{"id":21305,"date":"2020-01-25T10:57:34","date_gmt":"2020-01-25T05:27:34","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=21305"},"modified":"2021-07-02T15:27:00","modified_gmt":"2021-07-02T09:57:00","slug":"2nd-puc-basic-maths-model-question-paper-1","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/2nd-puc-basic-maths-model-question-paper-1\/","title":{"rendered":"2nd PUC Basic Maths Model Question Paper 1 with Answers"},"content":{"rendered":"<p>Students can Download 2nd PUC Basic Maths Model Question Paper 1 with Answers, Karnataka <a href=\"https:\/\/kseebsolutions.guru\/2nd-puc-basic-maths-model-question-papers-with-answers\/\">2nd PUC Maths Model Question Papers with Answers<\/a> helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.<\/p>\n<h2>Karnataka 2nd PUC Basic Maths Model Question Paper 1 with Answers<\/h2>\n<p>Time: 3.15 hours<br \/>\nMax. Marks: 100<\/p>\n<p>Instructions<\/p>\n<ul>\n<li>The question paper has 5 parts A, B, C, D, and E. Answer all the parts.<\/li>\n<li>Part &#8211; A carries 10 marks, Part &#8211; B carries 20 marks, Part &#8211; C carries, Part &#8211; D carries 30 marks and Part &#8211; E carries 10 marks.<\/li>\n<li>Write the question number properly as indicated in the question paper.<\/li>\n<\/ul>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\">Part &#8211; A<\/span><\/p>\n<p><span style=\"color: #0000ff;\">I. Answer all the questions: (10 \u00d7 1 = 10)<\/span><\/p>\n<p>Question 1.<br \/>\nDefine Diagonal Matrix<br \/>\nAnswer:<br \/>\nIn a square matrix, except the principal diagonal elements all other elements are zeros is called diagonal matrix.<br \/>\n\\(\\left[ \\begin{matrix} 2 &amp; 0 \\\\ 0 &amp; 3 \\end{matrix} \\right]\\) \\(\\left[ \\begin{matrix} 2 &amp; 0 &amp; 0 \\\\ 0 &amp; 1 &amp; 0 \\\\ 0 &amp; 0 &amp; 4 \\end{matrix} \\right]\\)<\/p>\n<p>Question 2.<br \/>\nIn how many ways can 9 soldiers stand in a queue.<br \/>\nAnswer:<br \/>\n9 soldiers can stand in a queue in 9! ways<\/p>\n<p>Question 3.<br \/>\nSymbolise the following proposition: 3x = 9 and x &lt; 7<br \/>\nAnswer:<br \/>\n(i) Let p:3x = 9, q = x &lt; 7<br \/>\nGiven in symbols is p \u2227 q<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 4.<br \/>\nFind the subtriplicate ratio of 125 : 64.<br \/>\nAnswer:<br \/>\nSubtriplicate ratio of 125 : 64<br \/>\n= 3\u221a125 : 3\u221a64 = 5 : 4.<\/p>\n<p>Question 5.<br \/>\nDefine Banker&#8217;s Discount.<br \/>\nAnswer:<br \/>\nBanker&#8217;s Discount is the Simple interest calculated by the banker on the face value of the bill i.e., BD = Ftr<\/p>\n<p>Question 6.<br \/>\nIf sin A = \\(\\frac { 1 }{ 2 }\\) find sin 2A<br \/>\nAnswer:<br \/>\nGiven sin A = \\(\\frac { 1 }{ 2 }\\) \u21d2 cos A = \\(\\frac{\\sqrt{3}}{2}\\) sin2A<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66131\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-1-1.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 1\" width=\"243\" height=\"53\" \/><\/p>\n<p>Question 7.<br \/>\nFind the equation of the circle with centre \u2018C and radius &#8216;r&#8217; of the following: c{-3, 2) and r = 5 units<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66233\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-44.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 44\" width=\"260\" height=\"58\" \/><br \/>\nEquation of the circle is(x &#8211; x<sub>1<\/sub>)<sup>2<\/sup> + (y &#8211; y<sub>1<\/sub>)<sup>2<\/sup> = r<sup>2<\/sup><br \/>\n(x-(-3))<sup>2<\/sup> + (y &#8211; 2)<sup>2<\/sup> = 5<sup>2<\/sup><br \/>\n(x + 3)<sup>2<\/sup> + (y &#8211; 2)<sup>2<\/sup> = 5<sup>2<\/sup><br \/>\nx<sup>2<\/sup> + y<sup>2<\/sup> + 6x &#8211; 4y &#8211; 12 = 0.<\/p>\n<p>Question 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66089\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-1.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 2\" width=\"98\" height=\"50\" \/><br \/>\nAnswer:<br \/>\n\\(=\\frac{4.4+3}{4-2}=\\frac{16+3}{2}=\\frac{19}{2}\\)<\/p>\n<p>Question 9.<br \/>\n5e<sup>x<\/sup> &#8211; logx &#8211; 3\\(\\sqrt{\\mathbf{x}}\\)<br \/>\nAnswer:<br \/>\nLet y = 5e<sup>x<\/sup> &#8211; log x &#8211; 3\\(\\sqrt{x}\\)<br \/>\n\\(\\frac{d y}{d x}=5 e^{x}-\\frac{1}{x}-3 \\frac{1}{2 \\sqrt{x}}\\)<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 10.<br \/>\nIntegrate the following x<sup>2<\/sup> &#8211; \\(\\frac { 6 }{ x }\\)\u00a0 + 5e<sup>x<\/sup><br \/>\nAnswer:<br \/>\n\\(\\int x^{2}-\\frac{6}{x}+5 e^{x} d x=\\frac{x^{3}}{3}-6 \\log x+5 e^{x}+C\\)<\/p>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\">Part &#8211; B<\/span><\/p>\n<p><span style=\"color: #0000ff;\">II. Answer any ten questions: (10 \u00d7 2 = 20)<\/span><\/p>\n<p>Question 11.