the central atom in a molecule or in a complex ion”. It is expressed in degrees.
Example: In CO₂ the bond angle is 180°. So CO₂ has linear shape.
(b) Bond order: It is the number of covalent bonds holding the atoms in the molecule. Example: If the bond is formed by the sharing of two electron pairs, then the bond order is 2. O = O or C = C bond in alkenes.
(c) Co-valent radius: A chemical bond formed by the sharing up of one or more electrons between the atoms.

Question 21.
Give any three important postulates of VSEPR theory.
Answer:
Bonding : The bond formation takes place if there exists impaired electron in the valance shell.
Shape : The geometry or the shape of a molecule depends on the number of valence shell electrons surroundings the central atom.
Repulsion : Electron pair tend to repell one another because electron clouds have similar charge.
Stability : As a result of electron pair repulsion these electron pairs try to stay apart as possible in order to attain minimum energy and maximum stability.
Repulsive interaction : Lane pair with lane pair electrons are having maximum repulsive interaction, bond pair-bond pair electrons are having minimum repulsive interaction. When angle of repulsion decreases angle between the electron pair increases (109°. 28′ less repulsion, 104° more repulsion).

Question 22.
Explain bonding in H₂ molecule based on the basis of Molecular orbital theory.
Answer:
Atomic number of hydrogen is 1 = Is’

(a) Electronic configuration of hydrogen molecule is σ1s²σ*1s⁰
(b) Bond order – \(\frac{2-0}{2}\) = 1
(c) Magnet property = diamagnetic.

Question 23.
(a) What is the oxidation number of Cl in KClO,sub>3 ?
Answer:
+5

(b) Write the separate equations for the oxidation and reduction reactions occuring in the given redox reaction. 2Fe + HCI → FeCL₂ + H₂
Answer:

Question 24.
Explain the process of softening of temporary hardness by Clark’s method.
Answer:
Clark’s process: Temporary hardness can be removed by the addition of a calculated amount of lime, where magnesium carbonate or calcium carbonate is precipitated.
Ca(HCO₃)₂ + Ca(OH)₂ → 2CaCO₃ +2H₂O
Mg(HCO₃)₂ + Ca(OH)₂ → CaCO₃ + MgCO₃ + 2H₃O

Question 25.
(a) Give the composition of plaster of paris and mention one use of it.
Answer:
Plaster of Paris is CaSO₄ + \(\frac{1}{2}\)H₂O It is prepared by heating gypsum at 373 K.

Uses:
(i) It is used for manufacture of statues,
(ii) It is used for filling gaps before white washing.

(b) Write any one biological importance of Magnesium.
Answer:
Biological importance of Mg and Ca are:
(a) Mg ion is present in chlorophyll which is responsible for photosynthesis.
(b) Ca²⁺ ions are required for maintaining heart beat.
(c) Ca²⁺ and Mg²⁺ ions are required for clotting of blood.

Question 26.
(a) Boron shows anamolous behaviour with other elements of the same group. Give reasons.
Answer:

1. Due to smaller size
2. High ionisation enthalpy
3. High electronegativity.

(b) Name the gas liberated when formic acid is heated with concentrated H₂SO₄.
Answer:
Pure carbon monoxide is formed by the dehydration of formic acid with cone. H₂SO₄.

Part – D

IV. Answer any FIVE of the following questions carrying FIVE marks: ( 5 x 5 = 25 )

Question 27.
(a) The percentage composition of an organic compound found to contain 39.9% carbon, 6.7% hydrogen and the rest is oxygen. If the molecular mass of the compound is 60 gmol^-1. Determine the molecular formula of the compound.
Answer:
Percentage of oxygen = 100 – (39.9 + 6.7) = 100 – 46.6 = 53.4

∴ Empirical formula = CH₂O
Molecular mass = Eq. mass x basicity = 60 x 1 = 60
Empirical formula weight = CH₂O = 12 + 2 + 16 = 30
Nows 30n = 60 => n = 2
∴ Molecular formula = (Empirical formula) x n = (CH₂O)₂ = C₂H₄O₂

(b) State Avagadro law.
Answer:
Avogadro’s law states that “Equal volumes of all gas under similar conditions of temperature and pressure contain equal number of mole cols.”

Question 28.
(a) Give any three postulates of Bohr’s theory of atomic model.
Answer:
Bohr’s model of an atom, the postulates are:

1. Electrons revolve around the nucleus of an atom in a certain definite path called orbit or stationary state of shell.
2. The shells are having different energy levels denoted as K, L, M, N…
3. As long as the electron remains in an orbit, they neither absorb nor emit energy.
4. The electron can move only in that orbit in which angular momentum is quantized,
   i.e., the angular momentum of the electron is an integral multiple of \(\frac{\mathrm{h}}{2 \pi}\)

(b) State Hund’s rule of maximum multiplicity.
Answer:
Hund’s rule or maximum multiplicity: Electron pairing does not take place until orbitals of same energy are singly occupied.

Question 29.
(a) Name the four quantum numbers and mention what they indicate?
Answer:
In order to define state energy and location of electron a set of four numbers are used. These numbers are called quantum numbers, (i) Principal quantum number (n). (ii) Azimuthal quantum number (1). (iii) Magnetic quantum number (m). (iv) Spin quantum number (s).

(b) What is node?
Answer:
The region where probability of finding the electron is zero is called a node.

Question 30.
(a) Write the important postulates of Kinetic theory of gases.
Answer:

1. Gases are made up of large number of the minute particles.
2. Pressure is exerted by a gas.
3. There is no loss of kinetic theory.
4. Molecules of gas attract on one another.
5. Kinetic energy of the molecule is directly proportional to absolute temperature.
6. Actual volume of the gaseous molecule is very small.
7. Gaseous molecules are always in motion.
8. There is more influence of gravity in the movement of gaseous molecule.

(b) What is Boyle’s temperature?
Answer:
The temperature at which real gases obey ideal behaviour for appreciable range of pressure is called Boyle’s temperature (or) Boyle’s point.

(c) Falling liquid droplets are spherical. Give reason.
Answer:
Due to surface tension.

Question 31.
(a) Calculate the standard enthalpy of formation of benzene from the following data.
Answer:
C₆H₆ + O₂ + \(\frac{15}{2}\)O₂  → 6CO₂ + 3H₂O_(l); ∆H= – 3264KJ
C_(s) + O_2(g)  → CO_2(g); ∆H = -393.5KJ
H₂ + \(\frac{1}{2}\)O₂ → H₂O_(l); ∆H = -285.9KJ

(b) What is entropy?
Answer:
Measure of disordemess of a system.

Question 32.
(a) Calculate the total work done when one mole of a gas expands isothermally and reversibly from an intial volume of 10dm³ to a final volume of 20dm³ at 298K.
Answer:
T = 27°C = 27 + 273 = 300K , V₁ = 10 dm³ V₂ = 20 dm³ , R = 8.314 J/K/mol
w = -2.303 nRTlog \(\left(\frac{v_{2}}{v_{1}}\right)\)
w = -2.303 x 1 x 8.314 x 300 x log \(\left(\frac{20}{10}\right)\)= -2.303 x 8.314 x 300 x log2
= -2.303×8.314x300x0.3010 = -1729 joule = -1.723 kJ.

(b) What is an intensive property? Give an example.
Answer:
Intensive property of a system is that property of the system which does not depend on the quantity of the substance present in the system. E.g; Density, Viscosity.

Question 33.
(a) For the hydrolysis of sucrose the equilibrium constant K_c is x x 10^-3 at 300K calculate ∆G° at 300K?
Answer:
Given K_c = 2 x 10^-3
T = 300K; ∆G° = ?
We know that ∆G° = -2.303 RT log K_c = -2.303 x 8.314 x 300 x 2 x 10^-3
= -2.303 x 8.314 x 3 x 2 = -11.488 J/mol.

(b) Explain common ion effect with suitable example.
Answer:
Suppression in the degree of dissociation of a weak electrolyte by the addition of a common ion is called common ion effect.

Question 34.
(a) Calculate the pOH of a solution obtained when 0.05 mol NH₄Cl is added and dissolved , in 0.025M ammonia solution. (Given Kb for ammonia = 1.77 x 10^-5).
Answer:
pK_b = -logK_b = -logl.8 x 10^-5 = -(5.2553) = 4.7447
p^OH = pK_b + log \(\frac{[\text { salt }]}{[\text { base }]}\) = 4.7447 + log \(\frac{0.05}{0.12}\) = 4.74 – 0.38 = 4.36
∴ pH = 14 – p^OH= 14 – 4.36 = 9.64

(b) What is solubility product?
Answer:
It is the product of the molar concentration of ions of the saturated solution of a sparingly soluble solution of the salt and the coefficients are raised to their powers at constant temperature.

Part – E

V. Answer any TWO of the following questions carrying FIVE marks: ( 2 x 5 = 10 )

Question 35.
(a) Write the principles involved in the estimation of
(i) Halogens (ii) Sulphur present in an organic compound by Carius method.
Answer:
(i) Halogens: When an organic compound containing halogen (Cl, Br or 1) is heated in a sealed tube with fuming nitric acid and excess of silver chloride, silver halide is formed from the mass of silver halide obtained, the percentage of the halogen can be calculated.

Procedure: In a hard glass tube (Carius tube), 5 ml of fuming HNO₃ and 2 to 2.5 g AgNO₃ are taken. A small narrow weighing tube, containing a small amount (nearly 0.15 -0.2g) of accurately weighed organic compound, is introduced in the Carius tube in such a way that nitric acid does not enter the weighing tube. The Carius tube is now sealed and heated in a furnace at 300°C for about six hours.

The tube is then cooled and its narrow end is cut off and the contents are completely transferred to a beaker by washing with water. The precipitate of silver halide formed is filtered through a weighed sintered glass crucible. It is washed, dried and weighed.

Observation and calculation:
(i) Mass of organic compound taken = W₁g
(ii) Mass of silver halide obtained = w₂g
(a) For chlorine:

143.5g of AgCl contains 35.5 g of chlorine.
w₂g of AgCl will contain \(\frac{35 \cdot 5 \times w_{2}}{143 \cdot 5}\) of chlorine
∴ % Cl₂ = \(\frac{35 \cdot 5 \times w_{2}}{143 \cdot 5} \times \frac{100}{w_{1}}\)

(b) For bromine:

188 g of AgBr contains 80 g of bromine
w₂ of AgBr will contain \(\frac{980 \times w_{2}}{188}\) g of bromine

(ii) Sulphur Present in an organic compound by carius method:
Principle: An organic compound containing sulphur to heated in Carius tube with fuming nitric acid or sodium peroxide. Sulphur present is oxidised to sulphuric acid. It is then precipitated as burium sulphate by adding excess of barium chloride solution. The precipitate formed is filtred, washed, dried and weighed. The % of S is calculated from the mass of barium sulphate.

Calculations: Mass of organic substance = ‘m’
Mass of barium sulphate formed = ‘x’ g.
Molecular mass of barium sulphate = 233 g.

(b) Name the element estimated by Kjeldahl’s method.
Answer:
Nitrogen.

Question 36.
(a) Describe the estimation of Carbon and Hydrogen by Liebig’s method.
Answer:

Principle: A known mass of an organic compound is strongly heated with dry cupric oxide (CuO), when carbon and hydrogen are quantitatively oxidized to CO₂ and H₂O respectively. The masses of CO₂ and H₂O thus formed are determined. From this, the percentages of carbon and hydrogen can be calculated.
Procedure : Pure and dry oxygen is passed through the entire assembly of the apparatus (Figure) till the CO₂ and moisture is completely removed.

A boat containing weighed organic substances is introduced inside from one end of the combustion tube by opening it for a while. The tube is now strongly heated till the whole of the organic compound is burnt up. The flow of oxygen is continued to drive CO₂ and water vapours completely to the U-tubes. The apparatus is cooled and the U-tubes are weighed separately.

Observation and calculations:

1. Mass of organic compound taken = w.g.
2. Mass of water produced = x g (Increase in mass of CaCl₂ tube).
3. Mass of carbon dioxide produced = y g (Increase in mass of KOH tube).

To determine % of carbon:
Molar mass of CO₂ = 44g mol^-1
Now, 44g of CO₂ = contains 12 g of C
y g of CO₂ will contain of \(\frac{12 y}{44}\) f of C
This amount of carbon was present in w. g. of the substance
∴ % C = \(\frac{12 y}{44} \times \frac{100}{w}\)

To determine % of Hydrogen
Molar mass of water = 18 g mol^-1
Now, 18 g of H₂O contains 2 g of H₂O
∴ x g of H₂O will contain \(\frac{2 x}{18}\) g of H₂O
This amount of hydrogen was present in weight of substance.
∴ H₂ = \(\frac{2 x}{18} \times \frac{100}{w}\)

(b) What is Cracking?
Answer:
The decomposition of higher alkane into a mixture of lower alkanes alkenes, etc. by the application

Question 37.
(a) Explain the mechanism of chlorination of Methane.
Answer:
Mechanism of chlorination of methane involves three types:

Step 1: Initiation: Chlorine absorbs energy and undergoes homolysis to give chlorine free radicals.

Step 2: Propagation: Chlorine free radical reacts with methane to give methyl free radical.

The methyl free radical reacts with chlorine to form methyl chloride and chlorine free radical.

Step 3: Termination: Free radials combine to form stable products.

(b) Name the product formed when phenol vapours are passed over heated zinc dust. Write the chemical equation.
Answer:
Benzene

Students can Download 1st PUC Chemistry Model Question Paper 2 with Answers, Karnataka 1st PUC Chemistry Model Question Papers with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

Karnataka 1st PUC Chemistry Model Question Paper 2 with Answers

Time: 3.15 Hours
Max Marks: 70

Instruction:

1. The questions paper has five parts A, B, C, D and E. All parts are compulsory.
2. Write balanced chemical equations and draw labeled diagram wherever allowed.
3. Use log tables and simple calculations f necessary (use of scientific calculations is not allowed).

Part – A

I. Answer ALL of the following (each question carries one mark): ( 10 × 1 = 1 )

Question 1.
Express 0.001023 into scientific notation.
Answer:
1.023 x 10^-3.

Question 2.
Define critical temperature.
Answer:
The temperature above which gas cannot be liquified.

Question 3.
Give the example which acts as Lewis base as well as Bronsted base.
Answer:
NH₃ or Ammonia.

Question 4.
How does electronegativity related to atomic size?
Answer:
Atomic size ∝ \(\frac{1}{\text { Electronegativity }}\)
Electronegativity

Question 5.
What is the oxidation state of oxygen in peroxide?
Answer:
-1 or minus 1

Question 6.
Which alkali metal is act as strong reducing agent?
Answer:
Lithium.

Question 7.
Write the formula of inorganic benzene.
Answer:
B₃N₃H₃

Question 8.
What is dry ice?
Answer:
Solid CO₂.

Question 9.
Complete the reaction NH₄CNO

Answer:

Question 10.
Write the name of the chain isomer of n-Butane.
Answer:
CH₃-CH₂-CH₂-CH₃

Part – B

II. Answer any FIVE of the following questions carrying TWO marks: ( 5 × 2 = 10 )

Question 11.
Calculate the average atomic mass of chlorine using the following data.

Answer:

Question 12.
Draw the graph of pressure versus volume of a gas at a different temperatures to illustrate the Boyle’s law.\
Answer:

Question 13.
Give any two conditions for hybridization of atomic orbitals.
Answer:
(i) Should contain half filled atomic orbitals.
(ii) Energy of the combining atomic orbitals should be equivalent.

Question 14.
Explain the reactivity of second group elements towards hydrogen.
Answer:
Hydrogen combines with second group elements to form metallic hydrides,
i.e. M + H₂ → MH₂
OR
Ca + H₂ → CaH₂
when M = Mg, Ca, Ba, etc.

Question 15.
How many sigma and pi bonds are in carbon monoxide?
Answer:
2σ bonds and one 7t-bond.

Question 16.
Write the structural isomers of an alkene with molecular formula C₂H₈.
Answer:
H₃C-H₂C-HC=CH₂ , CH₃-CH=CH-CH₃

Question 17.
What are the characteristics for any ring system to be called as aromatic compound?
(i) It should be planar.
(ii) Obeys Huckel rule i.e. (4n + 2)π electrons.
(iii) Should contain delocalized π – electrons above and below the plane of the molecule.

Question 18.
(a) Which oxide of nitrogen in higher concentration will retard the rate of photosynthesis in plants?
NO₂ or Nitrogen dioxide.
(b) Name the compound formed when carbon monoxide binds to haemoglobin.
Carboxyhaemoglobin (Hb + CO → HbCO).

Part – C

III. Answer any FIVE of the following questions carrying THREE marks: ( 5 × 3 = 15 )

Question 19.
Why Beryllium exhibit anomalous behaviour from the rest of the elements in the group.
Answer:
Due to

1. Smaller size compared to other elements in the group.
2. High ionisation enthalpy in the ground state.

Question 20.
With the help of hybridization explain the structure of methane.
Answer:
CH₄
EC of C = 1s²2s²2p_x¹2p_y¹2p_z¹
The four half filled orbitals overlaps with each other giving 4sp³ hybrid orbitals. These combines with s-orbital of hydrogen along the axis giving 4σ bonds with bond angle 109°28′ and tetraheral geometry.

Question 21.
(a) What is bond enthalpy? How it is related to the bond order?
Answer:

1. The amount of energy required to break one mole of bonds of same type to separate them into gaseous atoms.
2. Bond enthalpy oc Bond order.

(b) Write the resonance structure of CO₂.
Answer:

Question 22.
(a) Give any two differences between bonding and anti-bonding molecular orbitals.
Answer:
BMO :

1. Formed by addition overlapping Ψ_AB = Ψ_A + Ψ_B
2. Less energy than ABMO.
3. More stable.

ABMO :

1. Formed by the subtraction overlapping of atomic orbitals. of atomic orbitals i.e. Ψ_AB = Ψ_A -Ψ_B
2. More energy than BMO.
3. Less stable.

(b) What is the dipole moment of BeF2?
Answer:
Dipole moment is 0 (zero)
F ⇌ Be ⇌ F

Question 23.
Balance the following redox reaction by half reaction method.
MnO₄^– (aq) + 1^– (aq) → MnO₂ (s) + I₂(s) : Basic medium.
Answer:

Question 24.
Give the reactions to show amphoteric nature of water.
Answer:

(ii) Mention any one method of removal of temporary hardness of water.
Answer:
By boiling.

Question 25.
How caustic soda is commercially prepared from brine by Castner-Kellner cell.
Answer:
Caustic soda by Castner-Kellner cell: NaOH is manufactured by the electrolysis of aqueous solution of NaCl (Brine).
i.e. 2NaCl → 2Na⁺ + 2Cl^–
Sodium ions are discharged at mercury cathode.
Sodium deposited at mercury forms sodium amalgam.
Chlorine liberated at anode removed from the cell.
At cathode : 2Na⁺ + 2e → Na, Na + Hg → Na – Hg
At anode : 2Cl^– – 2e → Cl₂
Na-Hg is treated with water to form NaOH
i.e. Na/Hg + 2H₂O → 2NaOH + H₂ + Hg.

Question 26.
Give the example of element of group 14
(i) Shows maximum catenation capacity.
Answer:
Carbon

(ii) Used as semiconductor.
Answer:
Silicon

(iii) Which reacts with water.
Answer:
Tin

Part – D

IV. Answer any FIVE of the following questions carry ing FIVE marks: ( 5 x 5 = 25 )

Question 27.
(a) M atch the following :

Answer:
(i)-(c),
(ii)-(d),
(iii)-(a)

(b) Define molarity. Write the expression to calculate the molarity of the solution for the given mass and volume.
Answer:
It is the number of moles of solute present in 1000 ml solvent or 1dm3.
M = \(\frac{\mathrm{W}}{\mathrm{GMM}} \times \frac{1000}{\mathrm{V}}\)

Question 28.
(a) Give any three posulates of Bohr’s model for hydrogen atom.
Answer:

• Electrons are revolving around nucleus in a closed circular path called orbits or main shells or energy levels.
• When an electron jumped from higher energy level to lower energy level, the difference of energy emitted as radiation, i.e. E₂ – E₁ = ∆E= hγ
• The angular momentum of an electron has discrete values. It is given by the equation
  mvr = \(\frac{n h}{2 \pi}\)

(b) Calculate the mass of a photon with wavelength 5,OA°
Answer:

Question 29.
(a) Sketch the shapes of P_x and dz².
Answer:

(b) Identify the property exhibited by ₁₉K⁴⁰ and ₁₉Ca⁴⁰.
Answer:
Isobars (∵ mass number are equal).

(c) Write the orbital (box) type electronic configuration of p⁴ and d⁴ according to Hund’s rule of maximum of multiplicity.
Answer:

Question 30.
a) Derive ideal gas equation using gas laws.
Answer:
Ideal gas equation:
According to Boyle’s law V ∝ \(\frac{1}{P}\) T at constant T
According to Charle’s law V ∝ at constant P
According to Avogadro’s law V ∝ n at constant T and P
On coming V ∝ \(\frac{1}{P}\) V ∝ \(\frac{1}{P}\) x T x n
or PV=nRT
For ‘n’ moles, PV = RT for 1 mole.
R = gas constant, T = Kelvin Temp, P = Pressure, V = Volume of gas
n = Number of moles of gas.

(b) At 25°C and 760 mm of Hg pressure a gas occupies 600 mL volume. What will be its pressure at a height where temperature is 10°C and volume of the gas is 640 ml.
Initial conditions
P₁ = 760 mm
V₁ = 600 mm
T₁ = 250C = 298K

Final conditions
P ₂= ?
v₂ = 640 mL
T₂= 10°C + 273k = 283K

Question 31.
(a) If water vapour is assumed to be a perfect gas, molar enthalpy change for vapourization of 1 mole of water at 1 bar ad 100°C is 41kJ mole^-1. Calculate the internal energy change when 1 mole of water is vapourized at 1 bar pressure and 100°C.
H₂O (l) → H₂0 (g)
∆n_g = 1 – 0 = 1
W.K.T. LH = ∆U + ∆n_gRT
OR ∆U = ∆H – ∆n_gRT = 41 x 10³ – 1 x 8.314 x 373
= 41000— 3101,122 = 37898.878 J/mol
OR = 37.898878 K/J/mol.

(b) State Hess’s law of constant heat summation.
Answer:
The total amount of heat liberated or absorbed is same whether the reaction takes place in one step or more than one step / (or several steps).

(c) What is the value for standard enthalpy of formation of an element.
Answer:
Zero/0

Question 32.
(a) Calculate ∆G° for conversion of oxygen to ozone, -O₂(g) —> O₃(g) at 298K. If
K_p for this conversation is 2.47 x 10^-29.
Answer:
∆rG° = ? R = 8.314J/k/mol T = 298K K_p = 2.47 x 10^-29.
W.K.T. ∆rG° = -2.303RTlogK_p = 2.303x 8.314 x 298 x 2.47 x 10^-29.
= 163229 J/mol or 163.2 KJ/mol.

(b) What is thermochemical equation? Write the thermochemical equation for the molar combustion of ethanol (Given ∆_rH° = -1367 kJ mol^-1).

1. It is a balanced reaction, gives the information about physical state of reactants and product as well as heat liberated or absorbed.
2. C₂H₅OH_(l)+ 3O₂(g) → 2CO₂(g) + 3H₂0(/) ; ∆H° = -1367 KJ/mol

(c) What is the value of ∆G in a spontaneous process?
Answer:
∆G = -ve

Question 33.
For the equilibrium 2NOCl (g) ⇌ 2NO(g) + Cl₂(g) the value of the equilibrium constant Kc is 3.75 x 10^-6 at 1069K. Calculate the K_p for the reaction at this temperature?
Answer:
For the reaction 2NOCl (g) ⇌ 2NO(g) + Cl₂(g)
∆n = 3 – 2 = 1. ∴ K_p = K_c (RT)^∆n
K_p = (3.75 x 10^-6 x 0.0831 x 1069) x 1 = 3.75 x 0.0831 x 1069 x 10^-6 = 333.13 x 10^-6 OR K_p= 3.33 x 10^-4

(b) Write any two general characteristics of equilibria involving physical process.
Answer:

1. It is dynamic in nature.
2. It can be achieved in a closed vessel.
3. It depends only on temperature but not on concentration or pressure.

Question 34.
(a) The p^H of the blood is 7.4. Calculate the [H⁺].
p^H = 7.4 [H⁺] = ?
W.K.T [H⁺] = Antilog (-p^H)
[H⁺]= Antilog ₁₀ (-7.4)
Add-1 to-7 and +1 to-0.4 ∴ [H⁺] = Antilog \(\overline{8.6}\)
[H⁺] = 10^-8 x Antilog of (+0.6).

(b) Derive the Henderson-Hasselbalch equation for acid buffer.
Answer:
Henderson-Hasselbalch equation:
Consider a weak acid and its salt BA,

Part – E

V. Answer any TWO of the following questions carrying FIVE marks: ( 2 x 5 = 10 )

Question 35.
(a) For the following bond cleavage, use curved arrows to show electron flow, mention the type of bond cleavage, and reactive intermediate formed.
CH₃CH₂O + OCH₂CH₃ → CH₃CH₂O + OCH₂CH₃

1. Homolytic cleavage
2. Ethoxide free radicals.

(b) Give the hybridisation and geometry of carbocation.
Answer:
sp² and planar.

Question 36.
(a) 0.2033 g of an organic compound on combustion gave 0.3780 g of CO₂ and 0.1288 g H₂O. In a separate experiment 0.1877 g of the compound on analysis by Dumas method produced 31.7 ml. of nitrogen collected over water at 14°C and 758 mm pressure. Determine the percentage composition of the compound. (Aqueous tension of water at 14°C = 12 mm pressure).
Answer:
Given mass of organic compound = 0.2033 g |
Volume of nitrogen (V₁) = 31.7 mL
T₁ = 287K P₁ = (P – f) = 758 – 12 = 746 mm;
P₂ = 760mm U₂ = ? T₂ = 273K

To convert the volume of of N₂ at STP into mass
22400 mL of nitrogen at STP weighs = 28 g


% age of oxygen = 100 – (18.1985 + 50.71 + 7.03) = 24.06%

(b) What are nucleophiles? Give an example.
Answer:
The negatively charged species reacts at nucleus or +ve centre are called nucleophiles.
Example: Cl^–, Br^–, I^–, \(\mathrm{C} \overline{\mathrm{N}}\), NH₃, etc.

Question 37.
(a) Explain the mechanism of addition of HBr to propene in the presence of peroxide catalyst.
Answer:
It is a free radical mechanism.
It has the following steps:
(a) Initiation

(b) Propagation

(c) Termination

(b) Write the structures of cis and trans isomers of But-2-ene.
Answer:

Students can Download 1st PUC Maths Model Question Paper 5 for Practice, Karnataka 1st PUC Maths Model Question Paper with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

Karnataka 1st PUC Maths Model Question Paper 5 for Practice

Time: 3 Hrs 15 Min
Max. Marks: 100

Instructions:

1. The question paper has five parts namely A, B, C, D and E. Answer all the parts.
2. Part-A carries 10 marks. Part-B carries 20 marks. Part-C carries 30 marks. Part-D carries 20 marks, Part-E carries 10 marks.

Part – A

I. Answer all the questions ( 1 × 10 = 10 )

Question 1.
If set A = {1, 3, 5}, then find the number of elements in P(A)1

Question 2.
Find the value of tan \(\frac{19 \pi}{3}\).

