{"id":27329,"date":"2020-06-29T12:00:40","date_gmt":"2020-06-29T06:30:40","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=27329"},"modified":"2021-07-02T15:19:13","modified_gmt":"2021-07-02T09:49:13","slug":"2nd-puc-maths-previous-year-question-paper-march-2018","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/2nd-puc-maths-previous-year-question-paper-march-2018\/","title":{"rendered":"2nd PUC Maths Previous Year Question Paper March 2018"},"content":{"rendered":"<p>Students can Download 2nd PUC Maths Previous Year Question Paper March 2018, Karnataka <a href=\"https:\/\/kseebsolutions.guru\/2nd-puc-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 Maths Previous Year Question Paper March 2018<\/h2>\n<p>Time: 3 Hrs 15 Min<br \/>\nMax. Marks: 100<\/p>\n<p>Instructions<\/p>\n<ul>\n<li>The question paper has five parts namely A, B, C, D, and E. Answer all the parts.<\/li>\n<li>Use the graph sheet for the question on Linear programming in Part &#8211; E<\/li>\n<\/ul>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\">Part &#8211; A<\/span><\/p>\n<p><span style=\"color: #0000ff;\">Answer ALL the following questions: (10 \u00d7 1 = 10)<\/span><\/p>\n<p>Question 1.<br \/>\nDefine the bijective function.<br \/>\nSolution:<br \/>\nA function f: A \u2192 B is said to be bijective if it is both one-one and onto.<\/p>\n<p>Question 2.<br \/>\nWrite the principal value brach of cos<sup>-1<\/sup> x.<br \/>\nSolution:<br \/>\n(o, \u03c0)<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 3.<br \/>\nConstruct a 2 \u00d7 2 matrix, A = [a<sub>ij<\/sub>], whose elements are given by, a<sub>ij<\/sub> = \\(\\frac{i}{j}\\)<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63395\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q3.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q3\" width=\"246\" height=\"136\" \/><\/p>\n<p>Question 4.<br \/>\nIf A is an invertible matrix of order 2 then find |A<sup>-1<\/sup>|.<br \/>\nSolution:<br \/>\n|A<sup>-1<\/sup>| = \\(\\frac{1}{|A|}\\)<\/p>\n<p>Question 5.<br \/>\nIf y = \\(e^{x^{3}}\\), find \\(\\frac{d y}{d x}\\)<br \/>\nSolution:<br \/>\n\\(\\frac{d y}{d x}=e^{x^{2}} \\cdot 3 x^{2}\\)<\/p>\n<p>Question 6.<br \/>\nFind: \\(\\int \\frac{x^{3}-1}{x^{2}} d x\\)<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63396\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q6.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q6\" width=\"328\" height=\"61\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q6.png 328w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q6-300x56.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><\/p>\n<p>Question 7.<br \/>\nFind the unit vector in the direction of the vector \\(\\vec{a}=\\hat{i}+\\hat{j}+2 \\hat{k}\\)<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63397\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q7.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q7\" width=\"164\" height=\"63\" \/><\/p>\n<p>Question 8.<br \/>\nIf a line makes angle 90\u00b0, 60\u00b0 and 30\u00b0with the positive direction of x, y and z-axis respectively, find its direction cosines.<br \/>\nSolution:<br \/>\ncos 90\u00b0 = 0, cos 60\u00b0 = \\(\\frac {1}{2}\\), cos 30\u00b0 = \\(\\frac { \\sqrt { 3 } }{ 2 }\\)<br \/>\ndc&#8217;s are 0, \\(\\frac {1}{2}\\), \\(\\frac { \\sqrt { 3 } }{ 2 }\\)<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 9.<br \/>\nDefine the optimal solution in a linear programming problem.<br \/>\nSolution:<br \/>\nAny feasible solution of LPP which maximizes or minimizes the objective function is called an optimal solution.<\/p>\n<p>Question 10.<br \/>\nIf P(A) = \\(\\frac{7}{13}\\), P(B) = \\(\\frac{9}{13}\\) and P(A \u2229 B) = \\(\\frac{4}{13}\\), find P(A\/B)<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63399\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q10.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q10\" width=\"248\" height=\"80\" \/><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\">Part &#8211; B<\/span><\/p>\n<p><span style=\"color: #0000ff;\">Answer any TEN questions: (10 \u00d7 2 = 20)<\/span><\/p>\n<p>Question 11.<br \/>\nLet * be a binary operation on Q, defined by a * b = \\(\\frac{a b}{2}\\), \u2200 a, b \u2208 Q<\/p>\n<p>Question 12.<br \/>\nsin(\\(\\sin ^{-1} \\frac{1}{5}+\\cos ^{-1} x\\)) = 1 then find the value of x.<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63398\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q9.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q9\" width=\"450\" height=\"130\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q9.png 450w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q9-300x87.png 300w\" sizes=\"(max-width: 450px) 100vw, 450px\" \/><\/p>\n<p>Question 13.