<br \/>\nFind x and y given that \\(\\left[ \\begin{matrix} -9 \\\\ 2 \\end{matrix} \\right] -\\left[ \\begin{matrix} 5 \\\\ -1 \\end{matrix} \\right] =\\left[ \\begin{matrix} x \\\\ y \\end{matrix} \\right] \\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66133\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-3-1.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 3\" width=\"416\" height=\"112\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-3-1.png 416w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-3-1-300x81.png 300w\" sizes=\"(max-width: 416px) 100vw, 416px\" \/><\/p>\n<p>Question 12.<br \/>\nIf <sup>n<\/sup>C<sub>8<\/sub> = <sup>n<\/sup>C<sub>12<\/sub> find <sup>n<\/sup>C<sub>5<\/sub><br \/>\nAnswer:<br \/>\nGiven <sup>n<\/sup>C<sub>8<\/sub> = <sup>n<\/sup>C<sub>12<\/sub><br \/>\n\u21d2 n = 8 + 12 = 20<br \/>\n<sup>n<\/sup>C<sub>5<\/sub> = <sup>20<\/sup>C<sub>5<\/sub> = 15,504.<\/p>\n<p>Question 13.<br \/>\nWhat are independent events? Give one example.<br \/>\nAnswer:<br \/>\n(a) If two events cannot occur simultaneously in a random experiment then they are called mutually exclusive events<br \/>\n(b) Events are said to be independent, if the occurrence of one does not depend upon the occurrence of the other<br \/>\n(c) In a random experiment, let S be the sample space &amp; let E be an event then E C S, So &#8216;E\u2019 is also an event called the complementary of E.<\/p>\n<p>Question 14.<br \/>\nIf p, q and r are propositions with truth values F, T and F respectively, then find the truth value of the following compound proposition: (p \u2227 q) v ~ r<br \/>\nAnswer:<br \/>\n(p \u2227 q) \u2228 ~ r<br \/>\n(F \u2227 T) \u2228 ~ r<br \/>\nF \u2228 T<br \/>\n= T<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 15.<br \/>\nFind the ratio between two numbers such that their sum is 40 and their difference is 8.<br \/>\nAnswer:<br \/>\nLet the two numbers be x &amp; y<br \/>\nGiven x + y = 40 &#8230;&#8230;. (1)<br \/>\n&amp; x &#8211; y = 8 &#8230; (2)<br \/>\nSolving we get<br \/>\nAdding 2x = 48 \u21d2 x = 24 &amp; y = 40 \u2013 24 = 16<br \/>\n\u2234 Ratio of the numbers is 24 : 16 \u21d2 3:2.<\/p>\n<p>Question 16.<br \/>\nFind the BD on ? 1015, payable after 3 months at 6% p.a.<br \/>\nAnswer:<br \/>\nGiven<br \/>\nF = 1015,<br \/>\nF=1015, t = \\(\\frac{3}{12}\\) year, r = \\(\\frac{6}{100}\\) = 0.06, BD = ?<br \/>\nBD = Ftr = 1015 x \\(\\frac{3}{12}\\) \u00d7 0.06 = 15.22<\/p>\n<p>Question 17.<br \/>\nIf sin A = \\(\\frac { 3 }{ 5 }\\), cos B = \\(\\frac { 4 }{ 5 }\\) find sin(A + B) and cos(A &#8211; B). Where A and B are acute angles.<br \/>\nAnswer:<br \/>\nGiven sin A = \\(\\frac { 3 }{ 5 }\\) , cos B = \\(\\frac { 4 }{ 5 }\\)<br \/>\n\u21d2 cos A = \\(\\frac { 4 }{ 5 }\\) &amp; sin B = \\(\\frac { 3 }{ 5 }\\) \u2235 sin<sup>2<\/sup>A + cos<sup>2<\/sup>A = 1<br \/>\n(i) sin(A + B) = sinA cosB + cosA sinB = \\(\\frac{3}{5} \\cdot \\frac{4}{5}+\\frac{4}{5} \\cdot \\frac{3}{5}=\\frac{24}{25}\\)<br \/>\n(ii) cos(A &#8211; B) = COSA COSB + sinA sinB = \\(\\frac{4}{5} \\cdot \\frac{4}{5}+\\frac{3}{5} \\frac{3}{5}=\\frac{16}{25}+\\frac{9}{25}=\\frac{25}{25}=1\\)<\/p>\n<p>Question 18.<br \/>\n\\(\\cos \\left(\\frac{\\pi}{4}-A\\right)-\\sin \\left(\\frac{\\pi}{4}+A\\right)=0\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66134\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-4-1.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 4\" width=\"461\" height=\"163\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-4-1.png 461w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-4-1-300x106.png 300w\" sizes=\"(max-width: 461px) 100vw, 461px\" \/><\/p>\n<p>Question 19.<br \/>\nFind the equation of the parabola given that its. Vertex is (0,0) and focus is (4, 0)<br \/>\nAnswer:<br \/>\n(a) Given V = (0,0) and Focus, S = (4,0)<br \/>\nIt is a right handed parabola with<br \/>\na = 4 and standard form is<br \/>\ny<sup>2<\/sup> = 4ax<br \/>\nPut a = 4, then<br \/>\ny<sup>2<\/sup> = 16x.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66135\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-5-1.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 5\" width=\"275\" height=\"174\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 20.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66234\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-45.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 45\" width=\"532\" height=\"97\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-45.png 532w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-45-300x55.png 300w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><br \/>\nAnswer:<br \/>\nAlso f(x) at x = 5 is 10; i.e, f(5) = 10<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66237\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-46.