Question 3.
Express (5t)( \(-\frac{3}{5}\) i ) in the form a + ib,. where a, b ∈ R

Question 4.
If \(\frac{1}{6 !}+\frac{1}{7 !}=\frac{x}{8 !}\) find x.

Question 5.
Find the tenth term of G.P : 5, 25, 125, ……………..

Question 6.
Find the slope of the line \(\frac{x}{3}+\frac{y}{2}\) = 1.

Question 7.
Find the derivative of x² – 2 at x = 0.

Question 8.
Write the contrapositive of “if a number is divisible by 9 then it is divisible by 3”.

Question 9.
Define mutually exclusive events.

Question 10.
If for some non empty sets A and B containing 3 elements A × B – {(3,4), (5, -3), (6,1)} . Find the set A.

Part – B

II. Answer any Ten questions ( 10 × 2 = 20 )

Question 11.
If A = {1, 2, 3, 4}, B = {2, 3, 5} and C = {3, 5, 6}, find A ∪ (B ∩C).

Question 12.
If X and Y are the two sets such that n(X) = 17, n(Y) 23 and n(X ∪ F) = 38. Find n(X ∩ Y)

Question 13.
Find the range and domain of the real function f(x) = \(\sqrt{9-x^{2}}\)

Question 14.
The minute hand of a clock is 2.1 cm long. How far does its tip move in 20 minute? ( use π = \(\frac{22}{7}\)

Question 15.
If sin A = \(\frac{3}{5}\) and A is in I quadrant, then find sin 2A.

Question 16.
Evaluate: \(\lim _{x \rightarrow 0} \frac{\sqrt{1+x}-1}{x}\)

Question 17.
A die is thrown. Write the sample space. Also find the probability of the event “A number greater than or equal to 3 will appear”.

Question 18.
Write the component statement of the following compound statement and check whether the compound statement is true or false; “Zero is less than every positive integer and every negative integer “.

Question 19.
The co-efficient of variation and standard deviation are 60 and 21 respectively. What is the arithmetic mean of the distribution?

Question 20.
Find the equation of the line perpendicular to the line x + y + 2 = 0 and passing through the point (-1, 0).

Question 21.
Represent the complex number z = -1 + i in polar form.

Question 22.
Solve 3x + 2y > 6 graphically.

Question 23.
Find the distance between the parallel lines 3x – 4y + 7 = 0 and 3x – 4y + 5 = 0

Question 24.
Show that the points A(l, 2, 3), B(-l, – 2, -3), C(2, 3, 2) and D(4, 7, 6) are the vertices of a parallelogram.

Part – C

III. Answer any Ten questions ( 10 × 3 = 30 )

Question 25.
In a survey of 600 students in a school, 150 students were found to be taking tea and 225 taking coffee, 100 were taking both tea and coffee.
Find how many students were taking neither tea nor coffee?

Question 26.
Write the relationR defined as R = {(x,; x + 5):x∈ {0,1, 2, 3, 4}} in roster system. Write down its range and domain.

Question 27.
Provethat (cosx + cosy)² + (sinx – siny)² = 4cos² \(\left(\frac{x+y}{2}\right)\)

Question 28.
Solve the equation x² + 3x + 9 = 0.

Question 29.
Find the real 0 such that \(\frac{3+2 i \sin \theta}{1-2 i \sin \theta}\) is purely real.

Question 30.
In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that
(i) The student has opted for NCC or NSS
(ii) The student has opted for NCC but not NSS

Question 31.
Find the coefficient of x⁶y³ in the expansion of (x + 2y)⁶

Question 32.
Find the sum of the sequence : 7, 77, 777, 7777……………..  to n terms.

Question 33.
Find the value of n so that \(\frac{a^{n+1}+b^{n+1}}{a^{n}+b^{n}}\) may be geometric mean between a and b.

Question 34.
Find the derivative of the function ‘sin x’ with respect to ‘x’ from first principle.

Question 35.
Find the center and radius of the circle 2x² + 2y² + 8x + 10y – 8 = 0

Question 36.
Find the number of different 8-letter arrangements that can be made from the letters of the word DAUGHTER so that
(i) all vowels occur together
(ii) all vowels do not occur together.

Question 37.
Verify by the method of contradiction that √2 is irrational,

Question 38.
Find the probability that when a hand of 7 cards is drawn from a well shuffled deck of 52 cards, it contains
(i) 3 kings
(ii) At least 3 kings.

Part – D

IV. Answer any Six questions ( 6 × 5 = 30 )

Question 39.
The real-valued function f is defined by

Draw the graph of f(x) and hence find the domain and range

Question 40.
Prove that lim \(\lim _{\theta \rightarrow 0}\left(\frac{\sin \theta}{\theta}\right)=1\) (θ being in radians) and hence show that \(\lim _{\theta \rightarrow 0}\left(\frac{\tan \theta}{\theta}\right)=1\)

Question 41.
Prove by mathematical induction that

Question 42.
A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of:
(i) exactly 3 girls ?
(ii) atleast 3 girls ?
(iii) at most 3 girls ?

Question 43.
The second, third and fourth terms in the binomial expansion (x + a)ⁿ are 240, 720 and 1080, respectively. Find x, a and n.

Question 44.
Derive an expression for the coordinates of a point that divides the line joining the points A(x₁, y₁, z₁) and B (x₂, y₂, z₂) internally in the ratio m:n. Hence, find the coordinates of the midpoint of A body of mass where A(2, -3, 4) and B(-1, 2, 1).

Question 45.
Derive the equation of the line in the form x cos α + y sin α = p where p is the length of perpendicular from origin to straight line and α is the angle made by the perpendicular with positive direction of x axis. Using this find the equation of the straight line with p = 4 and α = 120°.

Question 46.
Prove that

Question 47.
Solve the following linear inequalities 2x + y ≥ 6 and 3x + 4y ≤ 12 graphically.

Question 48.
Find the mean deviation about the median age for the age distribution of 100 persons given below:

Part – E

V. Answer any ONE question ( 1 × 10 = 10 )

Question 49.
(a) Prove geometrically that cos (x + y) = cos x cos y – sin x sin y using unit circle method and hence write the formula for cos (x – y). (6)
(b) Find the sum to n terms of the series: 1.2.3 + 2.3. 4 + 3.4.5 ……………………  (4)

Question 50.
(a) Define Hyperbola as a set of points and
Derive its equation in the form \(\frac{x^{2}}{a^{2}}-\frac{x^{2}}{a^{2}}=1\)
(b)

Karnataka 1st PUC Maths Model Question Paper 1 with Answers

Time: 3 Hrs 15 Min
Max. Marks: 100

Instructions:

1. The question paper has five parts namely A, B, C, D and E. Answer all the parts.
2. Part-A carries 10 marks. Part-B carries 20 marks. Part-C carries 30 marks. Part-D carries 20 marks, Part-E carries 10 marks.

Part – A

I. Answer all the questions: ( 10 × 1 =10 )

Question 1.
If A= {1,2}, B = {x : x ∈ A and x² – 9 = 0}. Find A x B.

Question 2.
Define subset of a set.

Question 3.
Convert \(\frac{2 \pi}{3}\) radians into degree measure

Question 4.
Express \(\frac{5+i \sqrt{2}}{2 i}\) in the form x + iy.

Question 5.
Find n if (n – l)p₃: np₄ = 1: 9

Question 6.
Find the tenth term of G.P : 5, 25, 125………….

Question 7.
Find the slope of the line joining the points (3, -2) and (-1,4).

Question 8.
Evaluate: \(\lim _{x \rightarrow 0}\left(\frac{\cos x}{\pi-x}\right)\)

Question 9.
Write the contrapositive of “if a number is divisible by 9 then it is divisible by 3”.

Question 10.
Write the sample space for the experiment “a.coin is tossed repeatedly three times”.

Part – B

II. Answer Any Ten Questions ( 10 x 2 = 20 )

Question 11.
If the universal set U = { 1, 2, 3, 4, 5, 6, 7 } A = { 1, 2, 5, 7 } , B = { 3,4, 5, 6}. Verify (A ∪ B)’= A’ ∩ B’

Question 12.
In a class of 35 students, 24 likes to play cricket, 5 likes to play both cricket and football. Find how many students like to play football?

Question 13.
If A = { 1,2,3 }, B = { 3,4 },C={ 4,5,6 }. Find A x (B∪C).

Question 14.
A wheel makes 360 revolutions in one minute, through how many radians does it turn in one second ?

Question 15.
Find the value of (sin(15°))

Question 16.
Find the value of x and y, if (x + 2y) + i(2x – 3y) is the conjugate of 5 + 4i.

Question 17.
Solve 7x +1 ≤ 4x + 5 and represent the solution graphically on the number line.

Question 18.
Find the equation of the line passing through (-1, 1) and (2, -4)

Question 19.
Find the equation of the line passing through (-4, 3) with slope ( \(\frac{1}{2}\) )

Question 20.
Find the ratio in which the line segment joining the points (4, 8,10) and (6,10, -8) is divided by YZ-Plane.

Question 21.
Evaluate : \(\lim _{x \rightarrow 0} \frac{1-\cos x}{x}\)

Question 22.
Write the component statement of the following compound statement and check whether the compound statement is true or false; “ Zero is less than every positive integer and every negative integer”.

Question 23.
The co-efficient of variation and standard deviation are 60 and 21 respectively. What is the arithmetic mean of the distribution.

Question 24. One card is drawn from a well-shuffled deck of 52 cards. Calculate the probability that the card will be “not an ace”.

Part – C

III. Answer Any Ten Questions ( 10 x 3 = 30 )

Question 25. Let A = {1, 2, 3, 14} Define a relation R from A to A by R = {(.x, y): 3x -y = 0, x, y ∈ A} write its domain
and range.

Question 26.
Find the general solution of 2 cos² x + 3 sin x = 0.

Question 27.
Express √3 + i in the polar form.

Question 28.
Solve: 3x² – 4x + \(\frac{20}{3}\) = 0

Question 29.
How many numbers greater than 10,00000 can be formed by using the digits 1, 2, 0, 2, 4, 2, 4.

Question 30.
Using the Binomial theorem, which number is among (1.1)¹⁰⁰⁰⁰ and 1000.

Question 31.
In an A.P, if m^th term is n and n^th term is m. Then find p^th term (m # n).

Question 32.
Find the sum of n terms of an A.P whose k^th term is (5k + 1).

Question 33.
Find the co-ordinates of the foci and latus rectum of the hyperbola 3x² – y² = 3.

Question 34.
Find the derivative of sin x from first principle.

Question 35.
Given p : 25 is a multiple of 5 : q: 25 is a multiple of 8. Write the compound statement connecting these two statements with “and”, “or”. In 60^th cases check the validity of the statement.

Question 36.
The student Anil and Ashima appeared in the examination, the probability that Anil will qualify the examination is 0.05 and that Ashima will qualify the examination 0.10. The probability that the both will qualify the examination is 0.02. Find the probability that only one of them qualify the examination.

Question 37.
A letter is chosen at random from the ward ‘ASSASSINATION’, Find the probability that the letter is (i) an vowel (ii) consonant.

Question 38.
In a survey of 600 students in a school, 150 students were found to be taking tea and 250 taking coffee, 100 were taking both tea and coffee. Find how many student were taking neither tea nor coffee.

Part -D

IV. Answer any Six questions ( 6 x 5 = 30 )

Question 39.
Define a polynomial function. If the function from f: R → R is defined as f(x) = x² then draw the graph of/ and find the domain and range.

Question 40.
Prove that

Question 41.
Prove by mathematical induction that 1³ + 2³ + …………….n³ = \(\left[\frac{n(n+1)}{2}\right]^{2}\)

Question 42.
Solve graphically 2x + y ≥ 4,x + y ≤ 3, 2x – 3y ≤ 6

Question 43.
A group consists of 4 girls and 7 boys, In how many ways can a team of 5 members be selected if the team has
(i) No girl
(ii) At least one boy and one girl
(iii) At least three girls

Question 44.
State and prove Binomial theorem for all natural numbers.

Question 45.
Derive the formula for the angle between two straight lines with slopes m₁ and m₂ hence find the slope of the line which makes an angle \(\frac{\pi}{4}\) with the line x – 2y + 5.

Question 46.
Derive the formula for the distance between two points x – 2y + 5 and x – 2y + 5 And hence find the distance between (2, -1, 3) and (-2, 1, 3).

Question 47. Prove geometrically: \(\lim _{\theta \rightarrow 0} \frac{\sin \theta}{\theta}=1\) where θ is in radian and hence deduce that \(\lim _{\theta \rightarrow 0} \frac{\tan \theta}{\theta}=1\)

Question 48.
Find the mean deviation about the mean for the following data

Part – E

V .Answer any ONE ( 1 x 10 = 10 )

Question 49.
a) Prove geometrically that cos (x + y) = cos x cos y – sin x. sin y and hence prove that cos (x – y) = cos x. cos y + sin x. sin y. 6
b) Find the sum of first n terms of the series 1² + 2² + …. + n².

Question 50.
a) Define ellipse and derive the equation of the ellipse in standard form as \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}\) = 1 (a > b)
b) Find the derivation of \(\frac{x^{5}-\cos x}{\sin x}\) with respect to x.

Karnataka 1st PUC Maths Model Question Paper 2 with Answers

Time: 3 Hrs 15 Min
Max. Marks: 100

Instructions:

1. The question paper has five parts namely A, B, C, D and E. Answer all the parts.
2. Part-A carries 10 marks. Part-B carries 20 marks. Part-C carries 30 marks. Part-D carries 20 marks, Part-E carries 10 marks.

Part – A

I. Answer all the questions: ( 10 × 1 =10 )

Question 1.
Define an empty set.

Question 2.
If ( \(\frac{x+1}{2}\) ,7 ) find ‘x’

Question 3.
Convert ( \(\frac{7 \pi}{6}\) ) into degrees .

Question 4.
Find the real number x if (x – 2i) (1 + i) is purely imaginary.

Question 5.
Given 5 flags of different colours how many different signals can be made if each signal requires the use of 2 flags, one below the other .

Question 6.
For what value of x the numbers \(\frac{-2}{7}\), x, \(\frac{-7}{2}\) are in G. P.

Question 7.
Find the slope of the line \(\frac{x}{3}+\frac{y}{2}\) = 1

Question 8.
Find the derivative of x² – 2 at x = 0 .

Question 9.
Write the negation of ‘For all a, b ∈ I, a – b∈ I’.

Question 10.
Define sure event.

Part – B

II. Answer any Ten questions ( 10 × 2 = 20 )

Question 11.
In a school, there are 20 teachers who teach mathematics or physics. Of these 12 teach mathematics and 4 teach both physics and mathematics. How many teach physics?

Question 12.
If A ={1,2}, form the set A × A × A.

Question 13.
Taking the set of natural numbers as the universal set. If A = {x: x ∈ N, and 2x +1 > 10} and B = {x : x ∈ N, and 3x – 1 > 8 find A’ and B’.

Question 14.
Find the value of cos (- 1710°).

Question 15.
Prove that sin 2x = \(\frac{2 \tan x}{1+\tan ^{2} x}\)

Question 16.
Find the least positive integer m such that \(\left(\frac{1+i}{1-i}\right)^{4 m}\) =1

Question 17.
Solve {3 (2x-5 ) -7} ≥ 9(x-5).

Question 18.
Find the distance of a point (3,-5) from the line 3x – 4y – 5 =0.

Question 19.
Find the angle between the lines y – y√3 x – 5 = 0 and √3 y – x + 6 = 0.

Question 20.
Evaluate \(\lim _{x \rightarrow-2} \frac{\frac{2}{x}+\frac{1}{2}}{x+2}\) .

Question 21.
Show that the points P(-2, 3, 5), Q (1, 2, 3) and R (7,0,-1) are collinear.

Question 22.
Write the converse and contrapositive of ‘If a parallelogram is a square, then it is a rhombus’.

Question 23.
Write the mean of the given data 6,7,10,12,13,4,6,12 .

Question 24.
Given P(A) = \(\frac{3}{5}\) and P (B) = \(\frac{1}{5}\) find P (A or B)

Part – C

III. Answer any Ten questions ( 10 × 3 = 30 )

Question 25.
There are 200 individuals with a skin disorder. 120 has been exposed to the chemical A, 50 to chemical B and 30 to both chemical A and B. Find the number of individuals exposed to
(i) chemical A but not to chemical B
(ii) Chemical A or chemical B.

Question 26.
Let A = {1, 2}, B = {1, 2, 3, 4}, and C = {5, 6}. Verify that A × (B ∩C) = (A × B) ∩ (A × C)
sin A sin B sin C

Question 27.
Prove that in any triangle ABC, \(\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}\)

Question 28.
Express \(\frac{-1+i}{\sqrt{2}}\) in the polar form.

Question 29.
Solve the equation x² + \(\frac{x}{\sqrt{2}}\) + 2 = 0

Question 30.
In how many ways can 5 girls and 3 boys be seated in a row so that no two boys are together.

Question 31.
Find the middle term in the expansion of \(\left(\frac{x}{3}+9 y\right)^{10}\)

Question 32.
The number of bacteria in a certain time double every hour. If there are 30 bacteria present in the culture originally. How many bacteria will be present at the end of 2^nd hour, 4^th hour, and n^th hour.

Question 33.
The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120°. Find the number of sides of the polygon.

Question 34.
Find the equation of the ellipse whose center at origin, major axis on the X axis and passes through the point (4, 3) and (6, 2).

Question 35.
Find the derivative of tan x w. r. t x from first principle.

Question 36.
Verify by the method of contradiction that √2 is irrational

Question 37.
One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that the card will be
(i) diamond
(ii) not an ace
(iii) a black card.

Question 38.
A fair coin 1 marked on one face and 6 on the other and a fair die are both tossed. Find the probability that the sum of numbers that turn up is (i) 3 (ii) 12.

Part – D

IV. Answer any Six questions ( 6 × 5 = 30 )

Question 39.
Define modulus function. Draw the graph of modulus function, Write down its domain and range.

Question 40.
Prove that cos² 2x – cos² 6x = sin 4x . sin 8x

Question 41.
Prove by mathematical induction that

Question 42.
Solve the following system of inequalities graphically: 5x + 4y ≤ 40, x ≥ 2, y ≥ 3;

Question 43.
What is the number of ways choosing four cards from a pack of 52 playing cards. In how many of these
(i) Four cards of the same suit
(ii) are face cards
(iii) two red and two black card
(iv) cards are of the same colour.

Question 44.
For all real numbers a, b and positive integer V prove that,
(a + b)ⁿ = ⁿC₀aⁿ + ⁿC₁ a^n-1b + ⁿC₂ a^n-2b² + …………….+ⁿC_n-1 ab^n-1 + ⁿC_nbⁿ
Hence prove that C₂ + C₂ + C₂ + ………….C_n = 2ⁿ

Question 45.
Derive a formula for the perpendicular distance of a point (x₁, y₁) from the line Ax + By + C = 0.

Question 46.
Derive the section formula in 3-D for internal division. Also find the coordinates of the midpoint of the line joining the points A (1,-2,3) and B (3,4,8).

Question 47.
Prove that \(\lim _{\theta \rightarrow 0} \frac{\sin x}{x}\) = 1 (x being in radians) and hence evaluate \(\lim _{x \rightarrow 0} \frac{\sin a x}{\sin b x}\)

Question 48.
The mean and standard deviation of 20 observations are found to be 10 and 2 respectively. On rechecking it was found that on observation 8 was incorrect. Calculate the correct mean and the standard deviation in each of the following cases
(i) if wrong item is omitted
(ii) if it is replaced by 12

Part – E

V. Answer any One question ( 1 × 10 = 10 )

Question 49.
(a) Prove geometrically that cos(A + B) = cos A cos S-sin A sin B
(b) Find the derivative of f(x) = 2x² + 3x – 5, also prove that F'(0) + 3f'(-1) = 0

Question 50.
(a) Define parabola as a set of all points in the plane and derive its equation in the form y² = 4ax, a > 0 and hence also find the focus and vertex.
(b) Find the sum to ‘n’ terms of the series 1² + (1² + 2²) + (1² + 2² + 3²) + …………..

Karnataka 1st PUC Maths Model Question Paper 3 with Answers

Time: 3 Hrs 15 Min
Max. Marks: 100

Instructions:

1. The question paper has five parts namely A, B, C, D and E. Answer all the parts.
2. Part-A carries 10 marks. Part-B carries 20 marks. Part-C carries 30 marks. Part-D carries 20 marks, Part-E carries 10 marks.

Part – A

I. Answer all the questions ( 1 × 10 = 10 )

Question 1.
Write the set {x : x e R and – 4 < x ≤ 6} as an interval.

Question 2.
IfA = {1,2}, B = {3,4) then show that A x (B ∩ Φ) = Φ

Question 3.
If cos x = -3/5, x lies in the HI quadrant then find the value of sin x.

Question 4.
Evaluate: \(i^{24}+\left(\frac{1}{i}\right)^{26}\)

Question 5.
Find the number of 4 digits that can be formed using the digits 1, 2, 3, 4, 5. If no digit is repeated.

Question 6.
Which term of 2, 2√2, 4 is 128.

Question 7.
Reduce 6x + 3y – 5 = 0 into slope-intercept form.

Question 8.
Find \(\lim _{x \rightarrow 5}|x|-5\)

Question 9.
Write the negation of “Every natural number is greater than zero”.

Question 10.
If \(\frac{2}{11}\) is the probability of an event A then what is the probability of the event ‘not A’?

Part – B

II. Answer any ten questions ( 2 × 10 = 20 )

Question 11.
If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2,4, 6, 8} and B = {2, 3, 5, 7} verify (A ∩B)’ = A’ ∪ B’.

Question 12.
If X and Y are two sets such that X ∪ Y has 50 elements, X has 28 elements and Y has 32 elements. How many elements does X ∩ Y have?

Question 13.
If A = {1, 2} and B = {3, 4} write A × B. How many subsets will A × B have?

Question 14.
The minute hand of a clock is 1.5 cm long. How far does its tip move in 40 Minute? (Use π = 3.142)

Question 15.
Prove that sin 3x = 3 sin x – 4 sin³x.

Question 16.
If x + iy = \(\frac{p+i q}{p-i q}\) prove that x² + y² = 1.

Question 17.
Solve the inequality (2x – 5) > (1 – 5x) and represent the solution graphically on the number line.

Question 18.
By using the concept of equation of the line prove that the three points (3, 0), (-2, -2) and (8, 2) are collinear.

Question 19.
Find the equation of the line parallel to the line 3x – 4y + 2 = 0 and passing through the point (-2, 3).

Question 20.
Find the ratio in which the YZ-plane divides the line segment formed by joining the points (-2, 4, 7) and (3, -5, 8).

Question 21.
Compute the derivative of sin² x.

Question 22.
By giving a counter example, show that the following statements is false: “If n is an odd integer then n is a prime”.

Question 23.
The mean and variance of heights of XI students are 162.6cm and 127.69cm² respectively. Find the C.V.

Question 24.
A card is selected from a pack of 52 parts calculate the probability that the card is (i) an Ace (ii) a black card.

Part – C

III. Answer Any Ten Questions ( 3 x 10 = 30 )

Question 25.
In a survey of 400 students in a school, 100 were listed as taking apple juice, 150 as taking orange juice and 75 were listed as taking both apple and orange juices. Find how many students were taking neither apple juice nor orange juice.

Question 26.
If f(x) = x² and g(x) = 2x + 1 be two real functions find (i) (f + g) (x) (ii) (f – g) (x) (iii) (fg) (x)

Question 27.
Find the general solution of sec²2x = 1 – tan2x.

Question 28.
Express \(\frac{1-i}{1+i}\) into polar form

Question 29.
Solve: 2x² + √3x – 1 = 0

Question 30.
If 5.⁴P_r = 6.⁵P_r-1, then find r.

Question 31.
Find the coefficient of x⁵ of (x + 3 )⁸.

Question 32.
Insert five number between 8 and 26 such that resulting sequence is an A.P.

Question 33.
The sum of first three terms of a G.P. is \(\frac{13}{12}\) and their product if -1. Find the common ratio and the terms.

Question 34.
Find the equation of parabola with vertex at the origin, axis along x-axis and passing through the point (2, 3) also find its focus.

Question 35.
Differentiate \(\frac{x+1}{x}\) from first principle

Part – D

IV. Answer any six questions ( 5 × 6 = 30 )

Question 36.
Verify by the method of contradiction that √7 is irrational.

Question 37.
A bag contains 9 discs of which 4 are red 3 are blue and 2 are yellow. The discs are similar in shape and size.
The disc is drawn at random from the bag. Calculate the probability that will be ’
(i) red
(ii) no blue
(iii) either red or blue.

Question 38.
A and B are events such that P(A) = \(\frac{1}{4}\), P(B) = \(\frac{1}{2}\) and P(A and B) = \(\frac{1}{8}\). Find
(i) P(A or B)
(ii) P(not A and not B)

Question 39.
Define Signum function. Draw the graph of it and write down it Domain and Range.

Question 40.
Prove that cos2x cos \(\frac{x}{2}\) – cos3x cos \(\frac{9x}{2}\) = sin5x sin \(\frac{5x}{2}\)

Question 41.
Prove that 10^2n-1 + 1 is divisible by 11, ∀ n ∈ N by the principle of mathematical Induction.

Question 42.
Solve the following system of linear inequalities graphically. x + y ≥ 5, x – y ≤ 3.

Question 43.
Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls. If each selection consists of 3 balls of each colour.

Question 44.
Prove Binomial Theorem for positive integers with real numbers. Hence prove that
ⁿC₀ + ⁿC₂ + ⁿC₄+ …………………. = ⁿC₁ + ⁿC₃ + ⁿC₅ + ………………..

Question 45.
P(a. b) is the midpoint of the line segment between axes. Show that the equation of the line is \(\frac{x}{a}+\frac{y}{b}=2\)

Question 46.
Derive the formulae for distance between two points (x₁, y₁, z₁) and I(x₁, y₂, z₂) and hence find the distance between P(1, -3, 4) and Q(-4, 1,2).

Question 47.
Prove that \(\lim _{x \rightarrow 0} \frac{\sin x}{x}=1\) where x is in radian and hence evaluate: \(\lim _{x \rightarrow 0} \frac{\sin 4 x}{\sin 2 x}\)

Question 48.
The mean and standard deviation of 100 observations were evaluated as 40 and 5.1 respectively. By a student who took by mistake, 50 instead of 40 for one observation. What are correct mean and standard deviation?

Part – E

V. Answer Any One Question: ( 1 × 10 = 10 )

Question 49.
a) Define ellipse as a set of all points in the plane and derive its equation in the standard form as \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\)
a > b
b) Find the derivate \(\frac{2}{x+1}-\frac{x^{2}}{3 x-1}\)

Question 50.
a) Prove geometrically that cos(x+y) = cosxcosy-sinxsiny and hence show that cos ( \(\frac{\pi}{2}\) + x) = – sin x.
b) Find the sum to n terms of series:
\(\frac{1}{1.2}+\frac{1}{2.3}+\ldots \ldots \ldots \ldots\)

Karnataka 1st PUC Maths Model Question Paper 4 with Answers

Time: 3 Hrs 15 Min
Max. Marks: 100

Instructions:

1. The question paper has five parts namely A, B, C, D and E. Answer all the parts.
2. Part-A carries 10 marks. Part-B carries 20 marks. Part-C carries 30 marks. Part-D carries 20 marks, Part-E carries 10 marks.

