{"id":21683,"date":"2020-01-28T10:58:06","date_gmt":"2020-01-28T05:28:06","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=21683"},"modified":"2021-07-02T15:26:28","modified_gmt":"2021-07-02T09:56:28","slug":"2nd-puc-basic-maths-previous-year-question-paper-march-2019","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/2nd-puc-basic-maths-previous-year-question-paper-march-2019\/","title":{"rendered":"2nd PUC Basic Maths Previous Year Question Paper March 2019"},"content":{"rendered":"<p>Students can Download 2nd PUC Basic Maths Previous Year Question Paper March 2019, 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 Previous Year Question Paper March 2019<\/h2>\n<p>Time: 3 Hours 15 Min.<br \/>\nMax.Markss: 100<\/p>\n<p>Instructions:<\/p>\n<ul>\n<li>Write SI Nos of question correctly<\/li>\n<li>Visually challenged students need to answer Question No 31(B) instead of map Question No 31(A) in Part D<\/li>\n<li>Answer the questions according to the instructions given for the questions<\/li>\n<\/ul>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\">Part A<\/span><\/p>\n<p><span style=\"color: #0000ff;\">Answer all the Questions: (10 \u00d7 1 = 10)<\/span><\/p>\n<p>Question 1.<br \/>\nIf A = \\(\\left[ \\begin{matrix} 1 &amp; -2 \\\\ 3 &amp; 4 \\end{matrix} \\right] \\) then find 2A&#8217;.<br \/>\nAnswer:<br \/>\n2A&#8217; = \\(\\left[ \\begin{matrix} 2 &amp; 6 \\\\ -4 &amp; 8 \\end{matrix} \\right]\\)<\/p>\n<p>Question 2.<br \/>\nIn how many ways can 10 people be seated around a table?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65959\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-1.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2019 - 1\" width=\"122\" height=\"26\" \/><\/p>\n<p>Question 3.<br \/>\nSymbolise the proposition:<br \/>\n&#8220;If Oxygen is a gas then gold is a compound&#8221;.<br \/>\nAnswer:<br \/>\np \u2192 9<\/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 triplicate ratio of 5 : 4.<br \/>\nAnswer:<br \/>\n5<sup>3<\/sup> : 4<sup>3<\/sup> or 125 : 64<\/p>\n<p>Question 5.<br \/>\nFind the income obtained by investing \u20b9 3,600 in 5% stock at 90.<br \/>\nAnswer:<br \/>\nIncome = \\(\\frac{5 \\times 3600}{90}\\) = \u20b9200<\/p>\n<p>Question 6.<br \/>\nExpress sin 5A cos 3A as sum of difference of two trigonometric functions.<br \/>\nAnswer:<br \/>\n\\(\\frac { 1 }{ 2 }\\)[sin8A + sin 2A]<\/p>\n<p>Question 7.<br \/>\nFind the centre of the circle x<sup>2<\/sup> + y<sup>2<\/sup> &#8211; 4xy &#8211; 5 = 0.<br \/>\nAnswer:<br \/>\n\\(\\left(2,+\\frac{1}{2}\\right)\\)<\/p>\n<p>Question 8.<br \/>\nEvaluate : \\(\\lim _{x \\rightarrow 3}\\left(\\frac{x^{2}-4 x}{x-2}\\right)\\)<br \/>\nAnswer:<br \/>\n-3<\/p>\n<p>Question 9.<br \/>\nDifferentiate (5e<sup>x<\/sup> &#8211; logx &#8211; 3\u221ax) with respect to x.<br \/>\nAnswer:<br \/>\n\\(5 e^{x}-\\frac{1}{x}-\\frac{3}{2 \\sqrt{x}}\\)<\/p>\n<p>Question 10.<br \/>\nIntegrate (x<sup>2<\/sup> &#8211; \\(\\frac { 6 }{ x }\\) + 5e<sup>x<\/sup>) with respect to x.<br \/>\nAnswer:<br \/>\n\\(\\frac{x^{3}}{3} 6 \\log _{e} x+5 e^{x}+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- B<\/span><\/p>\n<p><span style=\"color: #0000ff;\">Answer any ten of the following Questions. (10 \u00d7 2 = 20)<\/span><\/p>\n<p>Question 11.<br \/>\nIf A = \\(\\left[ \\begin{matrix} 1 &amp; 3 &amp; -1 \\\\ -1 &amp; 0 &amp; 2 \\end{matrix} \\right] \\) and B = \\(\\left[ \\begin{matrix} 4 &amp; -1 &amp; 2 \\\\ 1 &amp; 3 &amp; -2 \\end{matrix} \\right] \\)<br \/>\nAnswer:<br \/>\n3B = \\(\\left[ \\begin{matrix} 12 &amp; -3 &amp; 6 \\\\ -4 &amp; -9 &amp; 8 \\end{matrix} \\right] \\)<br \/>\n\u2234 A = 3B = \\(\\left[ \\begin{matrix} -11 &amp; 6 &amp; -7 \\\\ -4 &amp; -9 &amp; 8 \\end{matrix} \\right] \\)<\/p>\n<p>Question 12.