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 46\" width=\"186\" height=\"33\" \/><br \/>\n\u2234 the function f(x) is continuous at x = 5<\/p>\n<p>Question 21.<br \/>\nDifferentiate e<sup>2x<\/sup> w.r.t. x from first principles.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66137\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-7-1.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 7\" width=\"519\" height=\"131\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-7-1.png 519w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-7-1-300x76.png 300w\" sizes=\"(max-width: 519px) 100vw, 519px\" \/><\/p>\n<p>Question 22.<br \/>\nThe displacement &#8216;s&#8217; of a particle at time \u2018t\u2019 is given by S = 4t<sup>3<\/sup> &#8211; 6t<sup>2<\/sup> + t &#8211; 7. Find the velocity and acceleration. when t = 2 sec.<br \/>\nAnswer:<br \/>\nGiven S = 4t<sub>3<\/sub> &#8211; 6t + t &#8211; 7<br \/>\nVelocity = v = \\(\\frac{\\mathrm{ds}}{\\mathrm{dt}}\\) = 12t<sup>2<\/sup> -12t + 1<br \/>\nAt t = 2secs, v = 12(2)<sup>2<\/sup> &#8211; 12(2) + 1 = 48 &#8211; 24 + 1 = 25 units\/sec.<br \/>\nAt t = 2 sec, acceleration = 24.2 &#8211; 12 = 48 &#8211; 12 = 36 units\/sec<sup>2<\/sup>.<\/p>\n<p>Question 23.<br \/>\nsec x(sec x &#8211; tan x)<br \/>\nAnswer:<br \/>\n\u222bsec x (sec x &#8211; tan x)dx = \u222bsec<sup>2<\/sup>x &#8211; sec x .tan x. dx<br \/>\n= tan x &#8211; sec x + c<\/p>\n<p>Question 24.<br \/>\nJsin2x dx<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66138\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-8-1.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 8\" width=\"331\" height=\"201\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-8-1.png 331w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-8-1-300x182.png 300w\" sizes=\"(max-width: 331px) 100vw, 331px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\">Part &#8211; C<\/span><\/p>\n<p><span style=\"color: #0000ff;\">III. Answer any Ten Questions: (10 \u00d7 3 = 30)<\/span><\/p>\n<p>Question 25.<br \/>\nFind A and B if 2A + B = \\(\\left[ \\begin{matrix} 1 &amp; -1 \\\\ 0 &amp; 1 \\end{matrix} \\right]\\) and A &#8211; 3B = \\(\\left[ \\begin{matrix} 0 &amp; 1 \\\\ 1 &amp; 0 \\end{matrix} \\right]\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66139\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-9-1.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 9\" width=\"603\" height=\"566\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-9-1.png 603w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-9-1-300x282.png 300w\" sizes=\"(max-width: 603px) 100vw, 603px\" \/><\/p>\n<p>Question 26.<br \/>\nShow that, if any row of column of a determinant contains sum of two terms then it can be expressed as sum of two determinants<br \/>\nAnswer:<br \/>\nIf any row of a column of a determinant contains sum of two terms then it can be expressed as sum of two determinants<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66140\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-10.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 10\" width=\"321\" height=\"56\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-10.png 321w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-10-300x52.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><br \/>\n= a<sub>1<\/sub>b<sub>2<\/sub> + \u03b1b<sub>2<\/sub> -a<sub>2<\/sub> &#8211; a<sub>2<\/sub>b1 &#8211; a<sub>2<\/sub>\u03b2<br \/>\n= (a<sub>1<\/sub>b<sub>2<\/sub> &#8211; a<sub>2<\/sub>b<sub>1<\/sub>) + \u03b1b<sub>2<\/sub> &#8211; \u03b2a<sub>2<\/sub><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66141\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-11.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 11\" width=\"192\" height=\"57\" \/><\/p>\n<p>Question 27.<br \/>\nFind the number of permutations of the letters of the word MISSISSIPPI. In how many of these<br \/>\n(a) the 4s&#8217;s are together<br \/>\n(b) the 4s&#8217;s are not together<br \/>\n(c) begin with MISS<br \/>\nAnswer:<br \/>\nTotal letters = 11, I = 4, S = 4, P = 2.<br \/>\n\u2234 The total number of permutations 7<br \/>\n4s&#8217;s are together can be taken as 1 unit i.e.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66142\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-12.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 12\" width=\"554\" height=\"55\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-12.png 554w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-12-300x30.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><br \/>\n\u2234 The number of permutations = \\(\\frac{8 !}{4 ! \\times 2 !}\\) (b)<br \/>\n4s&#8217;s are not together = Total number of ways &#8211; 4s&#8217;s are together = \\(\\frac{11 !}{4 ! \\times 4 ! \\times 2 !}-\\frac{8 !