Part – A

I. Answer all the questions ( 1 × 10 = 10 )

Question 1.
If A has 4 elements. How many subsets does A has?

Question 2.
Convert 520° in to radian measure.

Question 3.
Find the conjugate of √3i -1

Question 4.
If \(\frac{1}{6 !}+\frac{1}{7 !}=\frac{x}{8 !}\) then find x

Question 5.
Find the 20th term of the G.P. \(\frac{5}{2}, \frac{5}{4}, \frac{5}{8}, \cdots \cdots \cdots \cdots\)

Question 6.
Find the slope of the line making inclination of 60° with positive direction of x-axis.

Question 7.
Find the derivative of 2 × – \(\frac{3}{4}\)

Question 8.
Write the negation of ‘For all a, b ∈ I, a – b ∈ I’.

Question 9.
Define mutually exclusive events.

Question 10.
If for some non empty sets A and B containing 3 elements A × B = {(3,4), (5,-3), (6,1)}. Find the set A.

Part – B

II. Answer any Ten questions ( 10 × 2 = 20 )

Question 11.
If A = {1,2, 3, 4}, B = {2, 3, 5} and C = {3, 5, 6}, find A ∪ (b ∩ C).

Question 12.
If X and Y are the two sets such that n (X) = 17, n (Y) = 23 and n (X∪ Y) = 38. Find n (X ∩ Y).

Question 13.
Find the range and domain of the real function f(x) = \(\sqrt{9-x^{2}}\)

Question 14.
The minute hand of a clock is 2.1 cm long. How far does its tip move in 20 minute? ( use π = \(\frac{22}{7}\) )
tan A:-tan y

Question 15.
Prove that tan(x – y) = \(\frac{\tan x-\tan y}{1+\tan x \tan y}\)

Question 16.
Evaluate:
\(\lim _{x \rightarrow-1}\left[1+x+x^{2}+x^{2}+\cdots \cdots x^{10}\right]\)

Question 17.
A die is thrown. Write the sample space. Also find the probability of the event “A number greater than or equal to 3 will appear”.

Question 18.
Write the converse and contrapositive of ‘If a parallelogram is a square, then it is a rhombus’.

Question 19.
Two series A and B with equal means have standard deviations 9 and 10 respectively. Which series is more consistent?

Question 20.
Find the equation of the line perpendicular to the line x + y + 2 = 0 and passing through the point (-1, 0).

Question 21.
Represent the complex number z = -1 +i in polar form.

Question 22.
Solve 3x + 2y > 6 graphically.

Question 23.
Find the distance between the parallel lines 3x – 4y + 7 = 0 and 3x – 4y + 5 = 0.

Question 24.
Show that the points A(1, 2, 3), B(-1, -2, -3), C(2, 3, 2) and D(4, 7, 6) are the vertices of a parallelogram.

Part – C

III. Answer any TEN questions ( 10 × 3 = 30 )

Question 25.
In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis? How many like tennis only and not cricket?

Question 26.
Write the relation R defined as R = {(x,x + 5)}: x ∈ {0,1,2,3,4} in roster system. Write down its range and domain.

Question 27.
Prove that (cosx + cosy)² + (sinx – sin y)² =4cos² ( \(\frac{x+y}{2}\) )

Questioin 28.
Solve the equation x² + 3x + 9 = 0.

Question 29.
Find the real θ such that \(\frac{3+2 i \sin \theta}{1-2 i \sin \theta}\) is purely real.

Question 30.
In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that (i) the student has opted for NCC or NSS (ii) The student has opted for NCC but not NSS.

Question 31.
Find the coefficient of x⁶y³ in the expansion of (x + 2y)⁶

Question 32.
Find the sum of the sequence : 7,77,777,7777, ……………….

Question 33.
In If \(\frac{a^{n}+b^{n}}{a^{n-1}+b^{n-1}}\) is the A.M. between a and b, then find the value of n.

Question 34.
Find the derivative of the function ‘-x’ with respect to ‘x’ from first principle.

Question 35.
Find the centre and radius of the circle x² + y² + 8x + 10y – 8 = 0.

Question 36.
How many words with or without meaning can be made from the letters of the word MONDAY assuming that no letter is repeated, if (i) 4 letters are used at a time, (ii) All letters are used at a time (iii) All letters are used but first letters a vowel.

Question 37.
Verify by the method of contradiction that √2 is irrational.

Question 38.
Find the probability that when a hand of 7 cards is drawn from a well shuffled deck of 52 cards, it contains (i) 3 kings (ii) At least 3 kings.

Part – D

IV. Answer any Six questions ( 6 × 5 = 30 )

Question 39.
Define greatest integer function. Draw the graph of greatest integer function, Write the domain and range of the function.

Question 40.
Prove that \(\lim _{\theta \rightarrow 0}\left(\frac{\sin \theta}{\theta}\right)=1\) (0 being in radians) and hence show that \(\lim _{\theta \rightarrow 0}\left(\frac{\tan \theta}{\theta}\right)=1\)

Question 41.
Prove by mathematical induction that

Question 42.
How many words with or without meaning each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?

Question 43.
Find “a” if 17^th and 18^th terms of the expansion (2 + a)⁵⁰ are equal.

Question 44.
Derive an expression for the coordinates of a point that divides the line joining the points A(x₁, y₁, z₁) and B(x₂, y₂, z₂) internally in the ratio m : n. Hence, find the coordinates of the midpoint of AB where A(2,-3,4) and B(-1,2,1)

Question 45.
Derive the equation of the line with slope m and y-intercept c. Also find the equation of the line for which tan θ = \(\frac{1}{2}\) and y-intercept is \(\frac{-3}{2}\)

Question 46.
Prove that

Question 47.
A manufacture has 600 Utters of a 12% solution of acid. How many liters of a 30% acid solution must be added to it so that the acid content in the resulting mixture be more that 15% but less than 18%.

Question 48.
Find the mean deviation about the median age for the age distribution of 100 persons given below

Part – E

V. Answer any One question ( 1 × 10 = 10 )

Question 49.
(a) Prove geometrically that cos(x + y) = cosx cosy – sinx siny using unit circle method and hence find the value of cos ( \(\frac{\pi}{2}\) + x ) = – sin x. (6)
(b) Find the sum to n terms of the series: 1.2.3 + 2.3.4 + 3.4.5 …………….. (4)

Question 50.
(a) Define Hyperbola as a set of points. Derive its equation in the form \(\frac{x^{2}}{a^{2}}-\frac{x^{2}}{a^{2}}=1\)
(b) Suppose

What are the possible values of a and b?

Students can Download 1st PUC Maths Model Question Paper 4 with Answers, Karnataka 1st PUC Maths Model Question Paper with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

Karnataka 1st PUC Maths Model Question Paper 4 with Answers

Time: 3 Hrs 15 Min
Max. Marks: 100

Instructions:

1. The question paper has five parts namely A, B, C, D and E. Answer all the parts.
2. Part-A carries 10 marks. Part-B carries 20 marks. Part-C carries 30 marks. Part-D carries 20 marks, Part-E carries 10 marks.

Part – A

Answer ALL the questions. Each question carries one mark. (10 × 1 = 10)

Question 1.
Define power set of a set.
Answer:
All possible subset of a given set are called powerset.

Question 2.
If G = {7,8}, H = {5,4,2}, Find H × G.
Answer:
H × G = {(5.7),(5.8),(4,7),(4,8),(2,7),(2,8)}

Question 3,
Convert 225° into radian measure
Answer:

Question 4.
Express (2 – i) – (6 + 3i) in a + ib form.
Answer:
(2 – i) – (6 + 3i) = -4 -4i in the form (a + ib)

Question 5.
Find n, if nc₉ = ⁿc₈
Answer:
n = 9 + 8 = 17

Question 6.
Find 17th term of sequence whos: nth term is given by a = 4n – 3. term of sequence whos
Answer:
a₁₇ = 4(17) – 3 = 68 – 3 = 65

Question 7.
Define the slope of a straight line
Answer:
Slope = m = gradient or inclination of a line with respect to positive x-axis i.e., m = tan θ

Question 8.
Evalaute \(\lim _{x \rightarrow 0} \frac{(x+1)^{2}-1}{x}\)
Answer:

Question 9.
Write the negation of ” √2 is not a complex number.”
Answer:
~(√2 is not a complex no.) = √2 is a complex no.”

Question 10.
Two coins are tossed. Find a sample space.
Answer:
Sample space ={HH, HT,TT,TH}

Part – B

Answer any TEN Questions. (10 × 2 = 20 )

Question 11.
Let A = {1,2,3,4,5,6} and B = {2,4,6,8}, Find A – B and B – A.
Answer:
A – B = {1,3,5), (B – A) = {8}

Question 12.
If X and Y are two sets such that X ∪ Y has 50 elements, X has 28 elements, Y has 32 elements, how many elements does X ∩ Y have?
Answer:
n(x ∪ y) = n(x) + (n ∪ y) – n(x ∩ y)
50 = 28 + 32 (x ∩ y) ⇒ [∴ n(X ∩ Y) = 10]

Question 13.
A function f is defined by f(x) = 2x – 5 write the value of (i) f(7) (ii) f(-3)
Answer:
Given f(x) = 2x – 5
∴ (i) f(7) = 2(7) – 5 = 9. (ii) f(-3) = 2(-3) – 5 = -11.

Question 14.
Find the angle in radian through which a pendulum swings, if its length is 75 cm and the tip describes an arc of length 10 cm.
Answer:
θ = ? r = 75 cm, s = 10 cm
S = rθ, (formula) 10 = 75 x θ.
∴ θ = \(\frac{10}{75}=\frac{2}{15}\) ⇒ ∴ θ = [0.133 radian.]

Question 15.
Find the solution of sin x = \(-\frac{\sqrt{3}}{2}\)
Answer:
α = \(-\frac{\pi}{3}\) ∴ G.S. x = 2nπ ± α
∴ [x = -2nπ ± \(-\frac{\pi}{3}\)]

Question 16
Write the Multplicative inverse of 4 – 3i.
Answer:

Question 17.
Solve the inequality 3(1 – x) <2 (x + 4) and represent the solution graphically on the number line.
Answer:
Given 3(1 – x) <2 (x + 4)
3 – 3x < 2x + 8 = 3 – 8 < 2x + 3x
-5 < 5x or 5x > -5 i.e., [x > -1]

Question 18.
Find the equation of straight line passing through the point (-4, 3) and having slope \(\frac { 1 }{ 2 }\)
Answer:
Equation of a straight line is givenby the formula
y – y₁ = m(x – x₁)
y = 3 = \(\frac { 1 }{ 2 }\)(x + 4) = 2y – 6 = x + 4 ⇒ ∴ [x – 2y + 10 = 0]

Question 19.
Find the distance between parallel lines 15x + 8y – 34 = 0, 15x + 8y + 31 = 0
Answer:

Question 20.
Find the equation of set of the points P such that ies distances from the points A(3, -4, 5) and B(-2, 1, 4) are equal.
Answer:
Given PA= PB where P =(x, y ,z)
∴ flash distance formula
\(\sqrt{(x-3)^{2}+(y-4)^{2}+(2+5)^{2}}=\sqrt{(x+2)^{2}+(y+1)^{2}+(z-4)^{2}}\)
(squaring on both sides)
∴ (x – 3)² + (y –  4)² + (2 + 5)² = (x + 2)² + (y – 1)² + (z – 4)²

∴(-6x – 4x) + (-8y + 2y) + (102 + 82) + (50 + 21) = 0 = 10x – 6y + 182 + 71 = 0 or
[10x + 6y – 182 – 71 = 0] equation of the plane.

Question 21.
Evaluate: \(\lim _{x \rightarrow 0}\left[\frac{1-\cos x}{x}\right]\)
Answer:

Question 22.
Write converse and contrapositive of “something is cold implies that it has low temperature”
Answer:
Converse: q → p = “Something has low temperature implies it is cold”.
Contrapositive: = q → -p= something does not have low temperature implies it is not cold.

Question 23.
Coefficient of ‘variation of distribution arc 60 and the standard deviat,on is 21. What is the arithmetic mean of the distribution?
Answer:
Given variation = 60
σ = 21, X̄ = ?
Take coefficient of variation = \(\frac{\sigma}{\bar{X}} \times \omega_{0}\)

X̄ = Arithmatic mean = 35.

Question 24.
A card is selected from a pack of 52 cards. Calculate the probability that the card is (i) an arc (ii) black card.
Answer:

Part – C

Answer any TEN of the following questions. Each question carries THREE marks. (10 × 3 = 30)

Question 25.
In a group of 65 people, 40 like cricket, 10 like cricket and tennis. How many like tennis only and not cricket? How many like tennis?
Answer:
n(C) = 40, n(T) = ? n( C ∩ T) = 10
n(C ∪ T) = ? n(T – C) = n(C ∪ T) = n(C) + A(T) – n(C ∩ T)
40 = 40 + n(T) -10 – 40 – 30 = n(T)
∴ [N(T) = 10] ⇒ n(T – C) = n(T)n(C ∩ T) = 10 – 10 = 0

Question 26.
Let A = {1,2,3,…14). Define a relation R from A to A by R = {{(x,y)}}: 3x – 4 = 0, x,y ∈ A}. Write its domain, co-domain and Range.
Answer:
R={(x,y): x ∈ A, y ∈ B, 3x – y = 0}
3(1) – 3 = 0, 3(2) – 6 = 0, 3(3) – 9 = 0, 3(4) – 12 = 0
∴ R = {(1,3), (2,6),(3,9),(4,12)}
Domain of R = A ⇒ Co-domain of R = A
Range of R = {3,6,9,12}

Question 27.
Prove that cos3x = 4cos³x – 3cosx.
Answer:
Take cos(A+B) =cos Acos B – sin Asin B
Put A = x, B = 2x
∴ cos(x + 2x) = cos x.cos2x – sin x sin 2x
cos(3x) = cos x(2cos²x – 1) – sin x(2 sin cos x)
= 2cos³x – cosx – 2cosx(sin²x) = 2cos³x – cosx – 2cosx(1 – cos²x).
= 2 cos³x – cos x – 2 cos x + 2cos³x [4cos³r – 3 cosx.]

Question 28.
Convert the complex number -1 -i into polar form.
Answer:
-1 -i = r(cosθ + isinθ) polar form

∴ r = \(\sqrt{x^{2}+y^{2}}=\sqrt{1+1}=\sqrt{2}\)
θ = tan^-1y/x = tan^-1\(\left(\frac{-1}{-1}\right)\) = -(π – standard) = \(-\left(\pi-\frac{\pi}{4}\right)=-\frac{3 \pi}{4}\)

Question 29.
If x + iy = \(\frac{a+i b}{a-i b}\) prove that x² + y²
Answer:

Question 30.
How many words with or with out meaning can be made from the letters of the word “Monday” assuming that no letters is repeated if
(i) 4 letters are used at a time.
(ii) All letters are used at a time.
(iii) All letters are used but first letter is a vowel.
Answer:
Monday : Given number of letters = 6
∴ total number of permutation = 6P₆ = 6!= 720
(i) It 4 letters are together = 3! × 4!= 6 × 24 = 144
(ii) All letters are used at a time. = 6! = 720
(iii) All letters are used but 1st letter is a vowel = 5!= 120 .

Question 31.
Find the middle term in the expansion of \(\left(3-\frac{x^{3}}{6}\right)^{7}\)
Answer:
x = 3, a = \(-\frac{x^{3}}{6}\), n = 7, T_n = ? r = 3
T_n = ? r = 4
n = 7 (add) no. there are two middle terms.

Question 32.
Insert Five numbers between 8 and 26 such that the resulting sequence is an arithmetic progression.
Answer:
Let the five AM’s are A₁, A₂, A₃, A₄, A₅ ∴ 5 AM’s are
∴ 8, A₁, A₂, A₂₃, A₄, A₅, A₆ ∴ A₁ = 11
n = 7, a = 8, d = ?, a_n = 26. A₂ = 14
an = a + (n – 1) d. A₃ = 17.
2b = 8 + (7-1)d A₄ = 20
∴ [d = 3] A₅ = 23

Question 33.
Find sum t0 n terms of sequence 8, 88, 888, 88888,..
Answer:
Let S_n = 8 + 88 + …… + n terms
S_n = 8{1 + 11 +……… + n terms}
X^ly by 9 on both side
∴ \(\frac{95 n}{8}\) = 9 + 99 + 999 +…. + to n term
GP

Question 34.
Find the coordinates of focus, directrix and latus rectum of parabola y² = 8x.
Answer:
Equation of parabola y² = 8x compare with the standard form
y² = 4ax ∴ 4a = 8 ∴ a = 2
∴ focus = (a,0) = (2,0)
Equation of directrix : x = -a.
x = -2 or [x + 2 = 0]
Latus rectum = 4a = 8.

Question 35.
Find the derivative of sin x with respect to x from 1st principle.
Answer:
y = sin x as x → x + Δx, y + Δy
∴ (y + Δy) = sin(x + Δx)
Δy = sin(x + Δx) – y
Δy = sin(x + Δx) – sin x
÷ Δx and apply lt Δx → 0 on both side

Question 36.
Using method of contradiction verify “√2 is irrational.”
Answer:
Let us assume that √2 is rational i.e.. the gives statement is false.
∴ √2 = \(\frac { 1 }{ 2 }\) ≠ 0 a and b have no conunon factor.
Squaring ∴ 2 = \(\frac{a^{2}}{b^{2}}\) ⇒ [a² = 2b²] ⇒ 2 divides a
Again put a = 2C(C ∈ Z) ⇒ ∴ (2c)² = 2b²
∴ 4c² = 2b² or [b² = 2c²] 2 divide b
i.e., 2 divides both a and b hence our assumption is i.e.. a and b does flot have common contradict out statement √2 is rational is false.
∴ √2 is irrational.

Question 37.
If A and B are events such that P(A) = 0.42, P(B)=0.48, P(A and B) = 0.16 determine
(i) P (not A)
(ii) P (not B)
(iii) P (A or B).
Answer:
P(A) = 0.42 P(8) = 0.48, P(A ∩B) = 0.16
(i) P( A¹ = 1 – 0.42 = 0.58 (ii) P(B¹) = 1 – 0.48 = 0.52
(iii) P(A ∪ B) = P(A) + P(B) – P(A ∩ B) = 0.42 + 0.48 – 0.16 = 0.50 – 0.16 = 0.74.

Question 38.
A committee of two persons is selected from two men and two women. What is the probability that the committee will have
(i) no man ?
(ii) one man?
(iii) two men?
Answer:

(i) Probability (no man) = women × men = 2C₂, × 2C₀ = 1
(ii) Probability (one man) = 2C₁ × 2C₁ = 2 × 2 = 4
(iii) Probability (two even) = 2C₀ × 2C₂ = 1

Part – D

Answer any SIX Questions. (6 × 5 = 30)

Question 39.
Define signum function. Draw the graph. Also write its Domain and Range.

Question 40.
Prove that \(\frac{\sin 5 x-2 \sin 3 x+\sin x}{\cos 5 x-\cos x}=\tan x\)
Answer:

Question 41.
Prove by Mathematical induction that for all n ≥ 1
1² + 2² + 3² +…+ n² = \(\frac{n(n+1)(2 n+1)}{6}\)
Answer:

Question 42.
Solve the system of inequalities graphically x + 2y ≤ 10, x + y ≥1, x – y ≤ 0, x ≥ 0, y ≥ 0.
Answer:

Question 43.
A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected, if the team has (i) no girls (ii) atleast one boy and one girl? (iii) atleast 3 girls
Ans.
Given 4 girls, 7 boys
Select 5 members

(ii) atleast 1 B and 1 G
(a) 4C₁ × 7C₄ = 140
(b) 4C₂ × 7C₃ = 210
(e) 4C₃ × 7C₂ = 21
(d) 4C₂ × 7C₁ = 7
Total number of selection: 378ways.

Question 44.
State and prove Binomial theorem for positive integer n.
Answer:

Question 45.
Derive the equation of straight line in the form xcosω + ysin ω = P, where P is length of normal to the line from origin, w is the inclination of normal with positive x-axis.
Answer:
Carried a line cutting X-axsis at A and Y axis at B.
Let OA = a, OB = b are x and y interscept.
∴ By intercept form of equation of line.
\(\frac{x}{a}+\frac{y}{b}=1\) is the equation of the line AB.
Draw OM ⊥ AB. i.e., normal line
Let OM = P. ∴ In O OAM
cosω = \(=\frac{O M}{O A}=\frac{P}{\cos w}\)  ⇒ ∴ a = \(\frac{O M}{O B}=\frac{P}{b}\)

Question 46.
Derive an expression for the co-ordinates of a point that divides the line joining points A(x¹, y¹, z¹) and B(x², y², z²) internally in the ratio m : n. Hence find the coordinates of the mid point of AB where A = (1,2,3) and B = (5,6,7).
Answer:
Proof: Let p(x₁, y₁, z₁) and Q(x₂, y₂, z₂) be the given points
Let R(x, y, z) divide PQ internally in the ratio m : n
Draw PL, QM, RN perpendicular to xy-plane.
∴ PL ∥ RN ∥ QM
∴ PL, RN, QM lie in one plane
So that the points L, N, M lie in a straight line which is the intersection of the plane and XY plane.
Through the point R draw a line AB It to the line LM. The line AB intersect the line LP externally at A and the line MQ at B.

Triangle APR and LIQR are similar.

∴ n(z – z₁) = m(z₂ – z)
∴ nz = nz₁ = mz₂ – m₂
∴ (nz + mz) = (mz₂ + nz₁)
∴ z(m + n) = mz₂ + nz₁

Question 47.
Prove that \(\lim _{x \rightarrow 0} \frac{\sin x}{x}=1\), where x measured in radians. Also evaluate \(\lim _{x \rightarrow 0}\left(\frac{\sin 4 x}{x}\right)\)

Question 48.
Find mean deviation about mean for the data.

Answer:

Part – E

Answer any ONE question. (1 × 10 = 10)

Question 49.
(a) Prove geometrically that cos(x + y) = cos x cos y – sin xsin y. and hence deduce that cos 2x cos²x – sin²x.
Answer:
Prove that cos(x + y) = cos x cos y.sin x sin y

Proof Consider a unit circle (radius = 1 unit) with centre is (0, 0).
Consider 4 point P₁, P₂, P₃ and P₄

The co-ordinate of P₁, P₂, P₃ and P₄ are given by
P₁ = (cosx,sinx) P₂ = [cos(x + y). sìn(x + y)]
P₃ = [cos(-y) sin(-y)] P₄ = [1,0]
From the figure OP₁OP₃ is congruent to ∆P₂OP₄
∴ From distance formula
P₁p₃ = P₂P₄ …… (1)
Takè the distance (P₁P₃)² = [cosx – cos(-y)]² + [sin x – sin (-y)]²
= (cosx – cosy)² + (sin x + sin y)²
= cos²x + cos²y = cosxcosy + sin²x + sin²y + 2sin cosy = 1 + 1 + 2(cosxcosy – sinxsiny)
(p₁, P₃)² = 2 – 2 cos (x + y)
Again (P₂P₄)² = [1^{(a-b)2-cos(x+y)}]² + |q – sin (x + y)|²
= 1 + cos²(x + y) -2cos(x + y) + sin²(x + y) = 1 + 1 – 2cos(x + y) = 2 – 2cos(x + y)

⇒ LHS = RHS
∴ [cos(x + y) = cosx cosy – sin x sin y]

(ii) Show that cos 2x = cos²x – sin x²x
Take cos(x + y) = cos xcos y – sin xsin y
Put y = x
∴ cos(x + x) = cosx cosx – sinx sinx
cos2x = cos² x – sin²x

(b) Find the sum to n terms of the series 1 × 2 + 2 × 3 + 3 × 4 +…
Answer:
(1 × 2) + (2 × 3) + (3 × 4) +……+ n term nth term.

n^2th term, 9n = n(n + 1), an = n² + n
to find the sum apply Σ on both side
∴ Σan = Σn² + n

Question 50.
(a) Define hyperbola as a set of points. Derive its equation in the standard form \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\)
Answer:
Definition: “Hyperbola is the set of all points in a plane the difference of where distances from the fixed point in the plane is constant.”
Derivain: prove that \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\) (standard hyperbola equation)
Let F₁, and F₂, are the two fixed point called focii of the hyperbola. The unit point of the sine segment. Joining the Foci is called the centre of the hyperbola.

A line through the Foci is called the transverse axis. And the line through the centre of perpendicular to the transverse axis is called conjugate axis.
Assume the distances between the two focii is “2c’ the distance between two and define the quantity ‘b’ as b = \(\sqrt{c^{2}-a^{2}}\) and 2b is the length of the conjugaton, (PF₂ – PF₁ = 2a = transverse axis)

The coordinate of F₁ = (-0,0) and F₂, =(0,0)
Let P(x,y) be a junction the hyperbola such that the distance of the distance from P to the farter point be “2a’ i.e., PF₁ – PF₂ = 2a ∴ from the distance formula


Again squaring on both side. \(\therefore\left(\frac{x c}{a}-a\right)^{2}=(x-c)^{2}+y^{2}\)
On simplification further to get \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{c^{2}-a^{2}}=1\)
put c² – a² = b²
∴ the standard form of hyperbola equation is
\(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\)

(b) Find the derivative of \(\frac{x^{5}-\cos x}{\sin x}\) with respect to x
Answer:

Students can Download 1st PUC Maths Model Question Paper 3 with Answers, Karnataka 1st PUC Maths Model Question Paper with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

Karnataka 1st PUC Maths Model Question Paper 3 with Answers

Time: 3 Hrs 15 Min
Max. Marks: 100

Instructions:

1. The question paper has five parts namely A, B, C, D and E. Answer all the parts.
2. Part-A carries 10 marks. Part-B carries 20 marks. Part-C carries 30 marks. Part-D carries 20 marks, Part-E carries 10 marks.

Part – A

Answer ALL the questions. Each question carries one mark. (10 × 1 = 10)

Question 1.
Write the set {x : x ∈ R and -4< x ≤ 6) as an interval.
Answer:
{-3, -2, -1,0,1,2,3,4,5,6} ∴ x ∈ (-3,6)]

Question 2.
If (x + 1, y – 2) = (3,1), find the value of x and y.
Answer:
x + 1 = 3, ∴ x = 2
y – 2 = 1, ∴ y = 3.

Question 3.
Convert \(\frac{2 \pi}{3}\) radians into degree measue.
Answer:

Question 4.
Evaluate 7! – 5!
Answer:
7! – 5! = (7 × 6 × 5 × 4 × 3 × 2 × 1) – (5 × 4 × 3 × 2 × 1) = 5040 – 120 = 4920

Question 5.
Find the 20^th term of the GP. \(\frac{5}{2}, \frac{5}{4}, \frac{5}{8}, \ldots \ldots\)
Answer:

Question 6.
Find n if nC₇ = nC₆
Answer:
If nC₇ = nC₆
∴ n = 7 + 6 = 13 (∵ nC_r = nC_r-1).

Question 7.
Find the slope of the joining the points (3, 2) and (-1, 4)
Answer:
Slope of the line = m = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{(4)-(2)}{(-1)-(3)}=\frac{2}{-4}=\left[\frac{-1}{2}\right]\)

Question 8.
Evalaute \(\lim _{x \rightarrow 0} \frac{\cos x}{x-x}\)
Answer:

Question 9.
Write the negation of the statement “√2 is a complex number. ”
Answer:
“√2 is not a complex no.”