<br \/>\nIn how many ways the word &#8220;CARROM&#8221; be arranged such that the 2R&#8217;s are always together?<br \/>\nAnswer:<br \/>\n\u20b9 2 as 1 unit<br \/>\n\u2234 No. of letters = 6 &#8211; 2 + 1 = 5<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65958\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-2.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2019 - 2\" width=\"183\" height=\"26\" \/><\/p>\n<p>Question 13.<br \/>\nA box contains 8 red marbles 6 green marbles and 10 pink marbles. One marble in drawn at random from the box. What is the probability that the marble drawn is either red or green?<br \/>\nAnswer:<br \/>\nWriting 8R + 6G + 10P = 24 OR No. of R &amp; G = 14<br \/>\n\u2234 Probability = \\(\\frac{14}{24}=\\frac{7}{12}\\)<\/p>\n<p>Question 14.<br \/>\nIf the truth values of the propositions p,q,r are T,T,F respectively, then find the truth values of p \u2192 (q <sup>\u2227<\/sup> r).<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65957\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-3.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2019 - 3\" width=\"170\" height=\"51\" \/><\/p>\n<p>Question 15.<br \/>\nWhat must be added to each term in the ratio 5 : 6 so that it becomes 8 : 9?<br \/>\nAnswer:<br \/>\nLet x be added<br \/>\n\\(\\therefore \\quad \\frac{5+x}{6+x}=\\frac{8}{9}\\)<br \/>\nSolving to get x = 3<\/p>\n<p>Question 16.<br \/>\nTrue discount on a bill was \u20b9 900 and Banker&#8217;s gain was \u20b9 27. What is the face value of the bill?<br \/>\nAnswer:<br \/>\nGetting BD = \u20b9 927<br \/>\n\u20b9 F = Rs. 30,900<\/p>\n<p>Question 17.<br \/>\nFind the value of cos 15\u00b0.<br \/>\nAnswer:<br \/>\ncos 15\u00b0 = cos (45\u00b0 &#8211; 30\u00b0)<br \/>\n= cos 45\u00b0. cos30\u00b0 + sin 45\u00b0. sin 30\u00b0<br \/>\nGetting answer = \\(\\frac{\\sqrt{3}+1}{2 \\sqrt{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 18.<br \/>\nIf tan A = \\(\\frac { 1 }{ 2 }\\), tan B = \\(\\frac { 1 }{ 3 }\\), then find tan (A + B).<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65956\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-4.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2019 - 4\" width=\"291\" height=\"82\" \/><br \/>\nSimplifying to get answer = 1<\/p>\n<p>Question 19.<br \/>\nFind the equation of parabola whose vertex is (0,0) and focus is (3,0).<br \/>\nAnswer:<br \/>\nIdentifying y<sup>2<\/sup> = 4ax<br \/>\nGetting a = 3 and hence y<sup>2<\/sup> = 12x<\/p>\n<p>Question 20.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65955\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-5.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2019 - 5\" width=\"553\" height=\"53\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-5.png 553w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-5-300x29.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><br \/>\nAnswer:<br \/>\nGetting LHL = 0 and RHL = -2<br \/>\nConcluding f(x) is not continuous at x = 1.<\/p>\n<p>Question 21.<br \/>\nIf y = (a<sup>2<\/sup> &#8211; x<sup>2<\/sup>)<sup>10<\/sup>, find \\(\\frac{d y}{d x}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{d y}{d x}\\) = 10(a<sup>2<\/sup> &#8211; x<sup>2<\/sup>)<sup>9<\/sup>(0 &#8211; 2x)<br \/>\n= &#8211; 20x(a<sup>2<\/sup> &#8211; x<sup>2<\/sup>)<sup>9<\/sup><\/p>\n<p>Question 22.<br \/>\nIf the cost function of a firm is given by C(x) = x<sup>3<\/sup> &#8211; 3x + 7. Find the average cost and marginal cost.<br \/>\nAnswer:<br \/>\nAC = x<sup>2<\/sup> &#8211; 3 + \\(\\frac{7}{x}\\)<br \/>\nMC = 3x<sup>2<\/sup> &#8211; 3<\/p>\n<p>Question 23.