}{4 ! \\times 2 !}\\) (c)<br \/>\nBegin with MISS: The remaining 7 letters can be arranged in \\(\\frac{7 !}{3 ! \\times(2 !)^{2}}\\) (d)<br \/>\nBegin with SIP: The remaining 8 letters (I = 3, S = 3) can be arranged in \\(\\frac{8 !}{(3 !)^{2}}\\)<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 28.<br \/>\nA box contains 4 defective and 6 non defective bulbs. Find the probability that atleast 3 bulbs are defective when 4 bulbs are selected at random.<br \/>\nAnswer:<br \/>\nA box contains 4 defective and 6 non def when 4 bulbs are selected at random.<br \/>\nAnswer:<br \/>\nn(S) = (6 + 4)C<sub>4<\/sub> = 10 \\(c_{4}-\\frac{10 \\times 9 \\times 8 \\times 7}{4 \\times 3 \\times 2 \\times 1}\\) = 210<br \/>\nLet A: at least 3 are defective<br \/>\nHere 4 defective 6non defective<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66143\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-13.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 13\" width=\"454\" height=\"124\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-13.png 454w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-13-300x82.png 300w\" sizes=\"(max-width: 454px) 100vw, 454px\" \/><\/p>\n<p>Question 29.<br \/>\nTwo taps fill a cistern separately in 20 minutes and 40 minutes respectively and a drain pipe can drain off 30 litres per minute. If all the three pipes are opened, the cistern fills in 72 minutes what is the capacity of the cistern?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66144\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-14.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 14\" width=\"186\" height=\"81\" \/><br \/>\nPersons &amp; days are in inverse proportion<br \/>\n\u2234 10:20 = x : 60<br \/>\nX= \\(\\frac{60 \\times 10}{20}\\) = 30days 20<\/p>\n<p>Question 30.<br \/>\nRefrigerator is marked for sales for ?17,000 which include sales tax at 10% Calculate the sales tax in<br \/>\nAnswer:<br \/>\nGiven S.P = \u20b9 17,000, Sales Tax = 10% Let<br \/>\nC.P = x\u20b9<br \/>\nW.K.T selling price = CP + Sales Tax<br \/>\n17,000 = x + 10% of<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66145\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-15.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 15\" width=\"363\" height=\"118\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-15.png 363w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-15-300x98.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><\/p>\n<p>Question 31.<br \/>\nThe difference between banker&#8217;s discount and true discount on a bill due after 6 months at 4% interest p.a. is t20. Find the true discount, banker&#8217;s discount and face value of the bill.<br \/>\nAnswer:<br \/>\nGiven<br \/>\nBG = \u20b9 20, r = 4% = 0.04, t = 6 Months = \\(\\frac{6}{12}=\\frac{1}{2}\\)<br \/>\nTD = ?, BD = ?, F = ?<br \/>\nW.K.T. = BG = TD. tr<br \/>\n20 = TD \\(\\frac{1}{2}\\) x 0.04<br \/>\n40 = 0.04 TD \u21d2 TD = \\(\\frac{40}{0.04}\\) = \u20b9 1000<br \/>\nBD = BG + TD; = 20 + 1000 = 1020<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66146\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-16.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 16\" width=\"334\" height=\"54\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-16.png 334w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-16-300x49.png 300w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><\/p>\n<p>Question 32.<br \/>\nA man invests equal sums of money in 4%, 5% and 6% stock, each stock being at par. If the total income of the man is \u20b9 3,600. Find his total investment.<br \/>\nAnswer:<br \/>\nLet the amount invested be x<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66147\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-17.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 17\" width=\"467\" height=\"215\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-17.png 467w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-17-300x138.png 300w\" sizes=\"(max-width: 467px) 100vw, 467px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 34.<br \/>\nFind \\(\\frac{\\mathrm{d} y}{\\mathrm{d} x}\\) if x = a sec \u03b8, y = b tan \u03b8 dx<br \/>\nAnswer:<br \/>\nGiven a = sec\u03b8, y = b tan \u03b8<br \/>\nDifferentiate both w.r.t. \u03b8 we get<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66148\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-18.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 18\" width=\"282\" height=\"130\" \/><\/p>\n<p>Question 35.<br \/>\nThe radius of sphere is increasing at the rate of 0.5mt\/sec. Find the rate of increase of its surface area and volume after 3 sec.<br \/>\nAnswer:<br \/>\nGiven \\(\\frac{\\mathrm{dr}}{\\mathrm{dt}}\\) = 0.5 , t = 3 sec, \\(\\frac{\\mathrm{ds}}{\\mathrm{dt}}\\) = ? \\(\\frac{\\mathrm{dv}}{\\mathrm{dt}}\\) = ?