Question 10.
If \(\frac { 2 }{ 11 }\) is the probability of an event, then what is the probability of the event ‘not
Answer:
P(not A) = p(Ā) = 1 – \(\frac { 2 }{ 11 }\) = \(\left[\frac{9}{11}\right]\)

Part – B

Answer any TEN Questions. (10 × 2 = 20)

Question 11.
If A and B are two disjoint sets and n(A) = 15 and n(B) = 10. Find n(A ∪ B) and n(A ∩ B).
Answer:
n(A ∩ B) = 0
∵ A and B are disjoint net
∴ n(A ∪ B) = n(A) + n(B) = 15 + 10 = 25.

Question 12.
If U = {x : X ≤ 10 and x ∈ N} is the universal set and A = {x : X ∈ N and x is prime}, B = {x : X ∈ N and x is even} are the subsets of U, find A ∩ B’ in Roster form.
Answer:
u = {1,2,3,4,5,6,7,8,9,10}, A = {2,3,5,7), B = {2,4,6,8,10,….}
∴ B’ = {1,3,5,7,9} ⇒ ∴ A ∩ B’ ={3,5,7}.

Question 13.
If A = {1,2} B = (3,4), write A × B How many subsets will A × B have?
Answer:
A × B = {(1,3), (1,4),(2,3),(2,4)} and the number of subset = 2^m×n = 2^2×2 = 16

Question 14.
Find the value of sin 75°.
Answer:
sin 75° = sin (45° +30°) = sin Acos B + cos Asin B = sin 45o cos 30° + cos 45osin 30°

Question 15.
Find the radius of the circle in which a central angle of \(\frac{\pi}{3}\) radians intercepts an arc of length 37.4 cm (use π = \(\frac{22}{7}\))
Answer:

Question 16.
Express \(\frac{1+3 i}{1-2 i}\) in the form of a + ib.
Answer:

Question 17.
Solve 7x + 3 < 5x + 9. Show the graph of the solution on number line.
Answer:
7x + 3 < 5x + 9. ⇒ ∴ 7x – 5x < 9 – 3 ⇒ 2x < 6 ⇒ ∴[x < 3] x ∈ (-∞,3).

Question 18.
Find the equation of the line parallel to the line 3x – 4y + 2=0 and passing through the point (–2, 3)
Answer:
Line parallel to 3x – 4y + 2 = 0 can be assumed on
3x – 4y + k = 0 ∴ at (-2,3)
3(-2) – 4(3) + k = 0
∴ -6 -12 + k = 0
∴ k =18
∴ the line parallel to a given line is
3x – 4y + 18 = 0.

Question 19.
Find the distance between the parallel line 15x + 8y – 34= 0 and 15x + 8y + 31 = 0
Answer:
Distances between the parallel line is given by

Question 20.
Find the distance between the points (-3,7,2) and (2,4,-1)
Answer:
d = \(\sqrt{(-3-2)^{2}+(7-4)^{2}+(2+1)^{2}}=\sqrt{25+9+9}=\sqrt{43}\)

Question 21.
Evaluate \(\lim _{x \rightarrow 2}\left(\frac{x^{3}-2 x^{2}}{x^{2}-5 x+6}\right)\)
Answer:

Question 22.
Write the converse and contrapositive of the statement “If the two lines are parallel then they do not intersect in the same plane.
Answer:
P : the two lines are paraallel V : line do not internet in the some plane.
∴ converse = q → p = If the two lines do not internet in the same plane then they are parallel.
Contrapositive: If the two lines intersect in the same plane they are parallel.

Question 23.
If the coefficient of variation and standard deviation of the distributions are 60 and 21 respectively, find the arithmetic mean of the distribution.
Answer:
C.V. = 60, σ = 21, X̄ = 2, Formula: C.V.= \(\frac{\sigma}{\bar{X}} \times 100\)
60 = \(\frac{21}{\bar{X}} \times 100\) ⇒ ∴ X̄ = \(\frac{21 \times 100}{60}\) = 35

Question 24.
Three coins are tossed at once find the probability of getting atleast two heads.
Answer:
3 coins tossed the sample space.

Part – C

Answer any TEN of the following questions. Each question carries THREE marks. (10 × 3 = 30)

Question 25.
If U = (1,2,3,4,5,6), A = {2,3}, B = {3,4,5} show that (A ∪ B)’ = A’ ∩ B’
Answer:
LHS = (A ∪ B) = {2,3,4,5}’ = {1,6}
RHS = A’ ∩ B’ = {1,4,5,6} ∩ {1,2,6} = {1,6} ∴ LHS = RHS.

Question 26.
Let f : R → R and g : R → R be defined by f(x) = x + 1, g(x) = 2x – 3, find (f + g)(x),(f – g)(x) and \(\left(\frac{f}{g}\right)\)(x)
Answer:
(i) (f + g)(x) = f(x) + g(x) = (x + 1) + (2x – 3) = 13x – 21
(ii) (f – g)(x) = f(x) – g(x) = (x + 1) – (2x – 3) = x + 1 – 2x + 3 = 4 – x
(iii) (f/g)(x) = \(\left[\frac{x+1}{2 x-3}\right]\)

Question 27.
Find the general solution of the equation sin 2x + cos x = 0
Answer:
Given sin 2x + cos x = 0, sin 2x = -cosx

sin 2x + cos x = 0, ∴ cos x=-sin 2x
cosx = cos \(\left(\frac{\pi}{2}+2 x\right)\)
∴ GS
x = 2nπ ± α (n ∈ z)
Put x = 2x ⇒ α = \(\frac{\pi}{2}\) + 2x ⇒ x = 2nπ ± (\(\frac{\pi}{2}\) + 2x)
(x + 2x) = (2nπ ± \(\frac{\pi}{2}\)) ⇒ 3x = 2nπ ±\(\frac{\pi}{2}\)
∴ [x = 2nπ ± \(\frac{\pi}{6}\)]

Question 28.
Express √3 + i in polar form.
Answer:
(√3 + i) = [cose + isin) ….. (1)

r = \(\sqrt{x^{2}+y^{2}}=\sqrt{3+1}=2\) ⇒ θ = tan^-1 \(\frac{y}{x}\) = tan^-1 \(\frac{y}{x}\) = tan^-1 \(\left(\frac{1}{\sqrt{3}}\right)=\frac{\pi}{6}\)

Question 29.
Solve the equation x² + 3x + 9 = 0.
Answer:
Given

Question 30.
In how many ways can the letters of the word Permutations be arranged if (i) the words starts with P and end with S (ii) Vowels are all together. Answer:
n = 12
T repeats = 2 times ,
(i) the word starts with P and ends with S
(P ……… (5)
Total words = \(\frac{9 !}{2 !}\) = 9 × 8 × 7 × 6 × 5 × 4 × 3 = 1,81,440 ways

(ii) Vowels are together: vowels = E,U,A,I,O = S together
∴ they form 1 group remaining \(\frac{+7}{8}\) letters
∴ Total words = \(\frac{8 !}{2 !}\) = 8 × 7 × 6 × 5 × 4 × 3 = 20,160 ways.

Question 31.
Find the middle term in the expansion of \(\left(\frac{x}{3}+9 y\right)^{10}\)
Answer:
x = \(\frac{x}{3}\), a = 9y, n = 10, r = 5
n = 10 (even) there is only one middle term is \(\left(\frac{n}{2}+1\right)=\left(\frac{10}{2}+1\right)\) = 6^th term
General term T_r+1 = ⁿC_r x^n-r a^r ⇒ T_s+1 = ¹⁰C₅ \(\left(\frac{x}{3}\right)^{10-5}\) (9y)⁵
T₆ = ¹⁰C₅\(\left(\frac{x}{3}\right)^{5}\) g⁵ y⁵ ⇒ T₆ = ¹⁰C₅ . \(\frac{x^{5}}{3^{5}}\) × 9⁵ y⁵ = ¹⁰C₅ (xy)⁵ × \(\left(\frac{3^{10}}{3^{5}}\right)\)
T₆ = [¹⁰C₅ (xy)⁵ 3⁵] is the middle term.

Question 32.
Insert Five Arithmetic means between 8 and 26 such that resulting sequence is an A.P.
Answer:
a = 8, a_n, = 26, n = 7, d = ?
Let the 5 AM’s are A₁, A₂, A₃, A₄, and A₅
∴ (8), A₁, A₂, A₃, A₄, A₅ (26) ⇒ Take a_n, = a + (n – 1) d
26 = 8 + (7 – 1)d ⇒ 18 = 6d ∴ d = 3
∴ A_r, = a + d = 8 + 3 = 11 ⇒ A₂ = a + 2 = 8 + 6 =14 ⇒ A₃ = 17, A₄ = 20, A₅ = 23.

Question 33.
In an A.P. if m^th term is “n” and n^th term is “m” where m ≠ n, find p^th term..
Answer:
Given a_m = n, a_m = m a_p = ? a = ? d = ?
n^th term 2,
a_n = a + (n – 1)d

Question 34.
Find the co-ordinate of the focus, equation of the directrix and length of the Latus Rectum of the parabola y² = 8x.
Answer:
Equation of parabola y² = 8x compare with the standard form
y² = 4ax ∴ 4a = 8 ∴ a = 2
∴ focus = (a,0) = (2,0)
Equation of directrix : x = -a.
x = -2 or [x + 2 = 0]
Latus rectum = 4a = 8.

Question 35.
Find the derivative of sin x with respect of x from first principle.
Answer:
y = sin x as x → x + Δx, y + Δy
∴ (y + Δy) = sin(x + Δx)
Δy = sin(x + Δx) – y
Δy = sin(x + Δx) – sin x
÷ Δx and apply lt Δx → 0 on both side

Question 36.
Verify by the method of contradiction √2 is irrational
Answer:
Let us assume that √2 is rational i.e.. the gives statement is false.
∴ √2 = \(\frac { 1 }{ 2 }\) ≠ 0 a and b have no conunon factor.
Squaring ∴ 2 = \(\frac{a^{2}}{b^{2}}\) ⇒ [a² = 2b²] ⇒ 2 divides a
Again put a = 2C(C ∈ Z) ⇒ ∴ (2c)² = 2b²
∴ 4c² = 2b² or [b² = 2c²] 2 divide b
i.e., 2 divides both a and b hence our assumption is i.e.. a and b does flot have common contradict out statement √2 is rational is false.
∴ √2 is irrational.

Question 37.
If E and F are the evens such that P(E) = \(\frac { 1 }{ 4 }\) , P(F) = \(\frac { 1 }{ 2 }\) and P(E and F) = \(\frac { 1 }{ 8 }\) . Find (i) P (E or F) (ii) P (not E and not F)
Answer:
(i) P(E or F) = P(E ∪ F) = P(E) + P(F) – P(E ∩ F)
\(=\frac{1}{4}+\frac{1}{2}-\frac{1}{7}=\frac{7+14-4}{28}=\left[\frac{17}{28}\right]\)
(ii) P(E’ ∩ F’) = P(E ∪ F)’ = 1 – P(E ∪ F) = 1 – \(1-\frac{17}{28}=\frac{11}{28}\)

Question 38.
A bag contain 9 discs of which 4 are red, 3 are blue and 2 are yellow. The discs are similar in shape and size. A disc is drawn at random from the bag. Calculate the Probability that it will be (i) red (ii) yellow (iii) blue
Answer:
Total ball = 4 Red + 3 blue + 2 yellow = 9 ball
(i) P (red ball) = \(\frac{4}{9}\)
(ii) P (Yellow) = \(\frac{2}{9}\)

Part – D

Answer any SIX questions. (6 × 5 = 30)

Question 39.
Define a modulus function. Draw the graph and write down its domain and range.
Answer:
Definition of modulus function: The function f: R → R defined by f(x) = |x|. For each x ∈ R is called modulus function. For each non-negative value of n. f(x) = x. But for negative value

Question 40.
Prove that cos²x + cos² \(\left(x-\frac{\pi}{3}\right)=\frac{3}{2}\)
Answer:

Question 41.
Prove by Mathematical induction 1³ + 2³ + 3³ + ………. + n³ \(\frac{n^{2}(n+1)^{2}}{4}\), n ∈ N
Answer:
at n = 1, LHS = RHS, \(\mathrm{l}^{3}=\frac{\mathrm{l}^{2}(1+1)^{2}}{4}\) [1 = 1]
at n = k(+)
1³ + 2³ + 3³ + ………. + k³ \(\frac{k^{2}(k+1)^{2}}{4}\) ….. (1)
Add (k+1) on both side.



Hence the given series is true for n = 1, 2, …….., k, k + 1,….. for all positive integer of n.

Question 42.
Solve the following system of inequalities graphically 2x + y ≥ 4, x + y ≤ 3, 2x – 3y ≤ 6.
Answer:

Question 43.
A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has (1) no girl (ii) atleast one boy and one girl.
Answer:
Given 4 girls and 7 boy’s
(i) no girls:

(ii) atleast 1 boy and 1 girls
Girls × boys
(a) 4C₁ × 7C₄ = 7 (b) 4C₂ × 7C₃ = 84.
(c) 4C₃ × 7C₂ = 210 (d) 4C₄ × 7C₁ = 140
Total number of selection 441 ways .

Question 44.
State and prove Binomial theorem for all positive integers.
Answer:
Statement: (a + b)ⁿ =nC₀aⁿ + nc₁a^n-1 b + nC₂ a^n-2 b² + nC₃ a^n-3 b³ + …….. + nC_n-1 a.b^n-1 + nC_nbⁿ
Proof: By aplying principle of mathemaical induction
Let P(n) : (a + b)ⁿ = nC₀aⁿ + nc₁a^n-1b¹ + ……. + ⁿC _nbⁿ
For n = 1 p(1) = (a + b)¹ = 1C₀a¹ + 1C₁a^1-1b¹
[(a + b) = (a – b)] is true
For n = K(f). p(k) = (a + b)k = kC₀a^k + kC₁a^k-1b +….+ KC_kb^k …..(l)
is true for n = k
We shall prove that p(k + 1) is also true i.e..


Thus it has been proved that R(k + 1) is tense for p(K) is true and it is that for all positive integer n.

Question 45.
Derive an expression for the co-ordinate of a point that divides the line joining the points A(x₁, y₁, z₁) and B(x₂, y₂, z₂)internally in the m : n. Hence find the co-ordinate of the midpoint of AB where A = (1,2,3) and B = (5,6,7)
Answer:
Proof: Let p(x₁, y₁, z₁) and Q(x₂, y₂, z₂) be the given points
Let R(x, y, z) divide PQ internally in the ratio m : n
Draw PL, QM, RN perpendicular to xy-plane.
∴ PL ∥ RN ∥ QM
∴ PL, RN, QM lie in one plane
So that the points L, N, M lie in a straight line which is the intersection of the plane and XY plane.
Through the point R draw a line AB It to the line LM. The line AB intersect the line LP externally at A and the line MQ at B.

Triangle APR and LIQR are similar.

∴ n(z – z₁) = m(z₂ – z)
∴ nz = nz₁ = mz₂ – m₂
∴ (nz + mz) = (mz₂ + nz₁)
∴ z(m + n) = mz₂ + nz₁

Question 46.
Prove that \(\lim _{\theta \rightarrow 0} \frac{\sin \theta}{\theta}=1\) (being in radians) and hence show that \(\lim _{\theta \rightarrow 0} \frac{\tan \theta}{\theta}=1\)
Answer:
\(\lim _{\theta \rightarrow 0} \frac{\sin \theta}{\theta}=1\)
Proof: Consider a circle with centre ‘O’ and radius ‘r’. Mark two point A and B on the circumference of the circle so that

At ‘A’ draw a tangent to the circle produce OB to cut the tangent at C. Joint AB.
Draw BM ⊥ OA,
Here OA = OB = r
From the figure

Area of triangle OAB < area of the sector AOB < area of triangle OAC

∴ BM < rθ < AC … (1)
In triangle OBM : sinθ = \(\frac{B M}{O B}\)
∴ BM = OB sinθ = rsinθ
In triangle OAC: tan θ = \(\frac{AC}{O A}\) ∴ AC = OA tan θ = r tan θ

sin θ < 0< tan θ
÷ sin θ
\(1<\frac{\theta}{\sin \theta}<\frac{1}{\cos \theta}\)
apply lt θ → 0

Question 47.
Derive the expression for the length of the perpendicular drawn from the point (x₁ y₁) of the line ax + by + c = 0.
Answer:
Given ax + by + c = 0
∴ ax + by = -c
÷ C .



P(x, y)

Question 48.
Find the mean deviation about mean for the following data:

Answer:

Part – E

Answer any ONE question. (1 × 10 = 10)

Question 49.
(a) Prove Geometrically that cos(x + y) = cos x cos y.sin x sin y
Answer:
Prove that cos(x + y) = cos x cos y.sin x sin y

Proof Consider a unit circle (radius = 1 unit) with centre is (0, 0).
Consider 4 point P₁, P₂, P₃ and P₄

The co-ordinate of P₁, P₂, P₃ and P₄ are given by
P₁ = (cosx,sinx) P₂ = [cos(x + y). sìn(x + y)]
P₃ = [cos(-y) sin(-y)] P₄ = [1,0]
From the figure OP₁OP₃ is congruent to ∆P₂OP₄
∴ From distance formula
P₁p₃ = P₂P₄ …… (1)
Takè the distance (P₁P₃)² = [cosx – cos(-y)]² + [sin x – sin (-y)]²
= (cosx – cosy)² + (sin x + sin y)²
= cos²x + cos²y = cosxcosy + sin²x + sin²y + 2sin cosy = 1 + 1 + 2(cosxcosy – sinxsiny)
(p₁, P₃)² = 2 – 2 cos (x + y)
Again (P₂P₄)² = [1^{(a-b)2-cos(x+y)}]² + |q – sin (x + y)|²
= 1 + cos²(x + y) -2cos(x + y) + sin²(x + y) = 1 + 1 – 2cos(x + y) = 2 – 2cos(x + y)

⇒ LHS = RHS
∴ [cos(x + y) = cosx cosy – sin x sin y]

(ii) Show that cos 2x = cos²x – sin x²x
Take cos(x + y) = cos xcos y – sin xsin y
Put y = x
∴ cos(x + x) = cosx cosx – sinx sinx
cos2x = cos² x – sin²x

(b) Find the sum of the series 5, 55, 555, 5555, … to n terms.
Answer:
S_n = 5 + 55 + 555 + ……… to n term
S_n = 5[1 + 11 + 111 + ………to n term]
\(\frac{S_{n}}{5}\) = 1 + 11 + 111 +……. to n term.
Multiply both side by 9
∴ \(\frac{9 S_{n}}{5}\) = 9 + 99 + 999+ ………. n term
\(\frac{9 S_{n}}{5}\) = (90 – 1) + (100 – 1) + (1000 – 1) +
\(\frac{9 S_{n}}{5}\) = (10 + 100 + 1000 + … nth) GP (-1 – 1 – 1 … + n term)

Question 50.
(a) Define ellipse as a set of all points in the plane and derive its equation as \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\)
Answer:
Let F₂ and F₂, be the focii. ‘O’ be the mid point of the line segment F₁F₂. ‘0 be the origin. And a line from O through F₂, be + ve and F₁ be -ve ∴ the co-ordinate of F₁(C₁ .0) and F₂ (c₂ o)

Let p(x,y) be a locus on the ellipse.
∴ PF₁ + PF₂ = 2a
Using distance formula

Squaring on both side

(b) Find the derivative of \(\frac{x^{3}-\cos x}{\sin x}\) with respect to X.
Answer:

Students can Download 1st PUC Maths Model Question Paper 2 with Answers, Karnataka 1st PUC Maths Model Question Paper with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

Karnataka 1st PUC Maths Model Question Paper 2 with Answers

Time: 3 Hrs 15 Min
Max. Marks: 100

Instructions:

1. The question paper has five parts namely A, B, C, D and E. Answer all the parts.
2. Part-A carries 10 marks. Part-B carries 20 marks. Part-C carries 30 marks. Part-D carries 20 marks, Part-E carries 10 marks.

Part – A

Answer ALL the questions. Each question carries one mark. (10 × 1 = 10)

Question 1.
If n(A) = 3, then find n[P(A)].
Answer:
n(A) = 3 then n[p(A)] = 2³ = 8 elements.

Question 2.
If (x – 2, y + 3) = (5, -6), then find the values x and y.
Answer:
x – 2 = 5 ∴ x=7
y + 3 = -6 ∴ y=-9.

Question 3.
Convert 750° into radians.
Answer:

Question 4.
Find the conjugate of i(2 + i).
Answer:
Conjugate i(2 + i) = 2i + i² = -1 + 2i
∴ conjugate Z̄ = -1 -2i.

Question 5.
If nC₅ = nC₁₀, then find n
Answer:
n = 5 + 10 = 15

Question 6.
Find the 5^th term of the GP. \(1, \frac{1}{5}, \frac{1}{25},\)
Answer:
a₅ = (1)\(\left(\frac{1}{5}\right)^{5-1}\) = \(\left(\frac{1}{5}\right)^{4}=\left[\frac{1}{625}\right]\)

Question 7.
Find the slope of the straight line 3x – 4y + 6 = 0
Answer:
Stage = m = \(-\frac{(3)}{-4}=\left[\frac{3}{4}\right]\)

Question 8.
Evaluate \(\lim _{x \rightarrow 4} \frac{x^{3}-64}{x-4}\)
Answer:
= n : a^n-1 = 3 (4)^3-1 = 3(4)² = 48

Question 9.
Write the negation of “Every natural number is greater than 0″.
Answer:
“Every natural number is not greated than 0.”

Question 10.
Define “sample space”.
Answer:
Sample space: Set of all possible outcome of an event is called a sample space.

Part – B

Answer any TEN Questions. (10 × 2 = 20)

Question 11.
If U = {x : x ≤ 6 and x ∈ N}, A = {3,5}, B = {2,5,6} then find (A ∪ B)’.
Answer:
A ∪ B = {3,5} ∪ [2;5,6] = [2,3,5,6]
∴ (A ∪ B)’ = {1,4}.

Question 12.
If X and Y are two sets such that n(X ∩ Y) = 10, n(X) = 38, n(Y) = 25 then find – n(X ∪ Y).
Answer:
If n(X ∪ Y) = n(X) + n(Y) – n(X ∩ Y) = 38 + 25 – 10 = 53

Question 13.
Finid the domain and range of the real function f(x) = \(\sqrt{9-x^{2}}\)
Answer:
Domain of f(x) = {x : x ∈ 2, -3 ≤ x ≤ 3}, Range of f(x)=[x : x ∈ R]

Question 14.
If in two circles, arcs of the same length subtend angles 60° and 75o at the centre, then find the ratio of their radii.
Answer:
S₁, = 5, S₂ = 5, θ₁ = 60° = \(\frac{\pi^{c}}{3}\) r₁ : r₂ = ?

∴ r₁ : r₂ = 5 : 4

Question 15.
Find the value of sin 75°
Answer:
sin 75° = sin ( 45° +30°)
[sin (x + y)= sin x cos y + cosxsin y] = sin 45° . cos 30° + cos 45°. sin 30°

Question 16.
Express the following in a + ib form \(\left[\left(\frac{1}{3}+i \frac{7}{3}\right)+\left(4+i \frac{1}{3}\right)\right]-\left(-\frac{4}{3}+i\right)\)
Answer:

Question 17.
Solve thr inequality 3(1 – x) <2 (x + 4) and represent it on number line
Answer:
3(1 – x) <2 (x + 4) ⇒ ∴ 3 – 3x < 2x + 8
⇒ ∴ 3 – 8 < 2x + 3x
-5 < 5x ⇒ -1 < x or x > -1.

Question 18.
Find the acute angle between the straight lines 5x + 6y – 1 = 0 and x – 11y + 8 = 0.
Answer:

Question 19.
Find the distance between the parallel lines 3x – 4y + 7 = 0 and 3x – 4y + 5 = 0.
Answer:

Question 20.
Tind the ratio in which the YZ – plane divides the line segment formed by joining the points (-2,6,7) and (2,-5,6) internally.
Answer:

Let the ratio be m : n = k : 1 (Assume)
(x₁, y₁, z₁) = (-2,6,7) ⇒ (x₂, y₂,z₂) = (2,-5,6)
yz plane divides the x coordinate is = 0

∴ 0 = \(\frac{2 k-2}{k+1}\) ⇒ ∴ 0 = 2k – 2 ∴ k = 1 ∴ ratio is 1 : 1

Question 21.
Evaluate \(\lim _{x \rightarrow 0} \frac{1-\cos x}{x}\)
Answer:

Question 22.
Write the converse and contrapositive of “If two lines are parallel then they do not intereset in the same plane.”
Answer:
Converse: (q → p) If two line donot interest in the same plane then they are parallel,
Contrapositive (~q → -p): If two line intersect in the same plane then they are not paralle..

Question 23.
The coefficient of variation of a distribution is 60 and the standard deviatio is 21.What is the arithmetic mean of the distribution?
Answer:
C.V.= 60, σ = 21, X̄ = ? .

Question 24.
A letter is choosen at random from the word “ASSASSINATION”. Find the probability that the letter is (i) a vowel (ii) a consonant.
Answer:
Total letters = 13
Vowels = AAAIIO = 6
Consonant = SSSSNNT = 7
‘A’ repeas = 3 times. I repeats = 2
‘S’ repeats. 4 times. N repeats = 2
Probability of choosen a letter it a vowel

Probability of choosen a consonant = \(\frac{7 C_{1}}{13 C_{1}}=\left[\frac{7}{13}\right]\)

Part – C

Answer any TEN of the following questions. Each question carries THREE marks. (10 × 3 = 30)

Question 25.
In a class of 35 students, 24 like to play cricket and 16 like to play football. Also each student likes to play atleast one of the two grams. How many students like to play both cricket and football?
Answer:
Cricket = C, Football = F, n(C ∪ F) = 35, n(C ∩ F) = ?
n(C) = 24 2(F) = 16
n(C ∩ F) = n(C) + n(F) – n(C ∪ F) = 24 + 16 – 25 = 40 – 35 = 5

Question 26.
Let f = {1,1),(2,3)(0,-1),(-1-3}} be a linear function from Z into Z. Find f (x).
Answer:
Let the function be f (x) = ax + b
f (1) = a(1) + b = a + b = 1 ⇒ f(2) = a(2) + b = 2a + b = 2
f(0) = a(0) + b = [b = -1] …..(1)
f(-1) = a(-1) + b = -3
∴ b – a = -3 … (2)

(i) in (2) (-1) -a = -3
∴ -1 + 3 = a ⇒ ∴ a = 2 ⇒ ∴ f(x) = 2x – 1.