<br \/>\nEvaluate : \\(\\int \\frac{4 x+3}{2 x^{2}+3 x+5} d x\\)<br \/>\nAnswer:<br \/>\nSubstituting 2x<sup>2<\/sup> + 3x + 5 = t<br \/>\n\u2234 (4x + 3)dx = dt<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65954\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-6.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2019 - 6\" width=\"300\" height=\"77\" \/><\/p>\n<p>Question 24.<br \/>\nEvaluate : \\(\\int_{1}^{2} x e^{4} d x\\)<br \/>\nAnswer:<br \/>\nWriting \\(\\left[x e^{x}\\right]_{1}^{2}-\\int_{1}^{2} e^{x} \\cdot 1 d x\\)<br \/>\nSimplifying to get answer = e<sup>2<\/sup>.<\/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-C<\/span><\/p>\n<p><span style=\"color: #0000ff;\">Answer any ten of the following questions: (10 \u00d7 3 = 30)<\/span><\/p>\n<p>Question 25.<br \/>\nIf A = \\(\\left[ \\begin{matrix} 2 &amp; 3 \\\\ -4 &amp; 1 \\end{matrix} \\right] \\) and B = \\(\\left[ \\begin{matrix} -1 &amp; 5 \\\\ 6 &amp; 2 \\end{matrix} \\right] \\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65953\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-7.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2019 - 7\" width=\"781\" height=\"256\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-7.png 781w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-7-300x98.png 300w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-7-768x252.png 768w\" sizes=\"(max-width: 781px) 100vw, 781px\" \/><\/p>\n<p>Question 26.<br \/>\nProve that: \\(\\left| \\begin{matrix} 1+a &amp; b &amp; c \\\\ a &amp; 1+b &amp; c \\\\ a &amp; b &amp; 1+c \\end{matrix} \\right| \\) = 1 + a + b + c<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65952\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-8.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2019 - 8\" width=\"530\" height=\"275\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-8.png 530w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-8-300x156.png 300w\" sizes=\"(max-width: 530px) 100vw, 530px\" \/><\/p>\n<p>Question 27.<br \/>\nFrom a class of 9 boys and 7 girls 12 students are to be chosen for a competition which includes atleast 6 boys and atleast 4 girls. In how many ways can this be done if a particular boys is always chosen?<br \/>\nAnswer:<br \/>\nNo. of ways<br \/>\n= <sup>8<\/sup>C<sub>5<\/sub> \u00d7 <sup>7<\/sup>C<sub>6<\/sub> + <sup>8<\/sup>C<sub>6<\/sub> \u00d7 <sup>7<\/sup>C<sub>5<\/sub> + <sup>8<\/sup>C<sub>7<\/sub> \u00d7 <sup>7<\/sup>C<sub>4<\/sub><br \/>\n= 56 \u00d7 7 + 28 \u00d7 21 + 8 \u00d7 35 = 1260<\/p>\n<p>Question 28.<br \/>\nA couple appears in an interview for two vacancies in the same post. The probability of husband getting selected is \\(\\frac { 1 }{ 7 }\\) and the probability of wife getting selected is \\(\\frac { 1 }{ 5 }\\) . What is the probability that<br \/>\na. Both of them will be selected?<br \/>\nb. Only one of them will be selected?<br \/>\nc. None of them will be selected?<br \/>\nAnswer:<br \/>\nWriting:<br \/>\nP(husband not selected) = \\(\\frac { 6 }{ 7 }\\)\u00a0 and<br \/>\nP(Wife not selected) = \\(\\frac { 4 }{ 5 }\\)<br \/>\n(OR) Getting:<br \/>\na. P(Both slected) = \\(\\frac { 1 }{ 35 }\\)<br \/>\nb. P(Only one selected) = \\(\\frac { 10 }{ 35 }\\) = \\(\\frac { 2 }{ 7 }\\)<br \/>\nC. P(None selected) = \\(\\frac { 24 }{ 35 }\\)<\/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 29.<br \/>\nIn a fort, there was ration for 560 soldiers that would last the soldiers for 70 days after 20 days, 60 soldiers left the fort. For how many days the remaining ration can support the remaining soldiers?<br \/>\nAnswer:<br \/>\nWriting:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65951\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-9.