<br \/>\nsurface area = s = 4\u03c0r<sup>2<br \/>\n\\(\\frac{d s}{d t}\\) = 4\u03c0 . 2r . \\(\\frac{d r}{d t}\\)<\/sup><br \/>\n= 4\u03c0 \u00d7 2 \u00d7 1.5 \u00d7 0.5<br \/>\n= 6\u03c0 m<sup>2<\/sup>\/sec<br \/>\ndr = 0.5 \u00d7 dt<br \/>\n\u21d2 r = 0.5 t<br \/>\n= 0.5 \u00d7 3<br \/>\n= 1.5<\/p>\n<p>Question 36.<br \/>\nThe sum of two natural numbers is 48. Find the numbers when their product is maximum.<br \/>\nAnswer:<br \/>\nLet the two numbers be x &amp; y.<br \/>\nGiven x + y = 48 &amp; product: = xy where y 48 &#8211; x.<br \/>\nLet p = xy = x (48 &#8211; x) = 48x &#8211; x<sup>2<\/sup>.<br \/>\n\\(\\frac{d p}{d x}\\) = 48 &#8211; 2x<br \/>\n\\(\\frac{d p}{d x}\\) = 0 \u21d2 48 &#8211; 2x = 0 x = 24<br \/>\n\\(\\frac{\\mathrm{d}^{2} \\mathrm{p}}{\\mathrm{d} \\mathrm{x}^{2}}\\) = -2 &lt; 0 \u21d2 product is maximum<br \/>\nx = 24 \u21d2 y = 48 &#8211; 24 = 24<br \/>\n\u21d2 the two numbers are 24, 24.<\/p>\n<p>Question 37.<br \/>\nIntegrate the following \\(\\sqrt{1+\\sin 2 x}\\)<br \/>\nAnswer:<br \/>\n\\(\\int \\sqrt{1+\\sin 2 x} d x=\\int \\sqrt{(\\cos x+\\sin x)^{2}}=\\int(\\cos x+\\sin x) d x\\)<br \/>\n= sinx &#8211; cosx + c<\/p>\n<p>Question 38.<br \/>\nAnswer:<\/p>\n<p>Let<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66149\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-19.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 19\" width=\"269\" height=\"50\" \/><br \/>\n4x + 5 = A(x + 2) + B(x &#8211; 1)<br \/>\nput x = 1, 4 + 5 = A(1 + 2) + B(0)<br \/>\n9 = 3A \u21d2 A = 3<\/p>\n<p>put x = -2 -8 + 5 = A(0) + B(-2 -1)<br \/>\n-3 = -3B \u21d2 B = 1<\/p>\n<p>\u2234 \\(\\int \\frac{4 x+5}{(x-1)(x+2)} d x=\\int\\left(\\frac{3}{x-1}+\\frac{1}{x+2}\\right) d x\\) =3log(x &#8211; 1) + log(x + 2) +c<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\">Part &#8211; D<\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"color: #0000ff;\">IV. Answer any six questions: (6 \u00d7 5 = 30)<\/span><\/p>\n<p>Question 39.<br \/>\n\\((\\sqrt{3}+1)^{5}-(\\sqrt{3}-1)^{5}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66150\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-20.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 20\" width=\"593\" height=\"240\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-20.png 593w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-20-300x121.png 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><\/p>\n<p>Question 40.<br \/>\n\\(\\frac{x^{2}-10 x+13}{(x+1)\\left(x^{2}-5 x+6\\right)}\\)<br \/>\nAnswer:<br \/>\nLet<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66151\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-21.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 21\" width=\"629\" height=\"59\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-21.png 629w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-21-300x28.png 300w\" sizes=\"(max-width: 629px) 100vw, 629px\" \/><br \/>\nx<sup>2<\/sup> &#8211; 10x + 13 = A(x-2)(x &#8211; 3) + B(x +1) (x &#8211; 3) + C(x + 1) (x &#8211; 2)<br \/>\nPut x=-1, 1 + 10 + 13 = A (-3) (-4) + 0 + 0<br \/>\n24 = 12A \u21d2 A = \\(\\frac{24}{12}\\)=2<br \/>\nPut x = 2, 4 &#8211; 20 + 13 A(0) + B(3) (-1) + C(0)<br \/>\n-3 = -3B \u21d2 B = 1<br \/>\nPut x = 3, 9 &#8211; 30 + 13 = A(0) + B(0) + C(4) (1)<br \/>\n-8 = 47 \u21d2 C= -2<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66152\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-22.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 22\" width=\"405\" height=\"47\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-22.png 405w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-22-300x35.png 300w\" sizes=\"(max-width: 405px) 100vw, 405px\" \/><\/p>\n<p>Question 41.<br \/>\nDefine Tautology and show that (p \u2192 q) + (~ q \u2192 &#8211; p) is a Tautology.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66153\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-23.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 23\" width=\"839\" height=\"195\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-23.png 839w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-23-300x70.png 300w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-23-768x178.png 768w\" sizes=\"(max-width: 839px) 100vw, 839px\" \/><\/p>\n<p>Question 42.<br \/>\nDivide \u20b9 1800 is three parts such that three times of the first, five times of the second and six times the third are equal.<br \/>\nAnswer:<br \/>\nLet the 3 parts be x, y and z<br \/>\nGiven 3x = 5y = 62<br \/>\nLet 3x = 6z and 5y = =\\(\\frac{6}{5} \\)z<br \/>\nx = 2z, y = 2<br \/>\n\u2234 x : y : z = 2z : \\(\\frac{6}{5}\\)z : z= 10:6:5<br \/>\nSum of the ratios = 10 + 6 + 5 = 21<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66154\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-24.