Question 27.
Find the general solution of the euation cos 4x = cos2x.
Answer:
cos 4x = cos 2x , cos 4x – cos 2x = 0
By transformation formula cosC – cos D = -2 sin \(\left(\frac{C+D}{2}\right)\) sin² (-1)
-2 sin\(\left(\frac{6 x}{2}\right)\) × sin \(\left(\frac{2 x}{2}\right)\) = 0
∴ 2 sin 3x × sin x = 0 or sin 3x = 0 or sin x = 0
2 = 0°
∴ General Solution for sin x is
x = nπ + (-1)ⁿα ⇒ 3x = nπ + 0 ∴[x = \(\frac{n \pi}{3}\) or nπ]
or
cos 4x = cos 2x ⇒ assume α = 2x
∴ General solution
x = 2nπ ± 2 ⇒ 4x = 2nπ ± 2x ⇒ ∴ 2x = 2nπ and 6x = 2nπ
x = nπ, x = \(\frac{n \pi}{3}\)

Question 28.
Solve the equation √2x² + x + √2 = 0. .
Answer:
a = √2, b = 1, c = √2

Question 29.
Express the complex number -1 + i√3 in polar form.
Answer:
-1 + i√3 = r(cos θ + isin θ) polar form

∴ r = \(\sqrt{x^{2}+y^{2}}=\sqrt{1+3}=\sqrt{4}=2\)
θ = tan^-1(\(\left(\frac{y}{x}\right)\)) = tan^-1√3 – 1 = -(π – Standard angle) = \(-\left(\pi-\frac{\pi}{3}\right)=\frac{(-2 \pi)}{3}\)
∴ -1 + i√3 = 2cis\(\left(\frac{-2 \pi}{3}\right)\)

Question 30.
How much words.with or without meaning can be made from the letters of the word “MONDAY” assuming that no letter is repeated if
(i) Four letters are used at a time
(ii) All letters are used at a time
(iii) All letters are used but first letter is vowel?
Answer:
Monday: Given 6 letters
∴ number of arrangement = 6P₆ = 6!
(i) Taken 4 letters at a time
= 6P₄ = \(\frac{6 !}{2 !}\) = 6 × 5 × 4 × 3 = 360 ways

(ii) all letters at a limt = 6P₆ = 6! = 720 ways.

(iii) start with 0 ……… = 5P₅ = 120
Start with A ……… = 5P₅ = 120
240 ways.

Question 31.
Find the middle terms in the expansion of \(\left(\frac{n+1}{2}\right)\) and \(\left(\frac{n+1}{2}\right)\) + 1
Answer:
x = 3 , a = \(-\frac{x^{3}}{6}\), n = 9, T₅ = ?, r = 4
Formula T_r+1 = nC_r x^n-r, a^r

Question 32.
Insert five numbers between 8 and 26 such that the resulting sequence is an arithmetic progression.
Answer:
8A₁, A₂, A₃, A₄, A₅,26
a = 8, n = 7, a_n = 26, d = ?
a_n = a + (n-1)d ⇒ 26 = 8 + (7 – 1)d = 26 – 8 = 6d
18 = 6d ∴ d=3
Common difference
∴ A₁ = a + d = 8+3 =11, A₂ =11 + 3 = 14, A₃ = 17, A₄ = 20, A₅ = 23 are the 5 AM’s.

Question 33.
The sum of first three terms of a geometric progression is \(\frac { 39 }{ 10 }\) and their product is 1. Find the common ratio and the terms.
Answer:
Let the 3 term in GP are \(\frac { a }{ r }\) a and ar

Qudratic equation
∴ 10r² – 25r – 4r + 10 ⇒ 50(2r – 5) -2 (2r – 5) = 0
(2r – 5) = 0 or 5r – 2 = 0 ⇒ ∴ r = \(\frac{5}{2}\) or r = \(\frac{2}{5}\)
∴ the three terms are
at a = 1, r = \(\frac{5}{2}\)
I term \(\frac{a}{r}=\frac{1}{\frac{5}{2}}=\frac{2}{5}\)
II term a = 1
III term a_r = \(\frac{5}{2}\)

at a = 1, r = \(\frac{2}{5}\)
I term a_r = \(\frac{5}{2}\)
II term a = 1
III term = \(\frac{2}{5}\)

Question 34.
Find the equation of the circle with radius 5, whose centre lies on x-axis and passes through the point (2, 3).
Answer:
r = 5 .
Centre lies on X – axis ⇒ pt(2,3) = (x, y)
Let the circle equation be x² + y² + 2fx + 2gx + C =0 … (1)
∵ centre lies on x-axis ∴ f = 0
∴ (1) becomes
x² + y² +2 gx + c = 0) at (2,3)
4 + 9 + 2g(2) + c = 0 ∴ 48 + c = -13 …(2)
Given radius = 5
∴ \(\sqrt{g^{2}+f^{2}-c}=5 \mathrm{SBS}\)
Put f = 0. :g² – c = 25 …(3)

∴ g² + 4g – 12 = 0 ⇒ g² + 5g – 2y = 12 = 0 ⇒ g(g – 16) – 2(g + 6)=0
∴ g = -6 or g = -2
Substitute in (2) 4g + C = -13
at g = -6 4(-6) + C = -13 ⇒ C = -13 + 24 = 11
at g = -2 4(-2) + 1 = -13 ⇒ C =-13 + 8 = -5
∴ at g = -6, C = 11, f = 0 (1) becomes
x² + y² – 12x + 11 = 0
at g = -2, c = -5, f = 0
x² + y² – 4x – 5 = 0

Question 35.
Find the derivative of sin x with respect to x fron first principles.
Answer:
y = sin x as x → x + Δx, y + Δy
∴ (y + Δy) = sin(x + Δx)
Δy = sin(x + Δx) – y
Δy = sin(x + Δx) – sin x
÷ Δx and apply lt Δx → 0 on both side

Question 36.
Verify by the method of contradiction that “√7 is irrational.”
Answer:
Prove that √7 is irrational
Assume √7. is an rational :: √7 = \(\frac{p}{q}\)
Squaring on b.s.
∴ 7 = \(\frac{p^{2}}{q^{2}}\)
∴ 7q² = p² i.e., p in a multiple of again put p = 7k (k+1) :
∴ 7q² = (7k)² ⇒ 7q² = 49k² ⇒ q² = 7k²
⇒ q is also a multiple of q ⇒ ∴ both “p’ and ‘q’ are the factor of 7

∴ our assumption that √7 is an partial is wrong. ∴ √7 is an irrational.

Question 37.
A committee of two pers.ns ¡s selected from 2 men and 2 women. What is the probability that the committee will have
(i) no man (ii) one man.
Answer:
Given 2 mens × 2 women → select 2 person.

Question 38.
If E and F are two events such that P(E) = \(\frac { 1 }{ 4 }\) and P(F) = \(\frac { 1 }{ 2 }\) and P(E and F) = \(\frac { 1 }{ 8 }\) then find p(not E and not F)
Answer:
P(E) = \(\frac { 1 }{ 4 }\), P(F) = \(\frac { 1 }{ 2 }\), and p(E ∪ F) = \(\frac { 1 }{ 8 }\) P(A ∩ F) = 1
From addition rule
p(E ∩ F) = p(F) + p(F) – p(E ∪ F) = \(\frac{1}{4}+\frac{1}{2}-\frac{1}{8}=\frac{2+4-1}{8}=\frac{5}{8}\)

Part – D

Answer any SIX Questions. (6 × 5 = 30)

Question 39.
Define signum function Draw its garph. Write its domain, co – domain and range
Answer:
Signum function: The function f:R → R defined by

a signum function: The domain of the signum function is R (Real nos) and the bugs and the signum function is the set {-1,0,1}

Question 40.
Prove that \(\frac{\sin 5 x-2 \sin 3 x+\sin x}{\cos 5 x-\cos x}=\tan x\)
Answer:

Question 41.
Prove that 1.2 + 2.3 + 3.4 + ……….. +n(n – 1) = \(\frac{n(n+1)(n+2)}{3}\) ∀n ∈ N, by using principal of mathematical induction.
Answer:
at n = 1
LHS = RHS


Hence the given statement is true for n =1,2,…..k, k +1…. i.e., for all (+) integral value of n.

Question 42.
Solve the system of linear inequalities: 4x + 3y ≤ 60, y ≥ 2x, x ≥ 3, y ≥ 0 graphically.
Answer:

Question 43.
What is the number of ways of choosing 4 cards from a pack In how many of these (i) four cards are of the same suit? (ii) four card belong to four different suits?
Answer:
Given 52 cards → select 4 cards.
(i) 4 cards are of same smit.
∴ total number of selection \(=\left[\frac{13 C_{4}+13 C_{4}+13 C_{4}+13 C_{4}}{4}\right]\)

(ii) 4 cards are of different suits
Total number of selection = 13C₁ × 13C₁ × 13C₁ × 13C₁ = (134)⁴ = (13)⁴ = 28.561

Question 44.
Prove binomial theorem for any positive integer n.
Answer:
Prove binomial theorem for any positive integral.
Statement: (a + b)ⁿ =nC₀aⁿ + nc₁a^n-1 b + nC₂ a^n-2 b² + nC₃ a^n-3 b³ + …….. + nC_n-1 a.b^n-1 + nC_nbⁿ
Proof: By aplying principle of mathemaical induction
Let P(n) : (a + b)ⁿ = nC₀aⁿ + nc₁a^n-1b¹ + ……. + ⁿC _nbⁿ
For n = 1 p(1) = (a + b)¹ = 1C₀a¹ + 1C₁a^1-1b¹
[(a + b) = (a – b)] is true
For n = K(f). p(k) = (a + b)k = kC₀a^k + kC₁a^k-1b +….+ KC_kb^k …..(l)
is true for n = k
We shall prove that p(k + 1) is also true i.e..


Thus it has been proved that R(k + 1) is tense for p(K) is true and it is that for all positive integer n.

Question 45.
Derive the equation of straight line in the normal form x,cos θ + y,sinω = P, where Po is the length of normal to the line from the origin and ‘ω’ is inclination of normal with positive x-axis.
Answer:
Derive the eqn. of straight line in the following
x cos ω + y sin ω = p (normal form)
consider a line cutting x-axis at A and y-axis at B.
Let the x-intercept = OA = a y-intercept OB = b

Drawn OM ⊥ to AB from 0
OM is called the length of the normal = P. It makes an angle of the norma = P. It makes an angle w (omega) w.r.t. X-axis.
In the angle AOM

In the angle ROM

Equation of the line in intercept is given by \(\frac{x}{a}+\frac{y}{b}=1\) substitute ‘a’ and ‘b’ then

∴ [xcosα w + ysin α = p] in the equation of line AB is normal form.

Question 46.
Derive the expression for the co-ordinates of a point that divides the line joining points A(x₁,y₁,z₁) and B(x₂, y₂,z₂) internally in the ratio m:n, also find the midpoint of line AB, where A = (2,8,1) and B = (2,-2,5).
Answer:
Proof: Let p(x₁, y₁, z₁) and Q(x₂, y₂, z₂) be the given points
Let R(x, y, z) divide PQ internally in the ratio m : n
Draw PL, QM, RN perpendicular to xy-plane.
∴ PL ∥ RN ∥ QM
∴ PL, RN, QM lie in one plane
So that the points L, N, M lie in a straight line which is the intersection of the plane and XY plane.
Through the point R draw a line AB It to the line LM. The line AB intersect the line LP externally at A and the line MQ at B.

Triangle APR and LIQR are similar.

∴ n(z – z₁) = m(z₂ – z)
∴ nz = nz₁ = mz₂ – m₂
∴ (nz + mz) = (mz₂ + nz₁)
∴ z(m + n) = mz₂ + nz₁

Mid point of AB = \(=\frac{2+2}{2}, \frac{F-2}{2}, \frac{1+5}{2}=(2,3,3)\)

Question 47.
Prove that \(\lim _{x \rightarrow 0} \frac{\sin x}{x}=1\) Where “x” being measured in radians.
Answer:
\(\lim _{\theta \rightarrow 0} \frac{\sin \theta}{\theta}=1\)
Proof: Consider a circle with centre ‘O’ and radius ‘r’. Mark two point A and B on the circumference of the circle so that

At ‘A’ draw a tangent to the circle produce OB to cut the tangent at C. Joint AB.
Draw BM ⊥ OA,
Here OA = OB = r
From the figure

Area of triangle OAB < area of the sector AOB < area of triangle OAC

∴ BM < rθ < AC … (1)
In triangle OBM : sinθ = \(\frac{B M}{O B}\)
∴ BM = OB sinθ = rsinθ
In triangle OAC: tan θ = \(\frac{AC}{O A}\) ∴ AC = OA tan θ = r tan θ

sin θ < 0< tan θ
÷ sin θ
\(1<\frac{\theta}{\sin \theta}<\frac{1}{\cos \theta}\)
apply lt θ → 0

Question 48.
Find the mean deviation about mean for the following data:

Answer:

Part – E

Answer any ONE question. (1 × 10 = 10)

Question 49.
(a) Defind Hyperbola as a set of points and derive the equation of hyperbola in standard form \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\)
Answer:
Definition hyperbola: A Hyperbola is the act of all points in a plane the difference of whose distances.
From two fixed points in the plane is constant.
The two fixed points are called Focii and the mid point ‘O’ is called the centre of the hyperbola.
Distance between two focii F₁ and F₂ = 2c
Distance between two velocities = AB = 2a
(length of transverse axis) and b = \(\sqrt{c^{2}-a^{2}}\)
∴ 2b = length of conjugate axis and \(e=\frac{c}{a}\) is called the eccentricity of the hyperbola.
Derivation : Equation of hypergola in standard form \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\)

From the definition PF₁ – PF₂ = 2a
Using the distane formula
\(\sqrt{(x+1)^{2}+y^{2}}-\sqrt{(x-c)^{2}+y^{2}}=2 a\)
∴ \(\sqrt{(x+c)^{2}+y^{2}}-\sqrt{(x-c)^{2}+y^{2}}=2 a\)
Squaring on both side

(b) Find the deviation of \(\frac{x^{2}-\cos x}{\sin x}\) with repect to x.
Answer:
y = \(\left[\frac{x^{5}-\cos x}{\sin x}\right]\) by using quotient rule

Question 50.
(a) Prove geometrically that cos(x + y) = cos x, cos y – sin x.sin y.
Answer:
Prove that cos(x + y) = cos x cos y.sin x sin y

w
Proof Consider a unit circle (radius = 1 unit) with centre is (0, 0).
Consider 4 point P₁, P₂, P₃ and P₄

The co-ordinate of P₁, P₂, P₃ and P₄ are given by
P₁ = (cosx,sinx) P₂ = [cos(x + y). sìn(x + y)]
P₃ = [cos(-y) sin(-y)] P₄ = [1,0]
From the figure OP₁OP₃ is congruent to ∆P₂OP₄
∴ From distance formula
P₁p₃ = P₂P₄ …… (1)
Takè the distance (P₁P₃)² = [cosx – cos(-y)]² + [sin x – sin (-y)]²
= (cosx – cosy)² + (sin x + sin y)²
= cos²x + cos²y = cosxcosy + sin²x + sin²y + 2sin cosy = 1 + 1 + 2(cosxcosy – sinxsiny)
(p₁, P₃)² = 2 – 2 cos (x + y)
Again (P₂P₄)² = [1^{(a-b)2-cos(x+y)}]² + |q – sin (x + y)|²
= 1 + cos²(x + y) -2cos(x + y) + sin²(x + y) = 1 + 1 – 2cos(x + y) = 2 – 2cos(x + y)

⇒ LHS = RHS
∴ [cos(x + y) = cosx cosy – sin x sin y]

(ii) Show that cos 2x = cos²x – sin x²x
Take cos(x + y) = cos xcos y – sin xsin y
Put y = x
∴ cos(x + x) = cosx cosx – sinx sinx
cos2x = cos² x – sin²x

(b) Find the sum to n terms of the
Answer:
Let F₂ and F₂, be the focii. ‘O’ be the mid point of the line segment F₁F₂. ‘0 be the origin. And a line from O through F₂, be + ve and F₁ be -ve ∴ the co-ordinate of F₁(C₁ .0) and F₂ (c₂ o)

Let p(x,y) be a locus on the ellipse.
∴ PF₁ + PF₂ = 2a
Using distance formula

Squaring on both side

Students can Download 1st PUC Maths Model Question Paper 1 with Answers, Karnataka 1st PUC Maths Model Question Paper with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

Karnataka 1st PUC Maths Model Question Paper 1 with Answers

Time : 3 hrs 15 min
Max. Marks : 100

Instructions:
1. The question paper has five parts A, B, C, D and E and answer all parts,
2. Part-A carries 10 marks, Part-B carries 20 marks, Part-C carries 30 marks, Part-D carries 20 marks, Part-E carries 10 marks.

Part – A

Answer any TEN questions : (10 × 1 = 10)

Question 1.
Given that the numbers of subsets of a set A is 16. Find the number of elements of A.
Answer:
Let n(A) = m
n [P(A)] = 16 ⇒ 2^m = 16 ⇒ m= 4
n(A)= 4

Question 2.
If tan x = \(\frac { 3 }{ 4 }\) and x lies in the third quadrant, find sin X.
Answer:
tan x = \(\frac{3}{4}=\frac{-3}{-4}\)

ordinate = -3, abscissa = 4, distance = 5 sin x = \(\frac { -3 }{ 5 }\)

Question 3.
Find the modulus of \(\frac{1+i}{1-i}\)
Answer:
\(\frac{1+i}{1-i}=\frac{(1+i)^{2}}{1-i}=\frac{2 i}{2}\) = i Modulus of i= 1

Question 4.
Find ‘n’ if ⁿC₇ = ⁿC₆
Answer:
ⁿC_n-7 = ⁿC₆ ⇒ n – 7 = 6 ⇒ n = 13.

Question 5.
Find 20th term of GP. \(\frac{5}{2}, \frac{5}{4}, \frac{5}{8}—-\)
Answer:

Question 6.
Find the distance between 3r + 4y +5= 0 and 6x + 8y +2=0.
Answer:
3x + 4y + 5 = 0) ………….. (1)
3x + 4y + 1 = 0 …………. (2)
Required distance \(\left|\frac{5-1}{\sqrt{9+16}}\right|=\frac{4}{5}\) units

Question 7.

Answer:
\(\lim _{x \rightarrow 0+}\) f(x) = \(\lim _{x \rightarrow 0} \frac{x}{x}=\frac{1}{1}=2\) ∴ f(x) in Discontinuous

Question 8.
Write the negation of For all a, b ∈ I, a – b ∈ I’.
Answer:
“There exists a, b ∈ I, such that a – b € I’
or ‘∃ a, b ∈ I, a – b ∉ I’.

Question 9.
A letter is chosen at random from the word “ASSASINATION”. Find the probability that letter is vowel.
Answer:
No of ways of selecting one vowel out of six vowels (3A’S, 21’s, 10’s) = ⁶C₁ = 6.
P(1 vowel) = \(\frac{^{6} \mathrm{C}_{1}}{^{13} \mathrm{C}_{1}}=\frac{6}{13}\)

Question 10.
Let A = {2,3,4} and R be a relation on A defined by
R={(x,y)|x,y ∈ A,x divides y}, find ‘R’.
Answer:
R= {(2, 2), (2, 4), (3, 3), (4,4)}.

Part – B

Answer any TEN questions : (10 × 2 = 20)

Question 11.
If A and B are two disjoimt sets and n(A) = 15 and n(B) = 10 find n(A ∪ B), n(A ∩ B)
Answer:
n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
n(A ∩ B) = 0, n(A ∪ B) = 15 + 10 = 25.

Question 12.
If U = {x:r s≤10, r ∈ N} A = {x : x ∈ N, x is prime) B = {x : x ∈ N, x is even} write A ∩ B’ in roster form.
Answer:
U = {1, 2, 3 … 10), A = {2, 3, 5, 7}
B = {2, 4, 6, 8, 10} B¹ = {3, 5, 7,9}
[A ∩ B¹ = {3,5,7)]

Question 13.
If A × B = {(a,1) (a,2) (a,3) (b,1) (b,2) (b,3)}, find the sets A and B and hence fimnnd B × A
Answer:
A = {a, b}, B = {1, 2, 3}
B × A= {(1, a) (1, b) (2, a) (2, b) (3, a) (3, b)}

Question 14.
The difference between two acute angles of a right angled triangle is to \(\frac{3 \pi}{10}\) radiAnswer: Express the angles in degrees.
Answer:
Let A and B be acute angles
Given A + B = \(\frac{\pi}{2}\) = 90° : A – B = \(\frac{3 \pi}{10}\) = 54° ⇒ A = \(\frac{2 \pi}{5}\) and B = \(\frac{\pi}{5} \) ⇒ A = 72 and B = 18°.

Question 15.
Find sin \(\frac{x}{2}\) if tan x = \(-\frac{4}{3}\)and x lies in second quadrant,
Answer:
tan x = \(\frac{-4}{3}=\frac{4}{-3}\) ⇒ ∴ cos x = \(\frac{-3}{5}\)

Question 16.
\(\lim _{x \rightarrow 3} \frac{x-3}{x^{2}-5 x+6}\)
Answer:

Question 17.
CV = 60 σ = 21
Answer:

Question 18.
Write the inverse, converse of ‘If a parallelogram is a square, then it is rhombus’.
Answer:
Inverse: If a parallelogram is not a square then it is not a rhombus
Converse: If a parallelogram is a rhombus then it is a square.

Question 19.
On her vacations Veena visits four cities A, B, C and D in random order. What is the probability that she visits A before B?
Answer:
n (S) = 24
P(visiting A before B) = \(\frac{12}{24}\) = 1/2

Question 20.
In a triangle ABC with vertex A(2,3), B(4, -1) and C(1,2). Find the Length of the alitude from vertex A.
Answer:
Equation BC = x + y – 3 = 0
Length of the alitude from A (2, 3) = \(\left|\frac{2+3-3}{\sqrt{2}}\right|=\left|\frac{2}{\sqrt{2}}\right|=\sqrt{2}\) = √2.

Question 21.
Represent the complex number z = 1 + i in polar form.
Answer:
r = √2 and θ = \(\frac{\pi}{4}\) Polar form is √2 \(\left(\cos \frac{\pi}{4}+i \sin \frac{\pi}{4}\right)\)

Question 22.
Obtain all pairs of consecutive odd natural numbers such that in each pair both are more than 50 and their sum is less than 120.
Answer:
Taking the pair as x, x + 2,
we get x > 50, 2x + 2 < 120 ⇒ x < 59 and writing the required pairs are (51, 53), (53, 55), (55, 57), (57, 59).

Question 23.
A line cuts off equal intercepts on the co – ordinate axes. Find the angle made by the line with the positive x-axis.
Answer:
Slope =-1 ⇒ tanθ = -1
angle made = 135°.

Question 24.
If the origin is the centroid of the triangle PQR with vertices P (2a, 4, 6) Q(-4, 3b, -10) and R(8, 14, 2c) then find the values of a, b, c.
Answer:

Part-C

Answer any EIGHT of the following questions : (10 × 3 = 30)

Question 25.
Out of a group of 200 students (who know at least one language), 100 students know English, 80 students know Kannada, 70 students know Hindi. If 40 students know all the three languages, find the number of students who know exactly two languages.
Answer:
writing n(E)= 100, n(K)= 80, n(H)= 70 .
n(E ∪ K ∪ H) = 200, n (E ∩ K N ∩ H) = 40
We know that n(E ∪ K ∪ H) = n(E) + n (K) + n(H) –n (E ∩ K)
– n (K ∩ H) -n (H ∩ E) + n (E ∩ K ∩ H)
∴ n (E ∩ K) + n (K ∩ H) + n (H ∩ E) = 90

Question 26.
Let R: Z → Z be a relation defined by R = {(a,b) : a, b, ∈ Z, a – b ∈ z}. Show that
(i) ∀ a ∈ Z, (a, a) ∈ R.
(ii) (a, b) ∈ R ⇒ (b,a) ∈ R
(iii) (a, b) ∈ R, (b, c) ∈ R ⇒ (a, c) ∈ R
Answer:
∀ a ∈ Z, (a, a) ∈ R since a – a = 0 ∈ Z
(a, b) ∈ R ⇒ a – b ∈ Z ⇒ ∴ b – a ∈ Z ⇒ (b, a) ∈ R
(a, b) ∈ R, (b, c) ∈ R ⇒ a – b ∈ Z, b – C ∈ Z
∴ a – b + b – c ∈ Z ⇒ (a, c) ∈ Z

Question 27.
Prove that (cos x + cos y)² + (sin x – sin y)= 4cos² \(\left(\frac{x+y}{2}\right)\)
Answer:
LHS = cos²x + cos² y + 2 cos x cos y + sin²x + sin²y – 2sin x sin y
= 1 + 1 + 2 (cos x cos y – sin x sin y) = 2 [1 + cos (x + y)] = 4cos² \(\left(\frac{x+y}{2}\right)\)

Question 28.
Solve: √2x² + x + √2 = 0.
Answer:
√2x² + x + √2 = 0; Here a = √2, b = 1,c = √2
∴ D = 5² – 4ac = (1)² – 4(√2)(√2) = 1 – 8 = -7

Question 29.
How many letters words with or with out meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if.
(i) 4 letters are used at a time,
(ü) all letters are used at a time
(iii) all letters are used but first letter is a vowel?
Answer:
There are 6 letters in the word MONDAY. So, the total number of words is equal to the number of arrangements of these letters taken four at a time.
The number of such arrangements = ⁶P₄ = \(\frac{6 !}{(6-4) !}=\frac{6 !}{2 !}=\frac{6.5 .4 .3 .2 .1}{2.1}\) = 360
Hence, total number of words = 360
(ii) Total number of arrangements in this case = ⁶P₆ = 6! = 720
(ii) Total number of arrangements when all letters are used but the first letter is a vowel
= 2 × ⁵P₅ = 2 × 5! = 2 × 5 × 4 × 3 × 2 × 1 = 240.

Question 30.
If x + iy = \(\frac{2+i}{2-i}\) then prove that x² + y²
Answer:

Question 31.
Find the term independent of x in the expansion of \(\left(\frac{3}{2} x^{2}-\frac{1}{3 x}\right)^{6}\)
Answer:

The term will be independent of x if the index of x is zero, i.e., 12 – 3r= 0. Thus, r=4
Hence 5th term is independent of x and is given by (-1)^{4 6}C₄ \(\frac{(3)^{6-8}}{(2)^{6-4}}=\frac{5}{12}\)

Question 32.
8, A₁, A₂, A₃, 24
Answer:
T_n = a + (n − 1)d
24 = 8 + (5 – 1)d
16 = 4d ⇒ d = 4
3 Am’s are 12, 16, 20.

Question 33.
(i) At least one man.
Answer:
1 man and I woman
or 2
men and 0 women
= ²C₁ × ²C₁ + ²C₂ × ²C₀ = 2 × 2 + 1 × 1 = 4 + 1 = 5.

(ii) At most one man
Answer:
1 men and 1 women
or
0 men and 2 women
= ²C₁ × ²C₁ + ²C₀ × ²C₂ = 2 × 2 + 1 × 1 = 4 + 1 = 5.

Question 34.
Find the derivative of the function ‘cos x’ w.r.t ‘x’ from first principle
Answer:
Let f ‘(x) = \(\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}\)

Question 35.
A parabola with vertex at origin has its focus at the centre of x² + y² – 10x + 9 = 0 Find the direction its directrix and latus rectum.
Answer:
The centre of the circle = (5,0).
The equation y² = 20x ⇒ y² = 4ax ⇒ a = 5
directrix is x = -5, LR = 20.

Question 36.
If an A.P. if m^th term is n and the n^th term is m, where m ≠ n, find the p^th term
Answer:
We have
a_m = a + (m – 1) d = n, …… (1)
and a_n = a + (n – 1) d = m …….. (2)
Solving (1) and (2), we get
(m, n) d = n – m, or d = -1,
and a = n + m – 1 ……. (3)
Therefore a_p = a + (p – 1)d ……. (4)
= n + m – 1 + (p – 1) (-1)= n + m – p
Hence, the p^th term is n + m – p.