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2019 - 9\" width=\"361\" height=\"138\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-9.png 361w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-9-300x115.png 300w\" sizes=\"(max-width: 361px) 100vw, 361px\" \/><br \/>\nWriting:<br \/>\n560 : 500 = x : 50<br \/>\n\u21d2 x = 56 days<\/p>\n<p>Question 30.<br \/>\nFor 512.50 due 6 months at 15% p.a. Find the true present value and discounted cash value.<br \/>\nAnswer:<br \/>\nP = \\(\\frac{F}{1+t r}\\) = \u20b9 7476.74<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65950\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-10.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2019 - 10\" width=\"208\" height=\"54\" \/><br \/>\nOR<br \/>\nGetting P = \u20b9 476.74<br \/>\nGetting BD = F.tr = \u20b9 38.43<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65949\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-11.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2019 - 11\" width=\"256\" height=\"53\" \/><\/p>\n<p>Question 31.<br \/>\nSanjana invests 7 3240 in a stock at 108 and sells when price falls to 104. How much stock at 130 can Sanjana now by?<br \/>\nAnswer:<br \/>\nCase 1: (Buying) stock at 108<br \/>\nWorth of stock purchased = \\(\\frac{100 \\times 3240}{108}\\)<br \/>\n= \u20b9 3000<\/p>\n<p>Case 2: Stock sold at 104<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65948\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-12.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2019 - 12\" width=\"245\" height=\"66\" \/><\/p>\n<p>Case 3: Stock sold at 130<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65947\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-13.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2019 - 13\" width=\"199\" height=\"62\" \/><\/p>\n<p>Question 32.<br \/>\nSanju goes to a shop to buy a bicycle quoted at \u20b9 2,000. The rate of sales tax is 12% on it. He asks the shopkeeper for a rebate on the price of the bicycle to such an extent that he has to pay \u20b9 2016 inclusive of sales tax. Find the rebate percentage on the price of the bicycle.<br \/>\nAnswer:<br \/>\nSP = 2016, ST = 12% Let MP = X<br \/>\nSP = MP + 12% MP<br \/>\n\u2234 2016 = x + 0.12%<br \/>\n\u21d2 x = 1800<br \/>\n\u21d2 Rebate = 2000 &#8211; 1800 = \u20b9 200<br \/>\nRebate \\(\\%=\\frac{200}{2000} \\times 100=10 \\%\\)<\/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 33.<br \/>\nFind the equation of parabola when vertex is (0,0) and axis is y-axis and passes through the point(-1,-3)<br \/>\nAnswer:<br \/>\nIdentifying x<sup>2<\/sup> = 4ay [or x<sup>2<\/sup> = &#8211; 4ay]<br \/>\nSubstituting x = -1, y = -3<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65946\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-14.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2019 - 14\" width=\"360\" height=\"120\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-14.png 360w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-14-300x100.png 300w\" sizes=\"(max-width: 360px) 100vw, 360px\" \/><\/p>\n<p>Question 34.<br \/>\nDifferentiate y = \\(\\frac{e^{x}-1}{e^{x}+1}\\) with respect to x.<br \/>\nAnswer:<br \/>\n\\(\\frac{d y}{d x}=\\frac{\\left(e^{x}+1\\right) e^{x}-\\left(e^{x}-1\\right)\\left(e^{x}\\right)}{\\left(e^{x}+1\\right)^{2}}\\)<br \/>\nSubstituting x = -1, y=-3.<\/p>\n<p>Question 35.<br \/>\nFind the maximum and minimum value of y = x<sup>3<\/sup> &#8211; 9x<sup>2<\/sup> + 15 x &#8211; 1.<br \/>\nAnswer:<br \/>\nFor max or min.<br \/>\n\\(\\frac{d y}{d x}\\) = 0 \u21d2 3x<sup>2<\/sup> &#8211; 18x + 5 = 0<br \/>\nGetting x = 1, x = 5<br \/>\n\\(\\frac{d^{2} y}{d x^{2}}\\) 6x &#8211; 18<br \/>\nAt x = 1, \\(\\frac{d^{2} y}{d x^{2}}\\) = -12<br \/>\n\u2234 y has max at x = 1<br \/>\n\u21d2 y<sub>min<\/sub> = 6<br \/>\nAt x = 5, \\(\\frac{d^{2} y}{d x^{2}}\\) = 12<br \/>\n\u2234 y has min at x = 5<br \/>\n\u21d2 y<sub>min<\/sub> = -26<\/p>\n<p>Question 36.