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 25\" width=\"790\" height=\"71\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-24.png 790w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-24-300x27.png 300w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-24-768x69.png 768w\" sizes=\"(max-width: 790px) 100vw, 790px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 43.<br \/>\nThe time required to produce the first unit of a product is 1000 hours. If the manufacturers experiences 80% learning effect calculate the average time per unit &amp; the time taken to produce altogether 8 units. Also find the total labour charges for the production of 8 units at the rate of \u20b9 12.50 per hour.<br \/>\nAnswer:<\/p>\n<p>I. Table method<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66156\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-26.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 26\" width=\"568\" height=\"153\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-26.png 568w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-26-300x81.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><br \/>\nTotal time to produce 8 units = 4096 hrs.<br \/>\nGiven labour charges for 1 hour = \u20b9 12.50<br \/>\n\u2234Labour charges for 4096 hours = 4096 x 12.50 = \u20b9 51,200<\/p>\n<p>II. Formula Method:<br \/>\nGiven a = 1000, x = 8 units<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66155\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-25.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 25\" width=\"370\" height=\"116\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-25.png 370w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-25-300x94.png 300w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/><br \/>\ny = ax<sup>b<\/sup><br \/>\nlog y = loga + b log x = log1000 + (-0.3219) log 8<br \/>\n= 3.000 &#8211; 0.3219 x 0.9031 = 3.000 &#8211; 0.2907<br \/>\nlog y = 2.7093<br \/>\ny = AL (2.7093) = 512 hrs. per unit<br \/>\n\u2234 Total time for 8 units = 512 x 8 = 4,096 hrs.<br \/>\nLabour charges per hour = \u20b9 12.50.<br \/>\n\u2234 Labour charges for 4,096 hrs. = 4,096 x 12.50 = 51,200<\/p>\n<p>Question 44.<br \/>\nSolve the following linear programming problems using graphical method<br \/>\nMaximise z = 5x + 3y subject to<br \/>\n3x + 5y \u2264 15<br \/>\n5x + 2y \u2264 10<br \/>\nx \u2265 0, y \u2265 0<br \/>\nAnswer:<br \/>\nConsider 3x + 5y = 15<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66157\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-27.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 27\" width=\"276\" height=\"164\" \/><br \/>\nPlot the lines on the graph.<br \/>\nO ABC is the solution region.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66158\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-28.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 28\" width=\"270\" height=\"213\" \/><br \/>\nX is maximum at B( \\(\\frac{20}{19}, \\frac{45}{19}\\) )<br \/>\nz<sub>max<\/sub> = \\(\\frac{235}{19}\\) = 12.37<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66159\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-29.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 29\" width=\"314\" height=\"326\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-29.png 314w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-29-289x300.png 289w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 45.<br \/>\ncos10\u00b0.cos30\u00b0. cos50\u00b0.cos 70\u00b0 = \\(\\frac { 3 }{ 16 }\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66160\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-30.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 30\" width=\"603\" height=\"265\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-30.png 603w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-30-300x132.png 300w\" sizes=\"(max-width: 603px) 100vw, 603px\" \/><\/p>\n<p>Question 46.<br \/>\nFind the equation of the circle.Passing through the points (5,1), (3,4) and has its centre on the x &#8211; axis.<br \/>\nAnswer:<br \/>\nLet the required equation of the circle is x<sup>2<\/sup> + y<sup>2<\/sup> + 2gx + 2fy + c = 0<br \/>\nIt passes through (5, 1) &amp; (3, 4)<br \/>\n(5, 1) (5)<sup>2<\/sup> + (1)<sup>2<\/sup> + 2g(5) + 2f (1) +C = 0<br \/>\n10g + 2f + C + 26 = 0 &#8230;..(1)<br \/>\n(3,4) 3<sup>2<\/sup> + 4<sup>2<\/sup> + 2g (3) + 2f (4) +c= 0<br \/>\n68 + 8f + C + 25 = 0 &#8230;..(2)<br \/>\n&amp; the centre (- g, &#8211; f) lies on x-axis \u21d2 f = 0 &#8230;.(3)<br \/>\nSolving 1 &amp; 2 we get<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66161\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-31.