Question 37.
Verify by the method of contradiction that √2 is irrational
Answer:
If possible Let √2 is rational
∴ √2 = \(\frac{p}{q}\), p, q ∈ z, q ≠ 0
We assume that p and q donot have any common factor
p = √2q ⇒ p = 2q²
p² is a multiple of 2 ⇒ ∴ p is a multiple of 2
∴ p = 2k, k ∈ z ⇒ p² = 4k
2q² = 4k² ⇒ q² = 2k²
q² = 2k²
q² is a multiple of 2 ⇒ ∴ q is a multiple of z
∴ p and q are both multiple of 2 and hence has a common factor z which is a contradiction
∴ our assumption is wron
∴ √2 is irrational

Question 38.
Two students Anil and Sunil a appear in the examination The prpbability that Anil will qualify in the examination is 0.05 and that Sunil will qualify is 0.10. The probability that both will qualify in the examination is 0.02. Find the probability that Anil and Sunil will not qualify in the examination.
Answer:
Let A, B denote the events that Anil, Sunil qualify in the exam
P (A) = 0.05, P(B) = 0.1, P (A ∩ B) = 0.02
P(A ∪ B) = P(A) + P(B) – P(A ∩ B) = 0.05 + 0.1 – 0.02 = 0.13
P(A’ ∩ B’) = 1 – P (A ∪ B) = 1 – 0.13 = 0.87.

Part – D

Answer any Six questions : (6 × 5 = 30)

Question 39.
Define signum function. Draw the graph of the signum function. Also write its domain and range.
Answer:
Singum function :
The function f:R → R defined by


is called the signum function. The domain of the signum function is R and the range is the set {-1, 0, 1}.

Question 40.
Prove that \(\lim _{\theta \rightarrow 0} \frac{\sin \theta}{\theta}=1\) (q being in radians) and hence show that \(\lim _{\theta \rightarrow 0} \frac{\tan \theta}{\theta}=1\)
Answer:
Consider a circle with centre O and radius ‘r’ Mark two points A and B on the circle so that

Join AB. Draw BM ⊥ OA
From the figure it is clear that.
Area of ∆OAB < Area of sector OAB < sector of ∆OAC …. (1)
Area of ∆OAB = \(\frac { 1 }{ 2 }\) OA.BM
[In ∆OBM. Sin θ \(\frac{\mathrm{BM}}{r}\) ⇒ BM = r Sin θ ]

∴ Area of ∆OAB = \(\frac { 1 }{ 2 }\) r r. sin θ = \(\frac { 1 }{ 2 }\)r² sin θ
Area of sector OAB = \(\frac { 1 }{ 2 }\) r²θ
Area of ∆OAC = \(\frac { 1 }{ 2 }\) OA.AC
= \(\frac { 1 }{ 2 }\)r² tan θ [In ∆OAC, tan θ = \(\frac{A C}{O A}=\frac{A C}{r}\) ⇒ AC = r tan θ]
∴ (1) becomes

Question 41.
1² + 2² + 3² + ………… + n² = \(\frac{n(n+1)(2 n+1)}{6}\)
Answer:
Let P(n) : 1² + 2² + 3² + ………… + n² = \(\frac{n(n+1)(2 n+1)}{6}\)

step 1 : Prove that P(1) is true
when n= 1; L.H.S = 1² = 1
R.H.S = \(\frac{1(1+1)(2+1)}{6}\)
∴ L.H.S = R.H.S ⇒ ∴ P(1) is true

step 2: Assume that P(m) is true
i.e., 1² + 2² + 3² + ………… + m² = \(\frac{m(m+1)(2 m+1)}{6}\) …… (i)

step 3: Prove that P(m + 1) is true
i.e., 1² + 2² + 3² + ………… + m² + (m+1)² = \(\frac{(m+1)(m+2)(2 m+3)}{6}\)
L.H.S = [1² + 2² + 3² + ………… + m²] + (m+1)²

= R.H.S ⇒ ∴ P(m+1) is true
Conclusion: P(1) is true ⇒ P(m) is true ⇒ P(m+1) is true
∴ By principle of mathematical induction, the result is true for all natural numbers ‘n’.

Question 42.
A group consists of 7 boys and 5 girls. Find the number of ways in which a team of 5 members can be selected so as to have atleast one boy and one girl.
Answer:
Number of ways of selecting
1 B and 4 G = ⁷C₁ × ⁵C₄ = 35
2 B and 3G = ⁷C₂ × ⁵C₃ = 210
3 B and 2 G = ⁷C₃ × ⁵C₂ = 350
4. B and 1 G = ⁷C₄ ×⁵C₁ = 175
Total number of selections = 770.

Question 43.
State and prove binomial theorem for positive integers.
Answer:
Statement: “If’n’ is a +ve integer then
(x + a)ⁿ = ⁿC₀ xⁿ a⁰ + ⁿC₁ x^n-1 a¹ + ⁿC₂ x^n-2 a² + ………….. + ⁿC_n x⁰ aⁿ.

Proof : (By Mathematical induction):
Let p(n) : (x + a)ⁿ = ⁿC₀ xⁿ a⁰ + ⁿC₁ x^n-1 a¹ + ⁿC₂ x^n-2a² + ………….. + ⁿC_n x⁰ aⁿ.

Step1 : Prove that P(1) is true
when n = 1, L.H.S = (x + a)¹ = x + a; RHS = ¹c₀ x¹ a⁰ + ¹c₁ x⁰ a¹ = 1.x.1 + 1.1.a = x+a
L.H.S. = R.H.S. ⇒ ∴ P(1) is true

Step 2: Assume that P(m) is true
i.e., (x + a)^m = ^mc₀ x^m a⁰ + ^mc₁ x^m-1 a¹ + ^mc₂  x^m-2 a² + ………….+ ^mc^mx⁰a^m …….(i)

Step 3 : Prove that P(m + 1)^m+1 is true
i.e. (x + a)^m+1 = ^m+1c₀ x^m+1 a⁰ + ^m+1c₁ x^m a¹ + ^m+1c₂ x^m-1 a² + …….. + ^m+1c_m+1 x⁰ a^m+1
Multiply both sides of equation (i) by (x+a)
∴ (x + a)^m (x + a) = (x + a) [^mc₀ x^m a⁰ + ^mc₁ x^m-1 a¹ + ^mc₂ x^m-2 a² + ………….+ ^mc^mx⁰a^m]
(x + a)^m+1 = x [^mc₀ x^m a⁰ + ^mc₁ x^m-1 a¹ + ^mc₂ x^m-2 a² + ………….+ ^mc^mx⁰a^m] + a [^mc₀ x^m a⁰ + ^mc₁ x^m-1 a¹ + ^mc² x^m-2 a² + ………….+ ^mc^mx⁰a^m]
(x + a)^{m + 1} = ^mc₀x^m+1 a⁰ + ^mc₁x^ma¹ + ^mc₂ x^m-1 a² + ……. + ^mc_m x⁰ a^m+1
= ^mc₀x^m+1a⁰ + (^mc₁ + ^mc₀)x^m a¹ + (^mc₂ + ^mc₁) x^m-1 a² + ………… + (^mc_m + ^mc_m-1) x¹ a^m + ^mc^m x⁰ a^m+1

(x + a)^m+1 = ^m+1c₀ x^m+1 a⁰ + ^m+1c₁ x^m a¹ + ^m+1c₂ x^m-1 a² + …….. + ^m+1c_m+1 x⁰ a^m+1
[∴ ^mc_m = ^m+1c₀
^mc₁ + ^mc₀ = ^m+1c₁
^mc₂ + ^mc₁ = ^m+1c₂
^m+1c_m]
⇒ ∴ P(m + 1) is true
Conclusion: P(1) is true, P(m) is true ⇒ P(m+1) is true
∴ By principle of mathematical induction the result is true for all natural numbers n.

Notes: 1. The number of terms in the expansion of (x + a)ⁿ is n + 1.
2. The Gen term of binomial expansion is T_r+1 = ⁿc_r x^n-r a^r.

Question 44.
Derive an expression for the coordinates of a point that divides the line joining the points A(x₁, y₁, z₁,) and B (x₂, y₂, z₂.) internally in the ratio m : n. Hence, find the coordinates of the midpoint of AB where A = (1, 2, 3) and B = (5, 6, 7).
Answer:

Let the two given points be P (x₁, y₁, z₁,) and Q (x₂, y₂, z₂). Let the point R (x, y, z) divide PQ in the given ratio m : n internally, Draw PL,
QM and RN perpendicular to the XY-plane. Obviously PL ∥ RN ∥ QM and feet of these perpendiculars lie in a XY-plane. The points L, Mand N will lie on a line which is the intersection of the plane containing PL, RN and QM with the XY-Plane. Through the point R draw a line ST parallel to the line LM. Line ST will intersect the line LP externally at the point S and the line MQ at T, as shown in Fig 12.5.

Also note that quadrilaterals LNRS and NMTR are parallelograms.
The triangles PSR and QTR are similar. Therefore,


Similarly, by drawing perpendiculars to the XZ and YZ-planes, we get

Hence, the coordinates of the point R which divides the line segment joining two points P(x₁, y₁, z₁) and Q(x₂, y₂, z₂,) internally in the ratio m: n are

Question 45.
Derive a formula for the angle between two lines with slopes m¹ and m². Hence find the slopes of the lines which make an angle \(\frac{\pi}{4}\) with the line x – 2y + 5 = 0.
Answer:
m₁ = tan θ₁, m₂ = tan θ₂

Question 46.
Prove that \(\frac{\cos 4 x+\cos 2 x+\cos 3 x}{\sin 4 x+\sin 2 x+\sin 3 x}=\cot 3 x\)
Answer:

Question 47.
Solve graphically 2x + y ≥ 4, x + y ≤ 3, 2x – 3y ≤ 6
Answer:
2x + y ≥ 4, x + y ≤ 3, 2x – 3y ≤ 6 …..(1)
Points A(2, 0) and B(0,4) lie on 2x + y = 4
Plot the points and join them to get line AB
(0,0) does not satisfy 2x + y ≥ 4
⇒ Half plane given by 2x + y ≥ 4 is away from origin …..(2)
Points C(3, 0) and D(0, 3) lie on x + y= 3
Plot the points and join them to get line CD.
(0,0) satisfies x + y ≤ 3 ….. (3)
⇒ Half plane given by x + y ≤ 3 is towards origin
Points C(3, 0) and E(0, -2) lie on 2x – 3y = 6

Plot the points and join them to get line CE.
(0,0) satisfies 2x – 3y ≤ 6
⇒ Half plane given by 2x – 3y ≤ 6 is towards origin
From (2), (3), (4) common region shown shaded in figure represents solution of (1).

Question 48.
Find the mean deviation about the mean for the following data.

Answer:

Part – E

Answer any ONE questions : (1 × 10 = 10)

Question 49.
(a) To cos (A + B) = cos x. cos y – sin x sin y and hence find cos 75°.
Answer:

(i) becomes
∴ cos (A + B)= cos A.cos B – sin B
cos 75° = cos (45 +30)
= cos 45 cos 30 – sin 45 sin 30

(b) Find the sum to n terms of the series 1² + (1² + 2²) + (1² + 2² + 3²) + ……..
Answer:
nth term T_n = 1² + (1² + 2²) + (1² + 2² + 3²) + ……. + n² = \(\frac{n(n+1)(2 n+1)}{6}=\frac{2 n^{3}+3 n^{2}+n}{6}\)
∴ T_n = \(\frac{2 n^{3}+3 n^{2}+n}{6}\)
Sum to n terms, S_n = ΣT_n
= \(\frac{1}{6}\) [2Σn³ +3Σn² + Σn]

∴ S_n = \(\frac{n(n+1)^{2}(n+2)}{12}\)

Question 50.
(a) An elipse is the set of all ninte in a plane tha e of whose distance from two fived points in the need of all points in a plane the sun of whose distance points in the plane is a constant.
Answer:

Let F₁ and F₂ be the foci and O be the mid point of the line segment F₁F₂ Let O be the origin and the line from 0 through F₂ be the positive x-axis and that through F₁ as the negative x-axis. Let, the line through O perpendicular to the x-axis be the y-axis. Let the coordinates of F₁ be (-c, 0) and F₂ be (c, 0).

Let P(x, y) be any point on the ellipse such that the sum of the distances from P to the two foci be 2a
i.e., PF₁ + PF₂ = 2a. …(1)
Using the distance formula, we have
\(\sqrt{(x+c)^{2}+y^{2}}+\sqrt{(x-c)^{2}+y^{2}}=2 a\)
i.e., \(\sqrt{(x+c)^{2}+y^{2}}=2 a-\sqrt{(x-c)^{2}+y^{2}}\)
Squaring both sides, we get
(x + c)² + y² = 4a² – 4a \(\sqrt{(x-c)^{2}+y^{2}}\) + (x – c)² + y²
which on simplification gives
\(\sqrt{(x-c)^{2}+y^{2}}=a-\frac{c}{a} x\)
Squaring again and simplifying, we get

(b) \(y=\frac{x^{5}-\cos x}{\sin x}\)
Answer:

Students can Download 1st PUC Political Science Previous Year Question Paper 2017 (South), Karnataka 1st PUC Political Science Model Questions with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

Karnataka 1st PUC Political Science Previous Year Question Paper March 2017 (South)

Time: 3:15 Hours
Max. Marks: 100

I. Answer the following questions in ONE sentence each: (10 × 1 = 10)

Question 1.
Who is the father of Political Science?
Answer:
Aristotle is known as father of Political Science.

Question 2.
Give an example of ancient Greek City State
Answer:
Sparta/Athens is the example of Ancient Greek City Sate.

Question 3.
What is Sovereignty?
Answer:
A supreme power of the state is called sovereignty

Question 4.
Write the root word of constitution.
Answer:
The word Constitution is derived from the Latin word‘Constituere’

Question 5.
When ddi the Indian Constitution came into existence?
Answer:
The constitution of india came in to force on 26^th January 1950.

Question 6.
Who presides over the Rajyasabha?
Answer:
Vice – President Presides over the Rajyasabha.

Question 7.
What is a term of office of the President of Supreme Court of India?
Answer:
The term of office of the president of India is 5 years.

Question 8.
Who appoints the Chief Justice of India?
Answer:
The President of India appoints the chief justice of India.

Question 9.
Expand P.I.L.
Answer:
Public Interest Litigation.

Question 10.
How many family courts are there in India?
Answer:
There are 190 family courts in India.

II. Answer any Ten of the following questions in 2-3 sentences each. (10 × 2 = 20)

Question 11.
How is man a Social Animal
Answer:
Man is a social animal because he can fulfill his basic needs, desires requirements in society only. He cannot live away from the Society.

Question 12.
Who are called the Greek Philosopher ‘Trio’?
Answer:
Socrates, Plato, and Aristotle are the Greek Philosopher Trio.

Question 13.
What are the four elements of the State?
Answer:

1. Population
2. Definite Territory
3. Government
4. Sovereignty

Question 14.
Name any two political rights.
Answer:

1. Right to vote.
2. Right to contest for election.

Question 15.
What is the meaning of Liberty
Answer:
A power of man to do anything for the development of his individual personality is called liberty

Question 16.
What is written constitution? Give an example
Answer:
A written document deliberately framed by the constitutional experts is called written constitution
Ex:
India.

Question 17.
What do you mean by federal government?
Answer:
A government whee the powers have been distributed between union and state government is called federal government.

Question 18.
What do you mean by universal adult franchaise?
Answer:
All the citizens who attained the particular age are having right to vote irrespective of caste, creed, religion is called universal adult franchaise.

Question 19.
Name the two Houses of the American congress.
Answer:

1. House of Representative
2. Senate

Question 20.
Which are the qualifications necesary for Governor?
Answer:

1. He must be a citizen of india.
2. Must attained the age of 35 years
3. Must not be a member of either state or union legislature,

Question 21.
What is Revenue Court?
Answer:
The courts which deals with the cases relating to the maintenance of land records its assessment and collection of land revenue are called revenue courts.

Question 22.
Name subordinate courts.
Answer:

1. District courts
2. Revenue courts
3. Family courts
4. Consumer courts
5. Lokadalats

III. Answer any EIGHT of the following question in 15-20 sentences each : (8 × 5= 40)

Question 23.
Explain the scope of Political science.
Answer:
Aristotle described political science as a ‘master science’ which made it perhaps the greatest contribution to the making of political science scientific. Hie term “Scope” refers to the subject or the boundaries of a particular branch of knowledge. There is no perfect agreement among the political thinkers as to the problems, which come under the study of political science.

Broadly speaking, there are three groups of writers holding different views on the scope of political science.The first group of writers like Garies, Gamer, Goodnow, and Bluntschli restricted the scope of political science only to the study of the state.

The second group of writers like Prof. Sheley and Dr. Stephen Leacock said that political science deals with government only.

The third group of writers like Gettell, Gilchrist, Paul Janet, and Prof. Laski maintained that the scope of political science extends to both state and government. Prof. Laski maintains that the state, in reality, means the government.

We may agree with the third group of writers that political science is a study of both state and government is the steering wheel of the ship of the state. There can be no state without a government, the state remains the central subject of our study, and the whole mechanism of government revolves around it.

Scope according to the UNESCO; the international Political Science Association at its Paris Conference in 1948 discussed the scope of political science and marked out its subject matter as follows:

1. Political Theory:
Political Theory, History of Political Ideas.

2. Government:
The Constitution, the Government-Regional and Local Government, Public Administration, Economics and Social functions of government, Comparative political institutions.

3. Parties, Groups and Public Opinion:
Political Parties, Group and Associations, Citizen Participation in Government and administration, Public Opinion.

4. International Relations:
International relations, International organization, and Administration, International Law.

Question 24.
Distinguish between State and Association.
Answer:

State	Voluntary Association
1. Definite territory is essential element of state	1. Associations have no definite territory.
2. Membership is compulsory man cannot Give up the membership.	2. Membership is temporary; man can give up the membership.
3. Individual can get the membership of only a state.	3. Individuals can get the membership of various associations as he pleases.
4. State is permanent and continuous.	4. Associations are temporary. State can control and abolish them at any time.
5. State has sovereignty.	5. Associations have no sovereignty.
6. State’s functions are wider.	6. Functions of associations are narrower.

Question 25.
Discuss the kinds of Equality.
Answer:
1. Natural Equality:
It implies that nature has created all men equal. It can also be defined that it insists on removing all man-made and artificial inequalities and treat all equally.

2. Civil and legal Equality:
Implies that all are equal before law and all are protected equally irrespective of caste, class, colour, race, etc.,

3. Political Equality:
Implies that all the citizens, irrespective any type of difference are entitled to participate in the affairs of state. All have equal voice in the government. It is based on principle of universal adult Franchise.

4. Economic Equality:
Implies removal of inequalities based on wealth and insists on certain minimum standard of income to all to meet their basic needs.5. Social Equality:Implies every individual without any discrimination must be given equal opportunity for the development of their personalities.

Question 26.
Explain the features of Sovereignty.
Answer:
Jean Bodin – who was the first to explain the concept of sovereignty said: “Sovereignty is the supreme power over citizens and subjects unrestrained by law.”

According to Hugo Grotius: “Sovereignty is the supreme power vested in him whose acts are not subjected to any other who will can’t be can override.”

Characteristics of Sovereignty:
a. Permanent:
Sovereignty is permanent. Every state is sovereign it is accordingly permanent. The death of the rules or the change in government doesn’t mean any change in sovereign power. It comes to an end when the state is destroyed or is conquered and ruled by some external power.

b. Universality:
Sovereignty embraces each and every person and every association within the territory of the state. No individual or association in the state can disobey the sovereign authority of the state.

c. Sovereignty can’t be transferred:
The state has no right to give away its sovereignty. When a state loses or has to give up a part of the territory and population to another state, that part comes under the control of that state.

d. Indivisible:
Sovereignty can’t be divided. Division of sovereignty leads to the destruction of sovereignty.

e. Absoluteness:
Sovereignty is absolute. There can be no legal power within the state, superior to it. All individuals, associations come under the absolute power of the state. The state is completely independent.

Question 27.
Explain the features of unitary government.
Answer:
Features of Unitary Government:
1. Concentration of Power:
A Unitary government is characterized by the presence of a single centre, which is omnipotent and omnipresent all over the territory. All decisions of the state flow from one single centre.

2. No Provincial Autonomy:
The provinces or local units in a unitary system are created by the centre for the sake of administrative convenience. It carries out the orders of the centre without having any powers to make decisions. Thus, the local units only act as subordinate agents of the centre without any authority or autonomy.

3. Single legislature:
In a Unitary system of government there will be only one single supreme legislative assembly which makes laws for the whole country and are faithfully implemented by the local units.

4. Constitution may be written or unwritten:
The constitution, in a unitary government, may be written or unwritten as there is one single central authority wielding power all over the state without any other centres of power.

Question 28.
Write the essentials of an ideal Constitution.
Answer:
The essentials of an ideal constitution are explained as below
1. It should be definite :
An ideal constitution should not be vague but clearly narrate the provisions which relates to the organization of the government. The principles should be precise and clarity.

2. It should be comprehensive:
An ideal constitution must be comprehensive enough to mention the functions of the government and rights, duties of the citizens. The constitution should not be too big but include all the information on the government.

3. Method of amendment:
An ideal constitution should possess the method of amendment. As the social condition of the people is going on change, the constitution must also undergoes change. It should represent the future needs of the future generation.

4. It should correspond to reality:
An ideal constitution should correspond to the real, conditions obtained within the state, otherwise, it cannot work properly.

Question 29.
Write the text of the preamble of the India Constitution.
Answer:
The preamble of the constitution of India explains the aims and ideology and reads as: WE THE PEOPLE OF INDIA having solemnly resolved to constitute India into a SOVEREIGN, DEMOCRATIC, SOCIALIST, SECULAR and REPUBLIC Nation and securing to all its citizens.

• JUSTICE – social, economic and political.
• LIBERTY – of thought, expression, belief, faith, and worship.
• EQUALITY – of status and of opportunity and to promote among them all.
• FRATERNITY – assuring the dignity of the individual and the unity and the integrity of the Nation.

The idea of the preamble has been borrowed from constitution of U.S.A.

Question 30.
Write a short note on RTE
Answer:
RTE stands right to education which means all the children in India are entitled to get compulsory and free education. The 86th amendment act of 2002 provides an opportunity to get free and compulsory education to all the children from the age 6 to 14 years.

Parliament passed the compulsory education act on 2009 and in compliance of the central government, the Karnataka government framed rules and enforced from 28th April 2012. Main provisions of RTE

• All the children from the age of 6 to 14 should get free and compulsory education.
• The responsibility of the parents are to send their children to the school.
• The provisions are made to ensure the education facilities especially to the weaker section and child belonging to a disadvantaged group.
• The central and state government have jointly responsible to carry over this scheme.
• To provide the education to all the children, the government should establish the schools accesses to the children.
• The government should bear the expenses of education and should pay the same to education institutions.
• The concerned BEO and DDPI should have responsibility to look after this.

Question 31.
Write about composition of Vidhan Parishad of Karnataka State.
Answer:
The Composition of the legislative council is as follows:

• 1/3 – of the members are elected from the local bodies such as municipalities and district boards;
• 1/3 – of the members are elected from members of the Legislative Assembly;
• 1/12 – of the members are elected by the graduates from graduate constituencies.
• 1/12 – of the members are elected from teacher’s constituencies consisting of secondary- school, college and university- teachers; and
• 1/6- of the members are nominated by the Governor from the fields of science, art, social service, the co-operative movement, literature, etc.

Question 32.
Explain the emergency powers of the President.
Answer:
1. The President may declare internal emergency under Article 352, if, in his opinion, there is a threat to India’s security due to war or external aggression.

2. The President may impose ‘President’s Rule’ under Article 356 if he is convinced that in that particular state the law and order have completely deteriorated and it cannot be governed as per the constitution. Though the President’s rule is imposed on the recommendation of the governor of the concerned state, it is not compulsory.

3. If the President is convinced that the financial stability and prestige of the nation are at risk, he may impose a financial emergency under Article 360. However, the imposition of internal and financial emergency should be placed before Parliament and its consent was taken within 2 months of the declaration of emergency, otherwise, it is considered invalid.

Question 33.
Mention the measures necessary to ensure the Independent of the Judiciary.
Answer:

• Selection of judges regardless of their political affiliation.
• Appointment of judges by the Chief Executive.
• Long and Security of tenure.Salaries and allowances are paid from Consolidated Fund.
• Bar on practice after retirement.
• Separation of judiciary from the executive and legislature.
• Impartiality in the administration of justice.
• Avoiding ambiguity in the judgement.
• Appointment of highly qualified judges and making judicial process less expensive.

Question 34.
Explain the functions of Grama Panchayath
Answer:
Functions of gram panchayat.

• Formulate plans for the development of Gram panchayat.
• Preparation of Budget of Gram panchayat.
• Collection and maintenance of necessary information and statistics relating to the panchayat.
• Provide relief during natural calamities like floods, famine or earthquakes.
• Encouragement to agriculture.
• Encouragement and development of poultry and pisciculture.
• Support to khadi and cottage industries.
• Protection of public health and support family welfare programmes.
• Encouraging rural housing by providing houses and sites to weaker sections.
• Promote cleanliness through underground drainage system.
• Provide drinking water and prevent water pollution.
• Construction and maintenance of roads, buildings, and bridges.
• Rural electrification.Encourage primary and higher education.
• Support and implement poverty alleviation programmes.
• Support adult education and informal education.
• Construction and maintenance of libraries and reading rooms.
• Regulation of market and fairs.Strive for the welfare of women and children.
• Strive for the welfare of weaker sections.
• Preservation of Public distribution systemMaintenance of public gardens and stadiums.
• Maintenance of graveyards.
• Strive and support welfare of physically challenged (handicapped) and mentally retarded.
• Function as per directed by Panchayat Raj Act from time to time.

IV. Answer any Two of the following in 30 to 40 sentences each: (2 × 10 = 20)

Question 35.
Describe the features of democratic government.
Answer:
1. The government in a democracy is responsible to the people. The government will also have to function according to public opinion. Self-government makes the people more disciplined and there will be more responsible citizens than in any other form of government.

2. Democracy upholds the principles of liberty and equality. Political and economic equality are assured in a democracy.

3. Democracy respects the dignity of human being. It provides rights and liberties for the development of the personality of individual.

4. A democratic government promote the welfare of the people, where as in other forms of government only particular class may be benefitted.

5. Democratic government is stable and efficient government. It avoids the revolution because it tarried on according to the wishes of the people.

6. Unlike other forms of government, democracy is self-corrective. In democracy the freedom of speech and freedom of press creates an enlightened public opinion

7. Democracy is progressive and educative force. In a democracy, people have full civil and political rights. It is a training ground for active, healthy and intelligent citizenship.

8. In democracy, there is order, peace and progress. It is flexible government which adopts itself to change peacefully.

9. As the people have a share in the government of country, the spirit of patriotism is strengthened and everybody is willing to work and undergo sacrifices for the welfare of the community.

10. Democracy protects the minority. A written constitution guarantees the rights of the minorities.

Question 36.
Discuss the composition powers and functions of the Loksabha.
Answer:
The members of Lok Sabha are elected by the people. All adult citizens unless disqualified for other reasons have the right to select their representatives. Qualifications to become the members are must be a citizen of the country and must have attained the minimum age fixed by the constitution. The term of office is five years. Speaker is the presiding officer. He is elected from among the members of the house.