<br \/>\nA square plate is expanding uniformly, the side is increasing at the rate of 5cm \/ sec what is the rate at which the area and its perimeter is increasing when the side is 20 cm long?<br \/>\nAnswer:<br \/>\nArea, A = l<sup>2<\/sup> \u21d2 \\(\\frac{\\mathrm{d} \\mathrm{A}}{\\mathrm{dt}}\\) = 2l \u00d7 \\(\\frac{\\mathrm{d} l}{\\mathrm{dt}}\\)<br \/>\n= 2 \u00d7 20 \u00d7 5<br \/>\n\\(\\frac{\\mathrm{d} \\mathrm{A}}{\\mathrm{dt}}\\) = 200cm<sup>2<\/sup> \/ sec.<br \/>\nP = 41 \u21d2 \\(\\frac{\\mathrm{d} \\mathrm{P}}{\\mathrm{dt}}\\) = 4 \\(\\frac{\\mathrm{d} l}{\\mathrm{dt}}\\) 4 \u00d7 5= 20cm \/ sec<\/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 37.<br \/>\nIntegrate x<sup>2<\/sup> sin x with respect to x.<br \/>\nAnswer:<br \/>\n\u222bx sin xdx = -x<sup>2<\/sup> cosx &#8211; \u222b -cosx.2xdx<br \/>\n= -x<sup>2<\/sup> cosx + 2[xsinx &#8211; \u222bsinx.dx]<br \/>\n= -x<sup>2<\/sup> cosx + 2xsinx + 2cosx + C<\/p>\n<p>Question 38.<br \/>\nEvaluate: \u222b(2x + 3)(x<sup>2<\/sup> + 3x + 5)<sup>3\/2<\/sup> dx.<br \/>\nAnswer:<br \/>\nSubstituting x<sup>2<\/sup> &#8211; 3x + 5 = t to get (2x + 3) dx = dt<br \/>\n\u2234 Given integral becomes \u222bt<sup>3\/2<\/sup>dt<br \/>\nIntegrating to get \\(\\frac{t^{52}}{52}+C=\\frac{2}{5}\\left(x^{2}+3 x+5\\right)^{52}+C\\)<\/p>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\">Part &#8211; D<\/span><\/p>\n<p><span style=\"color: #0000ff;\">Answer any six questions: (6 \u00d7 5 = 30)<\/span><\/p>\n<p>Question 39.<br \/>\nFind the middle term in the expansion of \\(\\left(\\frac{2 x^{2}}{3}-\\frac{3}{2 x}\\right)^{10}\\)<br \/>\nAnswer:<br \/>\nIdentifying middle term as T<sub>6<\/sub><br \/>\nT<sub>r+1<\/sub> = <sup>10<\/sup>C<sub>r<\/sub>\\(\\left(\\frac{2 x^{2}}{3}\\right)^{10-r}\\left(\\frac{-3}{2 x}\\right)^{r}\\)<br \/>\nSubstituting r= 5 and simplifying to get T<sub>6<\/sub> = -252x<sup>5<\/sup>.<\/p>\n<p>Question 40.<br \/>\nResolve \\(\\frac{x-1}{x(x+2)(x+4)}\\) into partial fractions.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65945\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-15.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2019 - 15\" width=\"231\" height=\"44\" \/><br \/>\nGetting Getting A = \\(-\\frac { 1 }{ 8 }\\) B = \\(\\frac { 3 }{ 4 }\\) C = \\(\\frac { -5 }{ 8 }\\)<br \/>\nConclusion<\/p>\n<p>Question 41.<br \/>\nVerify whether the proposition (~p^q)^~r is a tautology or a contradiction or neither.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65944\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-16.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2019 - 16\" width=\"387\" height=\"277\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-16.png 387w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-16-300x215.png 300w\" sizes=\"(max-width: 387px) 100vw, 387px\" \/><\/p>\n<p>Question 42.<br \/>\nWalking 4 kmph a student reaches his college 5 minutes late and if he walks at 5 kmph he reaches \\(2 \\frac{1}{2}\\) minutes early. What is the distance from his house to the college?<br \/>\nAnswer:<br \/>\nLet required distance = x kms<br \/>\nAt 4 kmph, time taken = \\(\\frac { x }{ 4 }\\)<br \/>\nAt 5 kmph, time taken = \\(\\frac { x }{ 5 }\\)<br \/>\nGiven \\(\\frac{x}{4}=\\frac{5}{60}=\\frac{x}{5}+\\frac{2.5}{60} s\\)<br \/>\nGetting x = 2.5 km<\/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 \/>\nA motor company Ltd. Has observed that a 90\u00b0 learning effect applies to all labour related costs whenever a new product is taken up for production the anticipated production to 320 units. For the coming year. The at \u20b9 15\/hour. Calculate the total labour hours and labour cost to manufacture 320 units.