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 31\" width=\"584\" height=\"236\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-31.png 584w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-31-300x121.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><br \/>\n\u21d2 2x<sup>2<\/sup> + 2y<sup>2<\/sup> &#8211; x &#8211; 47 = 0.<\/p>\n<p>Question 47.<br \/>\nx<sup>logx<\/sup> + (log x)<sup>x<\/sup><br \/>\nAnswer:<br \/>\nLet y = x<sup>logx<\/sup> + (log x)<sup>x<\/sup><br \/>\ny = u + v<br \/>\n\\(\\frac{d y}{d x}=\\frac{d u}{d x}+\\frac{d v}{d x}\\) &#8230;(1)<br \/>\nWhere u = x and v = (log x)<sup>x<\/sup><br \/>\nTaking log<sup>m<\/sup> both sides<br \/>\nlog u = log x . log x log v = x log (log x)<br \/>\nDifferentiate both w.r.t. x<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66162\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-32.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 32\" width=\"428\" height=\"284\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-32.png 428w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-32-300x199.png 300w\" sizes=\"(max-width: 428px) 100vw, 428px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 48.<br \/>\nFind the area bounded by the parabola y<sup>2<\/sup> = 4ax and its latus rectum.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66163\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-33.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 33\" width=\"202\" height=\"208\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66164\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-34.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 34\" width=\"401\" height=\"243\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-34.png 401w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-34-300x182.png 300w\" sizes=\"(max-width: 401px) 100vw, 401px\" \/><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\">Part &#8211; E<\/span><\/p>\n<p><span style=\"color: #0000ff;\">V. Answer any one questions. (1 \u00d7 10 = 10)<\/span><\/p>\n<p>Question 49.<br \/>\n(a) Solve by Matrix Method x + y+ z = 5, 2x + y &#8211; z = 2, 2x &#8211; y + z = 2.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66165\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-35.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 35\" width=\"666\" height=\"432\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-35.png 666w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-35-300x195.png 300w\" sizes=\"(max-width: 666px) 100vw, 666px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66166\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-36.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 36\" width=\"765\" height=\"132\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-36.png 765w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-36-300x52.png 300w\" sizes=\"(max-width: 765px) 100vw, 765px\" \/><\/p>\n<p>OR<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 49.<br \/>\n(a) Show that the following points are concylic.<br \/>\n(0,0), (1,1), (5,-5), (6,-4)<br \/>\nAnswer:<br \/>\nFirst find the equation of the circle passing through the points (0,0) (1, 1) (5,-5) (6,-4)<br \/>\n(0,0) \u21d2 C = 0 &#8230;. (1)<br \/>\n(1, 1) \u21d2 2g + 2f + 2 = 0 &#8230;. (2)<br \/>\n(5,-5) \u21d2 10g -10f + 50 + c = 0 &#8230;. (3)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66167\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-37.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 37\" width=\"268\" height=\"103\" \/><br \/>\n\u2234 The equation of the circle is x<sup>2<\/sup> + y<sup>2<\/sup> &#8211; 6x + 4y = 0<br \/>\nSubstituting the fourth point (6,-4) we get<br \/>\n36 + 16 &#8211; 36 &#8211; 16 = 0 \u21d2 0 = 0<br \/>\n\u2234 The points are concyclic.<\/p>\n<p>Question 49.<br \/>\n(b) Smaran being a manufacturer produces nuts and bolts for industrial machinery. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts while it takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of ? 2.50 per package on nuts and ? 1 per package on bolts. Form a linear programming problem to maximize his profit, if he operates each machine for at most 12 hours a day.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66168\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-38.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 38\" width=\"808\" height=\"144\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-38.png 808w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-38-300x53.png 300w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-38-768x137.png 768w\" sizes=\"(max-width: 808px) 100vw, 808px\" \/><br \/>\nLet the number of units of nuts x &amp; bolts be y it takes 1 hour on machine A for a nut and 3 hours on machine 13 for a nut maximum time available for machine A is 12 hours.