The powers and functions of LokSabha are as follows
1. Legislative functions:
The power of Loksabha extends to all subjects falling under the Union List and the Concurrent List. In case of emergency in operation, its power also extends to the State list as well. No bill can become a law without the consent of Loksabha. The Loksabha has equal powers of law-making with Rajyasabha except on financial matters where the supremacy of Loksabha is total.

In case of disagreement between the two houses on a matter of legislation, it is resolved by a Joint Sitting of both the houses presided over by the Speaker. In a Joint Sitting, Loksabha would emerge triumphant because the decisions are taken by a majority of the total number of members of both the house present and voting in which the numerical superiority of Loksabha prevails.

2. Financial functions:
On financial matters, the supremacy of the Loksabha is total and complete. “One, who holds purse, holds power” said James Madison. By establishing its authority over the national purse, Loksabha establishes its authority over the Rajyasabha.

It is expressly stated that the Money bill can originate only in the house of people. Regarding budget, Loksabha being a representative house enjoys total authority. Loksabha’s position on financial matters is such that the demands for grants are placed only before the Loksabha.

3. Control over the executive:
The Loksabha enjoys direct control over the executive because; the executive is directly responsible to the lower house and stays in office as long as it enjoys the confidence of the house. The Loksabha not only makes laws but also supervises the implementation. The lower house being a debating house, the members are free to seek information from the executive and raise questions and seek clarifications.

The members can effectively seek information from the government by way of discussions and debates during the Question Hour (seek clarification), the Adjournment Motion (raises issues of national importance), the Zero Hour, the Cu motion, the Call-attention motion, etc. The soundest way of controlling the executive is by way of moving the No-confidence motion, if the executive fails to win the support of Lok sabha, they must step down.

4. Constituent functions:
The Loksabha shares equal powers in regard to amending provisions of the constitution. An amendment may be initiated either in the Rajyasabha or Loksabha and must be passed by a 2/3 majority in both the houses present and voting. The agreement of Rajyasabha is compulsory for the success of the constitutional amendment.

5. Electoral functions:
The Loksabha and Rajyasabha elect the highest constitutional functionaries such as the President and the Vice-president. The President is elected by the members of Loksabha and Rajyasabha along with the members of Legislative Assemblies of the states. The Vice-president is elected by members of Loksabha and Rajyasabha.

6. Judicial functions:
The Loksabha acts as a judge in the impeachment of the President. Either house can prefer the charge of impeachment. If. Rajyasabha prefers the charge, Loksabha investigates the charge and if it passes a resolution by a 2/3 majority of the total membership of the house. President stands impeached from the office.

The Loksabha also sits in Judgement along with the Rajyasabha, in removing high constitutional functionaries such as the Comptroller and Auditor General, The Chief Vigilance Commissioner, the Chief Election Commissioner, etc.

Question 37.
Explain the powers and functions of Chief Minister.
Answer:
The power and position of the Chief Minister is so powerful that he is referred to as “the first among equals’” (Primus intersperes). Article 164 of the constitution states that “there shall be a Council of ministers headed by the Chief Minister for the state”.

The Chief Minister is elected from among the members of the majority party in Vidhana Sabha. In case no party enjoys majority it is left to the discretion of the Governor to pick the Chief Minister, who in his opinion will prove majority’ in a stipulated time. Traditionally, the Chief Minister should be from the Vidhana Sabha.

1.Formation of Ministry:
The primary task of the Chief Minister on assuming office is the formation of the Council of ministers. Normally ministers are picked from the same political formation to ensure uniformity and continuity of policy. However, nothing prevents the Chief Minister from picking anyone as minister from any party. The Chief Minister enjoys the authority to pick and choose his ministry because he is responsible for the efficiency and performance of the government.

2. Allocation of Portfolios:
After forming the ministry the next important task is the allocation of responsibilities to ministers. Certain key or heavy’ weight portfolios such as Home, Revenue, Finance, Industry, Public works are to be given to key and heavyweights who enjoy clout and following among party workers. Also to ensure efficiency and stability of the government. The Chief Minister enjoys the power of expanding and reforming the ministry.

3. Chairman of the Cabinet:
The cabinet meetings are held under the chairmanship of the Chief Minister. The cabinet is a deliberating forum and differences may come up. It is the responsibility of the Chief Minister to mediate and soften things and arrive at decisions.

The Chief Minister has the authority to decide the matters to be taken up by the cabinet and may accept or reject proposals. Normally the proposals brought by ministers for discussion are not rejected. In the era of coalition politics, it is a challenge for the Chief Minister to hold the flock together. It is very difficult to chair a cabinet meeting full of divergent views, ideologies and principles.

4. Leader of Vidhana Sabha:
Chief Minister is the leader of Vidhana Sabha. All major decisions and announcements of the state government are made by the Chief Minister. It is the responsibility of the Chief Minister to ensure that all bills brought before Vidhana Sabha for approval are passed. And he has to defend the government on the floor of the house.

Though ministers are individually responsible to their ministries, it is the Chief minister who provides general leadership and direction. If any minister makes a mistake, the Chief Minister has the power to guide and correct him.

5. Leader of the Government:
The decisions of the government however good, are subjected to scrutiny and criticism. The opposition parties lose their identity if they do not criticize the government. So to guard against it, the Chief Minister, as leader of the government has to defend policies and programmes of the government both in and out of legislature.

6. Co-ordination and Supervision:
In running the administrative machinery Chief Minister will have to encounter numerous problems ranging from routine to serious. Under the circumstances it is essential to integrate different departments and see that they work smoothly and the ability of the Chief Minister is tested on this count. A Chief Minister should not only pick a team but also retain it as a team till the end of the term.

Whenever problems arise between departments, he has to mediate and sort it out amicably through dialogue and goodwill.The Chief Minister is the general head of the government. Hence he has the responsibility of supervising the administration. Though each minister is in charge of a ministry, lack of general supervision results in poor administrative quality.

To maintain quality in administration, the Chief Minister will have to supervise it, not only gives him a generalfeel of the administration but also makes the ministers more responsible. The Chief Minister may correct the working of a particular ministry and offer suggestions.

7. Bridge between the Governor and the State Legislature:
The Chief Minister acts as a link between the Governor and state legislature in a parliamentary government. As all executive powers are vested in the hands of the Governor, the Chief Minister is duty bound to keep the Governor informed about the decisions taken by the government.

Also, the Governor himself can call for any information from the government. The Chief Minister not only acts as a bridge but also as the advisor to the President. Whenever necessary’ the President will look forward for advice. For example, the Governor seeks the advice of the Chief Minister before dissolving Vidhana Sabha.

8. Power of Dissolution:
The Vidhana sabha exists as long as the Chief Minister wishes because even before the expiry of 5 years term, Chief Minister may seek the dissolution of Vidhana Sabha. The Vidhana Sabha may be dissolved if deep differences surface within the government or within the ruling party or the government loses a motion of no confidence.

9. Power of Appointment:
Though civil appointments are made by the Governor, it is based on the recommendation of the Chief Minister.

Question 38.
Describe the powers and functions of the Supreme court of India.
Answer:
The President of India appoints the judges of the Supreme court on the advice of the council of ministers in consultation with the Chief Justice of India. Article 124 which deals with the appointment of judges, makes it obligatory on the part of the President of India to consult the Chief Justice of India.

In appointing the Chief Justice of India, the President shall, besides the advice of the council of ministers, consult the judges of the Supreme Court and the High courts if he considers it necessary. But, neither the constitution nor the law provides for Chief Justice’s recommendation as to his successor. It is a practice sanctioned by convention.

Normally, the Chief Justice of India is appointed from among the senior-most judges of the Supreme Court. The following are the powers of the Supreme Court:
1. Original Jurisdiction:
Article 131 of the constitution deals with the original jurisdiction of the Supreme Court. The original jurisdiction of the Supreme Court is so exclusive that no court in India can take up cases falling under the original jurisdiction.

The original jurisdiction of the Supreme Court is purely federal in character. Matters relating to the problems and disputes arising between the union and the states or between the states are taken up by the Supreme Court. The disputes entertained under the original jurisdiction are:

• A dispute involving the Government of India Vs the state of Union of India.
• A dispute involving the Government of India plus one or more states Vs one or more states.
• A dispute involving one or more states on one side Vs one or more states on the other.

2. Appellate Jurisdiction:
The Supreme Court is the highest court in India. Under Appellate jurisdiction, the Supreme court only takes up such cases that come on appeal. It has no power to take up such cases, which is not asked to take up.The appellate jurisdiction can be studied under the following three heads:
a. Constitutional Cases:
The cases that come before the Supreme court are as follows:

• The cases involving a question of law relating to the interpretation of the constitution or certification by the High court.
• The Supreme Court can take up a case if the High court in its opinion feels that the case involves a substantial
• question of law, which should be decided by the Supreme court.

b. Civil Cases:
Originally Article 133 provided for an appeal against the high court order if it certified that the amount involved was less than Rs. 20,000 and the case is fit for appeal. But, the Law Commission found the logic unreasonable and as a result, the 30^th Amendment of 1972 did away with the ceiling of Rs. 20,000.

The Supreme Court can take up the civil appeal, if the High court certifies that the case involves a substantial question law of general importance. The certification by the High court is essential in these cases.

c. Criminal Cases:
Article 134 provide for an appeal to the Supreme court against the judgment of the High Court under the following conditions:

If the High Court has reversed a decision of release of an accused and has given him a death sentence.
In a case where the High court has exercised the authority of a lower court and given a death sentence to the accused.
In any criminal case if the High court certifies that the case is fit for appeal in the Supreme Court.

3. Special Leave Jurisdiction:
Article 136 confers a special power in the hands of the Supreme Court to grant special leave. In hearing appeals the Supreme Court may grant Special Leave petition against any judgment or order made by any court or tribunal, except military tribunal, in a case.

The decision is entirely left to the discretion of the Supreme Court. This power, however, is to be used only under exceptional circumstances like matters involving general public interest or in cases of grave injustice or cases in which no appeal is otherwise provided by law.

4. Advisory Jurisdiction:
Article 143 confers the power of advisory opinion. In order to break authoritative opinion, the President of India may seek the advisory opinion of the Supreme Court on the matter which is, in his opinion, important and necessary such as disputes arising out of treaty of agreement. However, the advice of the Supreme Court is purely advisory in nature and it is up to the executive to accept it or not. The Supreme Court may decline to give advisory opinion if it finds unnecessary.

5. Power of Judicial Review:
The supremacy of the Supreme Court as the guardian of the constitution is emphasized by the power of judicial review. The Supreme court has the power of declaring a law made by the legislature or an executive action as ultra vires (intra vires) or null and void or unconstitutional if it is not in tune with the provisions of the constitution or violative of the fundamental law of the land.

This acts as an effective, check on both the legislature and the executive as any decision made or action taken whimsically without regard to the constitution is declared invalid.

6. The Court of Records:
The proceedings and judgments of the Supreme Court are kept preserved to be made use of in future cases and judgments, whenever necessary by the lower courts. Those decisions are authoritative records on law whose validity cannot be questioned in any court. The courts of records also have the power to correct its own clerical errors.

7. The Contempt of court:
The Supreme Court enjoys the authority of imposing fines or imprisonment for violating the orders of the court (Article 129).

8. Self-correcting Court:
The Supreme Court has the power of correcting its own judgments. This is to ensure any loss or damage, physical, emotional or material that may be caused to any person seeking justice. To put it in legal terms, this is to ensure against ‘miscarriage of justice’.

9. Guardian of the Constitution:
The Supreme Court enjoys the privilege of protecting the constitution against violation of its provision either by the government or by the people, It is the responsibility of the Supreme Court to see that the laws of the constitution are respected and adhered to by all in India.

By acting as the watchtower of the constitution, it checks against the violation of laws. As guardian of the constitution, the Supreme Court also exercises the power of interpreting the contents of the constitution. Any matter relating to technical interpretation of details or definitions of terms in the constitution is the sole prerogative of the Supreme Court.

10. Enforcement of Fundamental Rights:
The Supreme Court is empowered by the constitution to act as the protector and guarantor of the fundamental rights. Under Article 32, the Supreme Court enjoys the power of issuing constitutional writs, also called as writ jurisdiction, for the enforcement of fundamental rights. The writs may be against the government or individuals. The writs are briefly explained as follows:

a. Habeas Corpus:
This literally means ‘to have a body’. It calls upon the authority, which arrests a person to produce in court, the person to set him free if he has done nothing wrong. It protects an individual against wrongful confinement.

b. Mandamus:
This literally means a command. It is a command issued by the court asking a person to perform his legal duty, which is of public nature.

c. Prohibition:
It is a writ issued by the Supreme court to an inferior court restraining it from exercising powers which are not invested in them.

d. Certiorari:
It is a writ by which a case is removed from a lower court, which does not enjoy jurisdiction to deal with it.

e. Quo warrato:
This writ is issued to prevent a person from illegally occupying a public office to which he is not entitled.

11. Defender of the Federation:
The constitution vests the power of settling the disputes and problems between the centre and the states. In order to prevent the conflict of power between the two, the Supreme Court interprets the laws, which help in maintaining the unity of the federation.

12. Miscellaneous functions:
The following are the miscellaneous functions of the Supreme court.

• The Supreme Court has the power of regulating the practice and procedure of the court.
• It appoints its own clerical establishment and exercises supervision over lower courts.
• The Supreme Court decides matters relating to the election of the President and Vice-president.
• The Supreme Court if satisfied, may withdraw a case on its own or on appeal pending before one or more High
• courts on a matter involving substantial question of law of general importance (Article 139).
• The Supreme Court, if necessary, can transfer any case pending before any Highcourt to any other High court.
• The Supreme Court may also transfer a criminal case from one high court to the other.

V. Answer any TWO of the following questions in 15-20 sentences each. (2 × 5 = 10)

Question 39.
Write a note on ‘Kannada Rajyotsava’ day celebration of your college.
Answer:
Kannada Rajyotsava is an exciting meaningful celebration for all the Kannadigas in Karnataka. A day before Rajyotsava the lecturers along with the students decorated the college ground. On the day of 1st November all lecturers, principal, parents, and students were present exactly at 9.A.M. The chief guest hoisted the Rajyotsava flag followed by Naada Geetha.

During the speech of chief guest highlights the ideals of Nadahabba and urges the students to have loyalty their mother tongue. Cultural programs attracted students. A senior lecturer of the college proposed vote of thanks, finally sweet were distributed and students were disbursed.

OR

Explain the meaning and importance of Democratic decentralization system.
Answer:
Distribution of constitutional powers from union level to village level is called democratic decentralisation The importance of local governments is so paramount that it is called the “Primary school of democracy”.

1. Welfare state:
Modern states are welfare states. If the overall development of the state is to take place; the development of local governments is very vital. Because national progress can’t be divorced from rural progress.

2. Cradle of Democracy:
A citizen, not aware of the working of democracy is a burden on the nation. In local governments, people are introduced to functioning of democracy step by step and over a period of time they learn the nuances of democracy. Democracy can survive only when majority of the masses living in rural areas participate. That’s why local governments are called “cradles of democracy”;

3. Power to the People:
The other name of local government is power of the people; the local governments take power to the doorsteps of the people and empower them not only identify problems but also to solve them.

4. Knowledge of Administration:
Local governments aim at imparting knowledge of administration to locals, though the local people are aware of the government, they are not aware of the working of administration. But when interacted with officials, due to proximity, they get working knowledge of administration.

5. Local Solutions:
The basic principle of local government is, local problems must be solved at the local level. The centre or state government can’t understand local problems due to paucity of time, interest and information. But locals can, based on experience, identify suitable solutions to problems.

Question 40.
Write a note on any one Indiain political leader.
Answer:
Dr. B.R. Ambedkar :
Dr. B.R. Ambedkar is acknowledged as the leader of the untouchables and underprivileged in the Indian social strata. For his work in piloting the constitution of Independent India he is also hailed as the modem ‘Manu” Qr. Ambedkar was the 14^th child of Ramojisakpal and Bhima bai of the Mahoba community in Maharastra. He was bom on 14^th April 1891.

He had his school education in Satara. He completed his graduation in Bombay with the support of Maharaja of Baroda. He did his MA and Ph.D degree from the Columbia University in 1951 and 1961 respectively. Later he got his law and D.Sc degrees also In 1924 he started an association for the welfare of the depressed classes. He started the News paper called “Mooka Nayaka” to motivate the people to fight for independence and also for the reform of depressed classes.

He was the chairman of Drafting Committee for framing an constitution In the interim government he was the law minister in Nehru cabinet. He dedicated his whole life for the welfare of downtrodden people. He passed away on 16^th December 1956.

OR

Explain the standing committees and financial sources of Mahanagar Palika.
Answer:
Corporations are constituted as per Karnataka Muncipal Corporation Act-1976. Wards are created on the basis of city population. A population exceeds more than 3 Laks can be called as Corporation. The members are called as corporators and elected by the city residents for a period of 5 years. Some seats are reserved for SC/ST, OBC, and Women. State government nominates 5 members to the corporation from different field.

The MP’s and MLA’s in that jurisdiction are also the members of corporation and can attend the meetings with voting right. The Mayor elected by the Corporators presides over the meetings. The state government appoints administrative head as a commissioner from the IAS cadre. The meetings are held once in two months.

The Standing committees of Pura Sabha are:

• Taxation, Finance and Appeal committee.
• Basic health, Education and Social justice committee.
• Tour planning and Improvement committee.
• Accounts and Audit committee.

Financial Sources:

• Taxes on assets, water, professions, and advertisements.
• Rents from markets, complexes, and other properties.
• Grants and contributions from the State government.
• Income collected for providing drainage and sanitary facilities.
• Loans raised from the public with government approval.

Students can Download 1st PUC Accountancy Model Question Paper 4 with Answers, Karnataka 1st PUC Accountancy Model Questions with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

Karnataka 1st PUC Accountancy Model Question Paper 4 with Answers

Time: 3.15 minutes
Max. Marks: 100

SECTION – A

I. Answer any eight questions. Each question carries one mark. (8 × 1 = 8)

Question 1.
Accounting begins with the identification of transactions and ends with the preparation of Statements.
Answer:
Financial

Question 2.
A concept that a business enterprise will not be sold or liquidated in the near future is known as:
(a) Going Concern.
(b) Economic Entity.
(c) Monetary Unit.
(d) None of the above.
Answer:
(a) Going Concern.

Question 3.
The process of recording transactions in Journal is called
Answer:
Journalising.

Question 4.
Ledger records transactions in
(a) Chronological order.
(b) Analytical order.
(c)Both a and b above.
(d)None of the above.
Answer:
(a) Chronological order.

Question 5.
Trial Balance is a Statement. (State True or False)
Answer:
True

Question 6.
A bill is drawn a 1/04/2017 for 3 months. Find out the date of Maturity.
Answer:
The maturity date of Bill is 4-6-2017.

Question 7.
How do you treat interest on capital while preparing Profit and loss account?
Answer:
How do you treat interest on capital is debited to profit and loss account

Question 8.
Why the Statement of Affairs is prepared?
Answer:
To find out capital i.e. both opening as well a/c losing capital.

Question 9.
Expand AIS.
Answer:
Accounting information system.

Question 10.
Give an example for Accounting Software.
Answer:
Tally, ERP.

SECTION – B

II. Answer any five questions. Each question carries two marks. (5 × 2= 10)

Question 11.
Define Accounting.
Answer:
“The art of recording classifying and summarising in a significant manner and in terms of money transactions event which are, in part atleast, of a financial character and interpreting the results there of “American certificed public accountants”.

Question 12.
What is Double Entry System?
Answer:
The system of making two sides in the books of each contracting party for recording a transactions completely called double entry system.

Question 13.
State the Rules of Debit and Credit of Assets Account.
Answer:
Debit what comes in credit what goes out.

Question 14.
Why the Bank Reconciliation Statement is prepared?
Answer:
To reconcile, two Balance i.e., Balance as per cash book, Balance as per pass book.

Question 15.
Purchase of Machinery for 25,000 has been entered in the Purchases Book. Give the Rectifying Entry.
Answer:
Machinery a/c Dr 25000
To purchase a/c 25000
(Being machinery purchased on credit wrongly entered in purchase book know rectified)

Question 16.
Name any two example of ‘Provision’.
Answer:

1. Provision for depreciation
2. Provision for taxation.

Question 17.
Give an example for Closing Entry.
Answer:
Trading a/c Dr XXX
To opening stock a/c XXX
(Being opening stock a/c closed by transferring to debit side of trading account)

Question 18.
What are the functional components of Computer System?
Answer:

• Input unit
• Untral processing unit
• Output unit

SECTION – C

III. Answer any four questions. Each question carries six marks. (4 × 6 = 24)

Question 19.
Classify the following Accounts into Assets, Liabilities, Capital, Revenue/Gains & Expenses/Losses:

Answer:
Cash a/c – Asset – Real A/c
Purchase a/c – Asset – Real A/c
Computer a/c – liability – personal a/c
Building a/c – Asset – Real a/c
Salary a/c – Expenses – Nominal A/c
Interestion investment a/c – Income – nominal a/c
Sales -a/c Assets – Real a/c
Liability-personal a/c
Liability- personal a/c
Asset-real A/c
Assets – personal a/c

Question 20.
Enter the following transactions in an Analytical Petty Cash Book:

Answer:

Question 21.
From the following transactions, prepare Purchases Book:

Answer:

Question 22.
From the following ledger balances, prepare the Trial Balance as on 31/03/2017:

Answer:

Question 23.
Compute cost of goods sold for the year 2017:

Answer:
Calculation of cost of goods sold for the year 2017:
Cost of goods sold = opening stock + Purchased + Direct expenses – closing stock
= 30,000 + 1,50,000 + (10,000 + 10,000) – 40,000
= 30,000 + 1,50,000 + 20,000 – 40,000
= 2,00,000 – 40,000
Cost of goods sold = ₹ 1,60,000
Note: Direct expenses includes both wages as well as carriage inwards.

Question 24.
Find out the Credit Sales by preparing Total Debtors A/c:

Answer:

Question 25.
Distinguish between Manual Accounting System and Computerised Accounting System.
Answer:

SECTION – D

IV. Answer any four questions. Each question carries twelve marks. (4 × 12 = 48)

Question 26.
Journalise the following transactions in the books of Shri Ganesh:


Answer:

Question 27.
From the following transactions, prepare Double Column Cash Book.

Answer:

Question 28.
From the following information, prepare Bank Reconciliation
Statement:

Answer:

Question 29
On 01/04/2013, Santosh Company Ltd. purchased a Plant costing ₹ 85,000 and spent ₹ 15,000 for its erection. On 31/03/2015, the Plant was sold ₹ 75,000. On 01/04/2015, a new Plant was purchased for ₹ 50,000. The firm charges depreciation @ 10% PA under Straight Line Method. Accounts are closed on 31^st March every year.
Prepare 1. Plant A/c and
2. Provision for Depreciation Ale for the first 4 years.
Answer:

Question 30.
On 01/04/2017, Prakash drew a Bill on Suresh for ₹ 50,000 payable after 3 months. Suresh accepted the Bill and returned it to Prakash. On the same date, Prakash endorsed the Bill to Ramesh: on the above date, the Bill is discounted by Ramesh @12% pa. On the due date the Bill is honoured.
Pass the Journal Entries in the books of Prakash, Suresh, and Ramesh.
Answer:


Note: No Journal entry in the books of endorser (Prakash) when the bill is honoured at the date of maturity.

Question 31.
From the following ledger balances and adjustments, prepare Trading Ale, Profit and Loss A/c and Balance Sheet.


Adjustments:

1. Closing Stock was valued at ₹4,000.
2. Depreciate furniture by 10% pa. and building by 15% pa.
3. Bad Debts written off ₹500.
4. Salary Outstanding ₹1,000

Answer:

Question 32.
Anand keeps his books under Single Entry System: From the following information, prepare Statement of Profit and loss and Revised Statement of Affairs as on 31/03/2017.

During the year, Anand withdrew ₹10,000 for his personal use and introduced a further capital of ₹7,500.
Adjustments:

1. Depreciate Machinery by 10% pa & Furniture by 12% pa.
2. Provide for Bad and Doubtful Debts @5% on Sundry Debtors
3. Prepaid Insurance ₹500.
4. Legal Expenses due but not paid ₹1,000.

Answer:

SECTION – E
(Practical Oriented Questions)

V. Answer any two questions. Each question carries five marks. (2 × 5 = 10)

Question 33.
Write the Accounting Equation for each item and find the missing figure:

Answer:
a. Assets = Liabilities + Capital
1,00,000 = 60,000 + Capital
Capital = 100000 – 60000
Capital = ₹ 40,000
Formula to find out capital:
Capital = Assets – liabilities

b. Formula to find out liability
Assets – Capital = Liability
90,000 – 45,000 = 45,000
Liability = ₹ 45,000

c. Formula to find out assets
Assets = Liabilities + capital
= 24,000 + 56,000
Assets = ₹80,000

Question 34.
Prepare Machinery Ale for two years with imaginary figures under. Written Down Value Method.
Answer:

Question 35.
Write the accounting equations and find out the missing figures

Answer:
a. Assets – Liabilities = Capital
₹ 50,000 – ₹ 30,000 = ₹ 20,000

b. Asset = liabilities + Capital
₹ 45000 = ₹ 25,000 + ₹ 20,000

c. Liabilities = Assets – Capital
₹ 24,000 = ₹ 40,000 – ₹ 16,000

Students can Download 1st PUC Political Science Previous Year Question Paper 2018 (North), Karnataka 1st PUC Political Science Model Questions with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

Karnataka1st PUC Political Science Previous Year Question Paper March 2018 (North)

Time: 3:15 Hours
Max. Marks: 100

I. Answer the following questions in ONE sentence each: (10 × 1 = 10)

Question 1.
Name the work of Aristotle.
Answer:
Aristotle wrote the book “The Politics”.

Question 2.
According to plato what should be the population of state?
Answer:
According to Plato, the population of the state is 5040.

Question 3.
Which is the root word of liberty?
Answer:
The root word of liberty is the Latin word; Liber which means free.

Question 4.
Give the best example for rigid constitution.
Answer:
America is having rigid constitution.

Question 5.
Which is the lengthiest constitution in the world?
Answer:
The Constitution of India is the lengthiest constitution in the world.

Question 6.
When the term of the Lok Sabha can be extended?
Answer:
During the National emergency, the term of the Lok Sabha can be extended.

Question 7.
What is executive?
Answer:
The executive is the second important branch of the government. It enforces the laws enacted by the legislature.

Question 8.
Who appoints the chiefs of Defence forces in india?
Answer:
President appoints the Chiefs of defence forces in India.

Question 9.
PIL-Expand.
Answer:
Public Interest Litigation.

Question 10.
Who is the guardian of the constitution?
Answer:
Judiciary.

II. Answer any Ten of the following questions in 2-3 sentences each. (10 ×2 = 20)

Question 11.
When and where was the international political science conference held?
Answer:
The International Political Science Conference was held in Paris in 1948 under the UNESCO conference.

Question 12.
Write about Greek city-states.
Answer:
In the ancient days, the Greeks lived in city-states. In those days, city-states were very small. People were living in small city-states and direct democracy was existing in those city-states.

Question 13.
Name the aspects of sovereignty.
Answer:

1. Internal sovereignty.
2. External sovereignty.

Question 14.
Mention any two kinds of law.
Answer:
There are different kinds of law the important among them are: National law, International law, constitutional law, common law, ordinary law, and administrative law, etc.,

Question 15.
What is equality?
Answer:
Facilities are provided to all the persons without any discrimination is called equality.