<br \/>\nAnswer:<br \/>\n10 units = 1 lot<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65943\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-17.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2019 - 17\" width=\"860\" height=\"220\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-17.png 860w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-17-300x77.png 300w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-17-768x196.png 768w\" sizes=\"(max-width: 860px) 100vw, 860px\" \/><br \/>\n\u2234 Total hours = 18,895.68<br \/>\nTotal labour cost = 18,956.68 \u00d7 15 = \u20b9 2,83,435.20<\/p>\n<p>Question 44.<br \/>\nSolve the following LPP graphically:<br \/>\nMaximize Z = 60x + 15y<br \/>\nSubjected to the constraints: x + y \u2264 50<br \/>\n3x + y \u2264 90<br \/>\nAnd x, y \u2265 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65942\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-18.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2019 - 18\" width=\"405\" height=\"312\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-18.png 405w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-18-300x231.png 300w\" sizes=\"(max-width: 405px) 100vw, 405px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65941\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-19.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2019 - 19\" width=\"311\" height=\"192\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-19.png 311w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-19-300x185.png 300w\" sizes=\"(max-width: 311px) 100vw, 311px\" \/><\/p>\n<p>Question 45.<br \/>\nIf A + B + C = 180\u00b0, then prove that sin 2A + sin 2B + sin 2C = 4 sin A sin B sin C.<br \/>\nAnswer:<br \/>\nsin 2A + sin 2B + sin 2C<br \/>\n\\(=2 \\sin \\left(\\frac{2 \\mathrm{A}+2 \\mathrm{B}}{2}\\right) \\cdot \\cos \\left(\\frac{2 \\mathrm{A}-2 \\mathrm{B}}{2}\\right)+2 \\sin \\mathrm{C} \\cos C\\)<br \/>\n= 2 sin C. cos (A &#8211; B) + 2 sin C. cos C<br \/>\n= 2 sin C (cos(A &#8211; B) + cos C]<br \/>\n= 2 sin C[cos (A &#8211; B) + cos {180 &#8211; (A + B)}]<br \/>\n= 2 sin C[cos (A &#8211; B) &#8211; cos (A + B)]<br \/>\n= 2 sin C[-2 sin A . sin(- B)]<br \/>\n= 4 sin A. sin B.sin C<\/p>\n<p>Question 46.<br \/>\nFind the equation of the circle passing through the points (5,3), (1,5) and (3,-1).<br \/>\nAnswer:<br \/>\nGetting 3 equations as<br \/>\n10g + 6f + C = &#8211; 34<br \/>\n2g + 10f + C = -26<br \/>\n6g &#8211; 2f + C = &#8211; 10<br \/>\nSolving to get g = -, f = -2, C = -2<br \/>\nFinal equation: x<sup>2<\/sup> + y<sup>2<\/sup> &#8211; 4x &#8211; 4y &#8211; 2 = 0<\/p>\n<p>Question 47.<br \/>\nIf y = log\\((x+\\sqrt{x^{2}+1})\\) show that (x<sup>2<\/sup> + 1)y<sub>2<\/sub> + xy<sub>1<\/sub> = 0.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65940\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-20.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2019 - 20\" width=\"305\" height=\"349\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-20.png 305w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-20-262x300.png 262w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><\/p>\n<p>Question 48.<br \/>\nFind the area bounded by the parabola y<sup>2<\/sup> = 4x and the line x = y.<br \/>\nAnswer:<br \/>\ny<sup>2<\/sup> = 4x &#8230; (1)<br \/>\nx = y &#8230;. (2)<br \/>\n(1) &amp; (2) \u21d2 x = 0, x = 4<br \/>\nRequired area<br \/>\n\\(=\\int_{0}^{4}[f(x)-g(x)] d x\\)<br \/>\n\\(=\\int_{0}^{4}[2 \\sqrt{x}-x] d x=\\left[2 \\times \\frac{2}{3} x^{3 \/ 2}-\\frac{x^{2}}{2}\\right]_{0}^{4}\\)<br \/>\n\\(=\\frac{32}{3}-\\frac{16}{2}=\\frac{8}{3}\\) sq.units<\/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; E<\/span><\/p>\n<p><span style=\"color: #0000ff;\">Answer any one of the following questions: (1 \u00d7 10 = 10)<\/span><\/p>\n<p>Question 49.