<br \/>\n\u2234 x + 3y \u2264 12<br \/>\n3x + y \u2264 12<br \/>\nNegative units cannot be produced: x, y \u2265 0 our objective is to maximum profit the LPP is Maximize = 2.5 x + y subject to<br \/>\nx + 3y \u2264 12<br \/>\n3x + y \u2264 12<br \/>\nand x \u2265 0, y \u2265 0<\/p>\n<p>Question 49.<br \/>\n(b) Find the average cost and Marginal cost if the total cost function of an article is given by c = 5x + 2x + 3(x = quantity).<br \/>\nAnswer:<br \/>\nGiven T.C = C(x) = 5x<sup>2<\/sup> + 2x + 3; M.C = \\(\\frac{d}{d x}\\) (T.C) = 10x + 2<br \/>\nA.C = \\(\\frac{C(x)}{x}=\\frac{T \\cdot C}{x}=\\frac{5 x^{2}+2 x+3}{x}\\) = 5x + 2 + \\(\\frac{3}{x}\\)<\/p>\n<p>Question 50.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66169\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-39.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 39\" width=\"421\" height=\"59\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-39.png 421w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-39-300x42.png 300w\" sizes=\"(max-width: 421px) 100vw, 421px\" \/><br \/>\nAnswer:<br \/>\nCase 1: Let n be a positive integer.<br \/>\nx<sup>n<\/sup> &#8211; a<sup>n<\/sup> = (x &#8211; a)<sup>n<\/sup>(x<sup>n-1<\/sup> + x<sup>n-2<\/sup> . a + x<sup>n-3<\/sup> . a<sup>2<\/sup> + &#8230;. + a<sup>n-1<\/sup>)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66170\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-40.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 40\" width=\"528\" height=\"199\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-40.png 528w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-40-300x113.png 300w\" sizes=\"(max-width: 528px) 100vw, 528px\" \/><br \/>\n= a<sup>n-1<\/sup> + a<sup>n-2<\/sup>.a<sup>2<\/sup> + &#8230;&#8230;. + a<sup>n-1<\/sup> = a<sup>n-1<\/sup> + a<sup>n-1<\/sup> + a<sup>n-1<\/sup> + &#8230;&#8230;. + a<sup>n-1<\/sup><br \/>\n= n . a<sup>n-1<\/sup><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66171\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-41.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 41\" width=\"211\" height=\"56\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Case 2: Let n be a negative integer<br \/>\nPut n = -m, m &gt; 0<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66172\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-42.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 42\" width=\"514\" height=\"312\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-42.png 514w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-42-300x182.png 300w\" sizes=\"(max-width: 514px) 100vw, 514px\" \/><\/p>\n<p>Case 3: Let n = p\/q where p and q are integers and q \u2260 0<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66173\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-43.png\" alt=\"2nd PUC Basic Maths Model Question Paper 1 with Answers - 43\" width=\"647\" height=\"450\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-43.png 647w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Model-Question-Paper-1-with-Answers-43-300x209.png 300w\" sizes=\"(max-width: 647px) 100vw, 647px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>(b). Use binomial theorem to evaluate upto 4 decmials place (102)<sup>6<br \/>\n<\/sup>Answer:<br \/>\n(102)<sup>6<\/sup> = (100 + 2)<sup>6<\/sup><br \/>\n= (100)<sup>6<\/sup> + <sup>6<\/sup>C<sub>1<\/sub>(1 0O)<sup>5<\/sup>. 2 + <sup>6<\/sup>C<sub>2<\/sub>(100)<sup>4<\/sup>.2<sup>2 <\/sup>+ <sup>6<\/sup>C<sub>3<\/sub>(100)<sup>3<\/sup>.2<sup>3<\/sup> +\u00a0<sup>6<\/sup>C<sub>4<\/sub>(100)<sup>2<\/sup> 2<sup>4<\/sup> + <sup>6<\/sup>C<sub>5<\/sub>.100.2<sup>5<\/sup> + <sup>6<\/sup>C<sub>6<\/sub>2<sup>6<\/sup><br \/>\n= 1000000000000 + 120000000000 + 6000000000 + 160000000 + 2400000 + 19200 + 64<br \/>\n= 1,126,162,419,264<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Students can Download 2nd PUC Basic Maths Model Question Paper 1 with Answers, Karnataka 2nd PUC Maths Model Question Papers with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations. Karnataka 2nd PUC Basic Maths Model Question Paper 1 with Answers Time: 3.15 hours Max. Marks: &hellip;<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[82],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/21305"}],"collection":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/comments?post=21305"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/21305\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=21305"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=21305"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=21305"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}