Question 16.
Write the meaning of federal government.
Answer:
It is the government which the powers of the state are divided and distributed between central and state government. It is, also known as dual polity. The federal government discharges its power and authority in accordance with constitution. Eg: U.S.A

Question 17.
Write any two features of parliamentary Government.
Answer:

• It ensures harmony between legislative and executive branches.
• There is no division of responsibility.
• Opposition keeps government on right path.
• There will be peaceful change of government.
• It ensures flexibility and elasticity.

Question 18.
What is Secular State?
Answer:
The government cannot extend special favour to any particular religion and treats equal is called secular state.

Question 19.
Mention any two qualifications for members of Rajyasabha.
Answer:

• Must be a citizen of India.
• “Should have attained the age of 30 years.
• Owe allegiance to the constitution.
• Must not hold any office of profit under the Government – National, Regional or local.
• Should not be insolvent or man of unsound mind.
• Must not have acquired the citizenship of a foreign state.

Question 20.
Who elects the Vice-president of India?
Answer:
The Vice-President of the Indian Union is elected by members of an electoral college consisting of members of both the Houses of Parliament.

Question 21.
What is Revenue court?
Answer:
The courts which deals with the cases relating to the maintenance of land records its assessment and collection of land revenue are called revenue courts. The revenue courts are organized as below.

• The boards of revenue
• The commissioner’s court
• The collectors court
• Tahsildar’s court

Question 22.
Name any two standing committees of Zilla panchayath.
Answer:

• General committee.
• The fiance, Auditing and planning committee.
• Social justice committee.
• Education and health committee.
• Agricultural and Industry committee.

III. Answer any Eight of the following in 15 to 20 sentences each : (8 × 5 = 40)

Question 23.
Explain the relevance of the study of Political science in the contemporary world.
Answer:
Aristotle says that man by nature is a social animal. He born in society, live in society and die in society only. To fulfill his needs, he created society. In society only he can enjoy all the facility’s love and affection. Away from society he maybe God or ghost. Man is a social being at the same time he is a political being also.

He is a selfish, egoist and quarrelsome by nature. The attitudes of selfish, egoist and jealousy of a man lead to anarchy in the society while leading the life. So the order of the society may be disrupted and man cannot lead his life happily and peacefully.

In order to control the bad behavior of such people and establish a peaceful society, there should be rules and regulations. The state has emerged to frame and implement these rules through its agency “The Government”. So the state controls the political activities of the human being and restore peace in the society. The subject which studies about the state, government, the political activities of a human being is regarded as political science.

Question 24.
Distinguish between state and Association.
Answer:

State	Voluntary Association
1. Definite territory is essential element of state	1. Associations have no definite territory.
2. Membership is compulsory man cannot Give up the membership.	2. Membership is temporary; man can give up the membership.
3. Individual can get the membership of only a state.	3. Individuals can get the membership of various associations as he pleases.
4. State is permanent and continuous.	4. Associations are temporary. State can control and abolish them at any time.
5. State has sovereignty.	5. Associations have no sovereignty.
6. State’s functions are wider.	6. Functions of associations are narrower.

Question 25.
Describe political Rights.
Answer:
a. Right to Vote:
All the citizens who have attained the age of 18 are eligible to vote through adult franchise without any discrimination.

b. Right to contest election:
All the citizens of a country who have attained a particular age are given the chance to contest elections and thus respect the aims and aspirations of various sections of society in government.

c. Right to Enter Government Service:
In a democracy, all the citizens are equally entitled to get government jobs on the basis of their qualifications.

d. Right to petition:
It gives an opportunity to all people to bring their problems to the notice of the government and seek remedies.

e. Right to Criticism:
It is one of the biggest boon of democracy. All citizens have the right to criticise the policies of the government.

Question 26.
Explain the features of Unitary Government.
Answer:
Features of Unitary Government:
1. Concentration of Power:
A Unitary government is characterized by the presence of a single centre, which is omnipotent and omnipresent all over the territory. All decisions of the state flow from one single centre.

2. No Provincial Autonomy:
The provinces or local units in a unitary system are created by the centre for the sake of administrative convenience. It carries out the orders of the centre without having any powers to make decisions. Thus, the local units only act as subordinate agents of the centre without any authority or autonomy.

3. Single legislature:
In a Unitary system of government there will be only one single supreme legislative assembly which makes laws for the whole country and are faithfully implemented by the local units.

4. Constitution may be written or unwritten:
The constitution, in a unitary government, may be written or unwritten as there is one single central authority wielding power all over the state without any other centres of power.

Question 27.
Discuss the essential elements of an ideal constitution.
Answer:
The essentials of an ideal constitution are explained as below
1. It should be definite :
An ideal constitution should not be vague but clearly narrate the provisions which relates to the organization of the government. The principles should be precise and clarity.

2. It should be comprehensive:
An ideal constitution must be comprehensive enough to mention the functions of the government and rights, duties of the citizens. The constitution should not be too big but include all the information on the government.

3. Method of amendment:
An ideal constitution should possess the method of amendment. As the social condition of the people is going on change, the constitution must also undergoes change. It should represent the future needs of the future generation.

4. It should correspond to reality :
An ideal constitution should correspond to the real, conditions obtained within the state, otherwise, it cannot work properly.

Question 28.
List out the fundamental duties of Indian citizens.
Answer:
The 42^nd amendment has incorporated a number of fundamental duties.

• Abide by the constitution and respect its ideals and institutions, the national flag and, national anthem.
• Uphold and protect the sovereignty, unity, and integrity of India.
• Defend the country and render national service.
• Promote common brotherhood and harmony.
• Value and preserve our composite culture.
• Protect the natural environment.
• Develop the scientific temper.
• Strive towards excellence in all sphere.

Question 29.
Explain the different kinds of writs.
Answer:
1. Habeas corpus: It is an order issued by the court to produce the person who has wrongly detained within 24 hours.

2. Mandamus: It is a command issued by the court to ask the government official for performing his duties.

3. Prohibition: It is issued by a higher court to lower court to prevent their exceeding jurisdiction.

4. Certiorari: It is issued by a higher court to lower court to transfer a case pending with the later in a case.

5. Quo – warranto: It is issued by a court to enquire into the legality of claim of a person to public office.

Question 30.
What are the powers and functions of the speaker of Loksabha?
Answer:
The presiding officer of Loksabha is the Speaker who is elected from among the members along with the Deputy Speaker and stays in office till the life of the House i.e., 5 years. His primary task is to protect the dignity and decorum of the House and to see that the proceedings of the House are conducted in an orderly and a focused manner. He is the principal spokesperson of the House and must be impartial and even-handed in dealing as the custodian of the House.

In order to ensure impartiality, the speaker resigns his party membership in the election. The Deputy speaker discharges the duty even the office of the speaker falls vacant due to resignation, death or removal by a 2/3 majority of the total membership of the House or in the absence of the speaker. The salary of the speaker is determined by the parliament from time to time. The Speaker’s position in the House is one of dignity and authority.

• All orders of the house are executed through the Speaker
• Communication from the President is made known through the Speaker.
• It is the power of the speaker to declare whether a bill is a money bill or not.
• He enjoys the authority of interpreting the Rules of procedure and has the power to vote except in case of a tie.
• No member can speak in the House without the permission of the speaker and it is the speaker who fixes the time limit for speech.
• He presides over the Joint sittings of the parliament.
• During discussions, the members must address the Chair.
• In case of a tie, the speaker has the right to cast a vote.
• Speaker’s decisions cannot be questioned in a court of law.

Question 31.
Explain the powers and functions of chief Minister.
Answer:
The functions of the Chief Minister is so powerful that he is referred to as “the first among equals” (Primus intersperes). Article 164 of the constitution states that “there shall be a Council of ministers headed by the Chief Minister for the state”. The Chief Minister is elected from among the members of the majority party in Vidhana Sabha.

In case no party enjoys majority it is left to the discretion of the Governor to pick the Chief Minister, who in his opinion will prove majority in a stipulated time. Traditionally, the Chief Minister should be from the Vidhana Sabha.

1. Formation of Ministry:
The primary task of the Chief Minister on assuming office is the formation of the Council of ministers. Normally ministers are picked from the same political formation to ensure uniformity and continuity of policy. However, nothing prevents the Chief Minister from picking anyone as minister from any party. The Chief Minister enjoys the authority to pick and choose his ministry because he is responsible for the efficiency and performance of the government.

2. Allocation of Portfolios:
After forming the ministry the next important task is the allocation of responsibilities to ministers. Certain key or heavyweight portfolios such as Home, Revenue, Finance, Industry, Public works are to be given to key and heavyweights who enjoy clout and following among party worker. Also to ensure efficiency and stability of the government. The Chief Minister enjoys the power of expanding and reforming the ministry.

3. Chairman of the Cabinet:
The cabinet meetings are held under the chairmanship of the Chief Minister. The cabinet is a deliberating forum and differences may come up. It is the responsibility of the Chief Minister to mediate and soften things and arrive at decisions.

The Chief Minister has the authority to decide the matters to be taken up by the cabinet and may accept or reject proposals. Normally the proposals brought by ministers for discussion are not rejected. In the era of coalition politics, it is a challenge for the Chief Minister to hold the flock together. It is very difficult to chair a cabinet meeting full of divergent views, ideologies, and principles.

4. Leader of Vidhana Sabha:
Chief Minister is the leader of Vidhana Sabha. All major decisions and announcements of the state government are made by the Chief Minister. It is the responsibility of the Chief Minister to ensure that all bills brought before Vidhana Sabha for approval are passed.

And he has to defend the government on the floor of the house. Though ministers are individually responsible to their ministries, it is the Chief Minister who provides general leadership and direction. If any minister makes a mistake, the Chief Minister has the power to guide and correct him.

5. Leader of the Government:
The decisions of the government however good, are subjected to scrutiny and criticism. The opposition parties lose their identity if they do not criticize the government. So to guard against it, the Chief Minister, as leader of the government has to defend policies and programmes of the government both in and out of legislature.

6. Coordination and Supervision:
In running the administrative machinery Chief Minister will have to encounter numerous problems ranging from routine to serious. Under the circumstances it is essential to integrate different departments and see that they work smoothly and the ability of the Chief Minister is tested on this count.

A Chief Minister should not only pick a team but also retain it as a team till the end of the term. Whenever problems arise between departments, he has to mediate and sort it out amicably through dialogue and goodwill.The Chief Minister is the general head of the government. Hence he has the responsibility of supervising the administration.

Though each minister is in charge of a ministry, lack of general supervision results in poor administrative quality. To maintain quality in administration, the Chief Minister will have to supervise it, not only gives him a general feel of the administration but also makes the ministers more responsible. The Chief Minister may correct the working of a particular ministry and offer suggestions.

7. Bridge between the Governor and the State Legislature:
The Chief Minister acts as a link between the Governor and state legislature in a parliamentary government. As all executive powers are vested in the hands of the Governor, the Chief Minister is duty-bound to keep the Governor informed about the decisions taken by the government.

Also, the Governor himself can call for any information from the government. The Chief Minister not only acts as a bridge but also as the advisor to the President. Whenever necessary the President will look forward for advice. For example, the Governor seeks the advice of the Chief Minister before dissolving Vidhana sabha.

8. Power of Dissolution:
The Vidhana sabha exists as long as the Chief Minister wishes because even before the expiry of 5 years term, Chief Minister may seek the dissolution of Vidhana sabha. The Vidhana sabha may be dissolved if deep differences surface within the government or within the ruling party or the government loses a motion of no confidence.

9. Power of Appointment:
Though civil appointments are made by the Governor, it is based on the recommendation of the Chief Minister.

Question 32.
Write about the significance of Judiciary.
Answer:
It is the third branch of government, which settles disputes. It is there for administration of justice.

1. Regulation of Civic Behavior:
It is the responsibility of the judiciary that if anyone, however big and mighty, does not follow the rules and regulations prescribed by the constitution, he is liable for punishment depending upon the magnitude of crime.

2. Protection of rights and liberties:
The Judicial system is not meant to punish only the individuals and groups but also the government. If the government violates the rights of the people, people can go to a court of law and seek suitable relief. This upholds the principle that all are equal in the eye of law and all are treated alike.

3. Instill confidence of the people:
The people look up to the judiciary as a ‘neutral umpire’ deciding a case purely on merit but not on any other consideration. A common man looks up to judiciary as the ultimate lamp of justice. If the judiciary fails to stand up to the expectations of the people by being partisan to any influence or power, people stop believing not only the judiciary but also in the constitution – the fundamental law of the land. So, it is the responsibility of judiciary to make people trust the judiciary and importantly respect the constitution.

Question 33.
Write about the 74^th constitutional amendment act.
Answer:
The 74^th constitutional amendment act which came into effect in 1993 can be explained as its provisions as below.

The state government can conduct the elections.
It ensures a firm relation between state government and urban local bodies with regards to taxation powers and revenue sharing.

• It provides adequate reservation facilities to SG, ST, Backward class and women.
• The state government has power to legislate about reservation in urban local bodies.
• The members should elect directly by the residents who are living in urban area.
• The tenure of the urban local bodies in 5 years.
• Elections shall be held within 6 months from the date of dissolution.
• Members of parliament and assembly are the ex-officio members of urban local bodies.
• The state government can nominate 5 members to the urban local bodies.
• The state government has power to prepare plan for economic and social development.
• State finance commission has been established to review the finances of urban local bodies.

Question 34.
Explain the functions of Taluk panchayath.
Answer:
The powers and functions of Taluk Panchayats are as below:

• Preparation of annual plans and submit to Z.P.
• Preparation of annual budget and report to Z.P.
• Providing basic felicities to victims of natural calamities.
• Promotion of agriculture and horticulture.
• Ensuring overall development of the Taluk.
• Constrictions and maintenances of roads, bridges, and buildings
• Promotes poverty alienation programmes, literacy programmes.
• Development of primary and secondary education.
• Promoting the welfare of women children and physically handicapped.
• Providing electric and water felicities.
• Promoting animal husbandry, poultry and fisheries.
• Promoting the welfare of SC, ST and backward class.
• Regulating the markets in rural areas.
• Conducting health and family welfare programmes.
• Encouraging small irrigation programmes.

IV. Answer any Two of the following in 30 to 40 sentences each: (2 × 10 = 20)

Question 35.
What is Dictatorial Government? Explain its features.
Answer:
1. Absolute power:
Dictatorship is characterized by absolute power where the dictator controls the constitution. He can make and unmake laws. All the laws must originate from him and there is neither a limit on his tenure nor is he subjected to any other authority.

2. Based on Force:
Dictatorship stands on the twin pillars of force and coercion. The word of the dictator should be honored in letter and spirit. Any violation of the order may result in severe punishment or even death.

3. Totalitarian state:
Dictatorial regimes regulate and control all aspects of human existence. It provides security, basic necessities such as food, shelter and clothing, education and order in society. In totalitarian state’s individual personality is suppressed and all aspects of an individual are regimented and brought under the control of the state. The totalitarian approach is well summarized by Mussolini when he says: “Everything within the state, nothing above the state, nothing outside the State’’. Thus, the State is the central point around which all human activities must revolve.

4. One Nation one party:
In a dictatorship, for the whole state, there is only one constitution and the administration is managed by one single party and that is responsible for the whole state. Any kind of criticism of the party or the leadership is not tolerated. The distinct feature of dictatorship is its intolerance to criticism and new ideas.

5. No individual liberty:
In a dictatorship, individual freedom and liberty do not find place. Freedom of thought and expression is restricted.

Question 36.
Describe the powers and functions of the Vidhana sabha.
Answer:
There is a legislative assembly for every state. The number of members depends upon the population of the state. But it can not have less than 60 and more than 500 members. The members are chosen by direct election by people of the state. The governor has been given the power to nominate one or two members of the Anglo Indian community legislative assembly is five years.The powers and functions of Vidhanasabha are as follows:

1. Legislative Functions:
The Legislative Assembly is entitled to pass laws on all subjects that fall under the state list such as police, public health, education, local-self governments, etc. Without the consent of the Vidhanasabha, no bill can become a law.

Though the Vidhanasabha is competent enough to make laws on subjects listed in the concurrent list along with the central legislature, if parliament passes a law contained in the concurrent list, the legislative assembly is not competent to pass a law on the same subject.However, some bills require the previous permission of the President before they are introduced in the state legislature.

In case of breakdown of constitutional machinery’ in a state or when the proclamation of emergency is in operation, parliament has the power of making laws on matters falling under the state list. In case of a conflict between state law and the law of the parliament, the law of the parliament shall supreme.

2. Financial Functions:
The Vidhanasabha enjoys total control over the finance of the state. No new tax can be levied or collected without the consent of the Vidhanasabha. The authority of the Vidhanasabha over Vidhanaparishad is strengthened by the fact that a Money bill or Financial bill can only originate in the Vidhanasabha and the Vidhanaparishad can at the most delay it by 14 days but cannot reject or amend the Bill.

The annual income-expenditure statement of the year the Budget must get the approval of the Vidhanasabha. Even year during March-April, the beginning of the financial year, it is the responsibility of the government to place the budget before the house and seek its approval.

3. Control over the Executive (Administration):
The Vidhanasabha enjoys direct control over the administration, as the executive is directly, collectively, responsible to the Vidhanasabha and remains in office as long as they enjoy the confidence of the house. The members of the house can seek information from the government through questions and supplementary questions.

It is the responsibility of the ministers to clarify points raised by members and give a satisfactory explanation.Any attempt to lie or mislead the house is considered an offence against the house punishable under Contempt of the House.

The debating occasions such as the Question Hour, Adjournment motion, the Emergency Adjournment motion, the Zero Hour, the Cut motion, the Call-attention motion keeps the executive under constant check and the executive must be alert and ready with answers. However, ministers can ask for time to answer questions. The most effective weapon in the hands of the Vidhanasabha is the No-confidence motion, which can bring down a government.

4. Electoral Functions:
The members of the Vidhanasabha along with the members of the parliament constitute an electoral college to elect the President of India. They also take part in electing the members of Rajyasabha and also of the members of Legislative council.

5. Constituent Functions:
The state legislative assembly takes part in amending a few constitutional provisions. The Assembly does not initiate any amendment to constitution neither does it has such powers. But ratification of at least not less than half of the State legislative assemblies is necessary for amending certain provisions of the constitution. For instance, if there has to be an amendment made to electoral procedure of electing president of India then it has to be ratified by 1/2 of the states, which in turn is done by state legislative assemblies.

Question 37.
Explain the powers and functions of the president of India.
Answer:
In the Parliamentary government, the position of the President is that of a respectful figure-head, representing the honor and dignity of the people of India. It has become a fashion to label the President as ‘a rubber stamp’, the impression is that he does nothing but signing bills brought before him. But there are occasions that offer scope for independent decisions. When no party enjoys a majority, the power to appoint Prime minister rests with the President (Article 75).

In case of sudden demise of Prime minister, if the party fails to elect its leader, at the earliest, President may appoint a person of his choice as the Prime minister. Importantly, if a government loses majority and recommends for the dissolution of the house (Lok sabha), it is purely power of the President to dissolve the parliament or not (Article 85).The powers and functions of the President are as follows:

1. Legislative Functions:
The legislative functions are detailed below:

a. To summon, prorogue and dissolve the Parliament.

b. The President enjoys the power to address the Parliament. It is normally done after general elections or the first session of the year. It is generally called Presidential speech. This inaugural speech outlines the objectives and priorities of the government.

c. In passing the bills, if a dead lock arises due to non-agreement between two houses . of the parliament, the President may call for joint session of both the houses.

d. The President may address Lok sabha or Rajya sabha or both any time and also may send a message to both the houses of parliament to look into a bill.

e. In the considered view of the President, if he is satisfied that the Anglo-Indian community is not adequately represented, he may nominate 12 members to Rajva Sabha and 2 members to Lok sabha.

f. Prior permission of the President is essential while dealing with bills relating to formation of new states, alteration of boundaries and some special bills like the finance bills.

g. No bill can become a law without the assent of the President. He enjoys the power to withhold a bill. This power is called ‘Veto power”. However he cannot refuse his assent for finance bills. But he can withhold assent for a nonmoney bill. But if the same is resubmitted for signature even without changes, he cannot refuse to sign it.

h. The President enjoys the power of issuing Ordinance when the parliament is not in session. It will have the same power and effect similar to that of a law made by the Parliament provided the same is ratified by the Parliament within 6 weeks of its passage. Otherwise it ceases to be a law and is considered null and void or zero.

2. Executive Functions:
The President is the administrative Head of the State and orders are executed in his name. Article 53 clearly states that the executive powers of the State must be vested in ‘the hands of the President’.

• All accords and agreements carried out on behalf of the Government of India is done in the name of the President.
• The President has the power to call for any information from the government.
• The President appoints the Prime minister and the Council of minister on recommendation of the Prime minister.
• The highest constitutional functionaries such as Comptroller and Auditor General (CAG), Chief Election Commissioner (CEC), ChiefVigilance Commissioner (CVC) are appointed by the President.
• The member of the Union Public Service Commission (UPSC), National Human Right Commission (NHRC), Backward Class Commission (BCC) and National Commission for Women (NCW) are appointed by the President.
• The President enjoys the power of removing highest constitutional functionaries.The President can call for reports from Scheduled Castes and Scheduled Tribes Commission, Linguistic Minorities Commission (LMC), Backward Class Commission (BCC) and other commissions.

3. Financial powers:

• It is the constitutional obligation of the President to see that the annual income expenditure statement. The budget is placed before the Parliament for approval.
• Financial bills cannot be presented in the Parliament without the consent of the President.
• The recommendation of the Finance Commissions and the Planning Commission are placed before the Parliament on orders of the President.
• The members of the Finance Commission and Planning Commission are appointed by the President.

4. Judicial Powers:
a. The President enjoys the power of pardoning the sentence of a person declared an offender by the Supreme Court. He is so powerful that he can reduce change or altogether cancel the punishment. This power is called Presidential Pardon. This is provided to ensure any miscarriage of justice (Article 72).

b. The Judges of the Supreme Court and High court are appointed by the President in consultation with the Chief Justice of India.

c. The President is entitled to legal advice on matters relating to the constitutional clarity of bills. However, it is not binding on the President to accept it.

5.Military Powers:
President is the Supreme Commander of the Armed Forces. President has the power to declare war or peace, but parliamentary approval is essential for such a decision. The President can raise funds for training and preservation of armed forces with prior approval of the Parliament. The Chiefs of Army, Navy, and Air force are appointed by the President.

6. Diplomatic Powers:
a. The diplomatic powers of the President are purely symbolic in nature. The President represents the country in international affairs. His visits are of courtesy nature aimed at strengthening bilateral relations; he does not sign any treaties or agreements.

b. The ambassadors representing the country abroad are appointed by the President.

c. The foreign ambassadors are received by the President. No person can be considered an ambassador unless he is given the ‘Letter of Accreditation’ by the president.

7. Emergency Powers:
The emergency powers of the President are enumerated in the constitution from Article 352 to Article 360. The President may declare emergency under three circumstances:

a. The President may declare internal emergency under Article 352, if, in his opinion, there is a threat to India’s security due to war or external aggression.

b. The President may impose ‘President’s Rule’ under Article 356 if he is convinced that in that particular state the law and order has completely deteriorated and it cannot be governed as per the constitution. Though the President’s rule is imposed on the recommendation of the governor of the concerned state, it is not compulsory.

c. If the President is convinced that the financial stability and prestige of the nation is at risk, he may impose financial emergency under Article 360.

However, the imposition of internal and financial emergency should be placed before Parliament and its consent taken within 2 months of the declaration of emergency, otherwise, it is considered invalid.

Question 38.
How is independence of the judiciary ensured? Explain the measures.
Answer:
In order to ensure independence of judicial system in India, the following steps have been taken so that the judicial officers are not under pressure in discharging their duties.

a. The Constitution has made it obligatory on the part of the President to consult the Chief Justice of India in appointing a judge of Supreme Court. This not only makes the appointment non-political but also saves judiciary from the influence of the executive (the council of ministers).

b. A judge of the Supreme Court cannot be removed from office by the President at his will, but on a motion passed by a two-third majority of the total membership of either house addressed to him. Thus, the legislative control over the executive ensures judicial independence.

c. A judge of the Supreme Court, though appointed by the President on the advice of the council of ministers, does not hold office during the pleasure of the President, but based on good behavior. He can be removed only on charges of proven misbehavior or incapacity by a motion addressed to the President by the Parliament.

d. The salaries and allowances of the judges of the Supreme Court are determined by a law of parliament and is not subject to discussion. The salary and allowances of the judges cannot be reduced or varied to his disadvantage during his term of office. This means that he will not be in any way affected by any law made by the parliament since the day of his appointment.

e. The administrative expenses of the Supreme court, the salaries, and allowances of the judges and staff are charged on the Consolidated Fund of India (CFI), a corpus fund of Rs. 50 crore which may be enhanced from time to time, and it can not be voted in parliament. Discussion of the conduct of the judges of the Supreme Court is not allowed in parliament except during removal of a judge This gives immunity from criticism.

f. A judge of the Supreme Court is not permitted to practice in any court in India after retirement. This prevents him from falling prey to temptations. To boost accountability in the judicial system, the Central Information Commission (CIC) has brought the office of the Chief Justice under the purview of the Right to Information Act (RTI).

IV. Answer any Two of the following in 15-20 sentences each: (2 × 5 = 10)

Question 39
Explain the standing committees of purasabha.
Answer:
The Standing committees of Pura Sabha are

• Taxation, Finance and Appeal committee.
• Basic health, Education and Social justice committee.
• Tour planning and Improvement committee.
• Accounts and Audit committee.

Financial Sources

• Taxes on assets, water, professions, and advertisements.
• Rents from markets, complexes, and other properties.
• Grants and contributions from the State government.
• Income collected for providing drainage and sanitary facilities.
• Loans raised from the public with government approval.

OR

Write about the life and achievements of a local politician.
Answer:
One of the most popular and familiar leader of a state which is also called as local politician is siddaramaiah. He is a leader of Backward class and Ahinda organisation. Mr. Siddaramaiah after assuming the power as chief Minister of Karnataka implemented so many plans and programmes for the welfare of depressed class and backward class. His main programmes are Anna Bhagya.

Ksheera Bhagya, Shaadi Bhagya, Arogya Bhagya, Anila Bhagya, Maatru Pooma Scheme, manaswini scheme, mythri scheme, All these schemes are relatede to below poverty line, farmers, minorities, farmers and sexual minorities. Siddaramaiah has taken drastic decision to uplift the Ahinda community expecially minorities in the society. He waived the crops loans of farmers recently.

Question 40.
Write a note on Economic liberty.
Answer:
Economic liberty means security and the Opportunity to find the earning of one’s daily bread. Individual should be free from constant fear of unemployment, underemployment, and starvation.

State has to provide all its citizens adequate means of livelihood. It implies democracy in industry that is in the absence of this liberty worker has to work at the behest of others. This is secured through economic liberty.

OR

Write about the independence Day celebration in your college.
Answer:
Write about the independence day celebration in your college. Independence day is an important national festival in all over India. Previous day all the students cleaned and decorated the college campus by the guidance of lecturers. They tied buntings and colour papers with colourful rangoli. On the independence day, guests are invited by the students with flowers. Our college principal presided over the function.

Firstly national flag was hoisted by the chief guest with national anthem. One of the lecturers proposes welcome speech. Guests highlighted the values of the great ideal of our freedom fighters, cultural programmes attracted the students. Our principal delivers presidential address. One of the leaders of student proposes vote of thanks. Finally. sweets are distributed.