<br \/>\n(a). A sales person Samanth has the following record of sales. He is paid a commission at fixed rate per unit but varying rates for products P, Q and R.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65939\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-21.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2019 - 21\" width=\"498\" height=\"134\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-21.png 498w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-21-300x81.png 300w\" sizes=\"(max-width: 498px) 100vw, 498px\" \/><br \/>\nFind the rate of commission payable on P, Q and R per unit sold<br \/>\nAnswer:<br \/>\nLet rates of commission per unit of sales be<br \/>\nx,y and z for P, Q and Rrespectively<br \/>\nWriting 9x + 10y + 2z = 780<br \/>\n15x + 5y + 4z = 900<br \/>\n6x + 10y + 3z = 820<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65938\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-22.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2019 - 22\" width=\"341\" height=\"355\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-22.png 341w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-22-288x300.png 288w\" sizes=\"(max-width: 341px) 100vw, 341px\" \/><br \/>\nNote: Proportionate marks should be given to any other appropriate method.<\/p>\n<p>(b). Find the value of (12.)<sup>5<\/sup>5 using Binomial theorem upto 4 places of decimals.<br \/>\nAnswer:<br \/>\n(1.2)<sup>5<\/sup>5 = (1 + 0.2)<sup>5<\/sup>5<br \/>\n= 1<sup>5<\/sup>5 + <sup>5<\/sup>C<sub>1<\/sub>(0.2) + <sup>5<\/sup>C<sub>2<\/sub>(0.2)<sup>2<\/sup>\u00a0+ <sup>5<\/sup>C<sub>3<\/sub>(0.2)<sup>3<\/sup>\u00a0+ <sup>5<\/sup>C<sub>4<\/sub>(0.2)<sup>4<\/sup> + (0.2)<sup>5<\/sup><br \/>\n= 1 + 5(0.2) + 10 (0.04) + 10(0.008) + 5(00004) + (0.00032)<br \/>\n= 2.4883<\/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 50.<br \/>\n(a). If&#8217;n&#8217; is a rational number and &#8216;a&#8217; is a non zero real number, then prove that \\(\\lim _{x \\rightarrow-}\\left(\\frac{x^{n}-a^{n}}{x-a}\\right)=n a^{n-1}\\)<br \/>\nAnswer:<br \/>\nProof for n positive integer<br \/>\nProof for n negative integer<br \/>\nProof for n rational number<\/p>\n<p>(b). A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 60\u00b0. When he returns 80 mts from the bank he finds the angle to be 30\u00b0. Find the height of the tree and the width of the river.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65937\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2019-23.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2019 - 23\" width=\"263\" height=\"270\" \/><br \/>\ntan 60\u00b0 = \\(\\frac { h }{ x }\\) \u2234 \u221a3 = \\(\\frac { h }{ x }\\) &#8230;. (1)<br \/>\ntan 30\u00b0 = \\(\\frac{h}{x+80}\\) \u2234 \\(\\frac{1}{\\sqrt{3}}=\\frac{h}{x+80}\\) &#8230;. (2)<br \/>\nSolving (1) &amp; (2) to get h = 40\u221a3m<br \/>\nAnd x = 40 m<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Students can Download 2nd PUC Basic Maths Previous Year Question Paper March 2019, 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 Previous Year Question Paper March 2019 Time: 3 Hours 15 Min. &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\/21683"}],"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=21683"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/21683\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=21683"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=21683"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=21683"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}