<br \/>\nWrite the simplest from of \\(\\tan ^{-1}\\left(\\frac{\\cos x-\\sin x}{\\cos x+\\sin x}\\right)\\), 0 &lt; x &lt; \\(\\frac{\\pi}{2}\\)<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63401\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q13.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q13\" width=\"483\" height=\"192\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q13.png 483w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q13-300x119.png 300w\" sizes=\"(max-width: 483px) 100vw, 483px\" \/><\/p>\n<p>Question 14.<br \/>\nFind the area of the triangle whose vertices are (-2, -3), (3, 2) and (-1, -8) by using the determinant method.<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63402\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q14.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q14\" width=\"290\" height=\"177\" \/><\/p>\n<p>Question 15.<br \/>\nDifferentiate x<sup>sin x<\/sup>, x &gt; 0 with respect to x.<br \/>\nSolution:<br \/>\nLet y = x<sup>sin x<\/sup><br \/>\nTaking logarithm on both sides, we have<br \/>\nlog y = sin x log x<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63404\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q15.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q15\" width=\"437\" height=\"168\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q15.png 437w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q15-300x115.png 300w\" sizes=\"(max-width: 437px) 100vw, 437px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63403\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q15.1.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q15.1\" width=\"236\" height=\"95\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 16.<br \/>\nFind \\(\\frac{d y}{d x}\\), if x<sup>2<\/sup> + xy + y<sup>2<\/sup> = 100<br \/>\nSolution:<br \/>\nx<sup>2<\/sup> + xy + y<sup>2<\/sup> = 100<br \/>\nDifferentiating with respect to x.<br \/>\n2x + x \\(\\frac{d y}{d x}\\) + y(1) + 2y \\(\\frac{d y}{d x}\\) = 0<br \/>\n\u21d2 (x + 2y) \\(\\frac{d y}{d x}\\) = -(2x + y)<br \/>\n\u21d2 \\(\\frac{d y}{d x}=-\\frac{(2 x+3)}{x+2 y}\\)<\/p>\n<p>Question 17.<br \/>\nFind the slope of the tangent to the curve y = x<sup>3<\/sup> &#8211; x at x = 2.<br \/>\nSolution:<br \/>\n\\(\\frac{d y}{d x}\\) = 3x<sup>2<\/sup> &#8211; 1<br \/>\nAt x = 2, \\(\\frac{d y}{d x}\\) = 3(4) &#8211; 1 = 11 = slope of the tangent.<\/p>\n<p>Question 18.<br \/>\nIntegrate \\(\\frac{e^{{tan}^{-1}} x}{1+x^{2}}\\) with respect to x.<br \/>\nSolution:<br \/>\n\\(\\frac{e^{{tan}^{-1}} x}{1+x^{2}}\\)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63406\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q18.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q18\" width=\"559\" height=\"133\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q18.png 559w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q18-300x71.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 19.<br \/>\nEvaluate \\(\\int_{2}^{3} \\frac{x d x}{x^{2}+1}\\)<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63424\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q19.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q19\" width=\"231\" height=\"326\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q19.png 231w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q19-213x300.png 213w\" sizes=\"(max-width: 231px) 100vw, 231px\" \/><\/p>\n<p>Question 20.<br \/>\nFind the order and degree of the differential equation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63425\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q20.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q20\" width=\"289\" height=\"60\" \/><br \/>\nSolution:<br \/>\nOrder = 3, degree = 2.<\/p>\n<p>Question 21.<br \/>\nFind the projection of Jhe vector \\(\\hat{i}+3 \\hat{j}-7 \\hat{k}\\) on the vector \\(7 \\hat{i}+\\hat{j}+8 \\hat{k}\\)<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63426\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q21.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q21\" width=\"534\" height=\"263\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q21.png 534w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q21-300x148.png 300w\" sizes=\"(max-width: 534px) 100vw, 534px\" \/><\/p>\n<p>Question 22.<br \/>\nFind the area of the parallelogram whose adjacent sides are determined by the vectors \\(\\vec{a}=3 \\hat{i}+\\hat{y}+4 \\hat{k}\\) and \\(\\vec{b}=\\hat{i}-\\hat{j}+\\hat{k}\\)<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 23.<br \/>\nFind the angle between the planes whose vector equations are \\(\\vec{r} \\cdot(2 \\hat{i}+2 \\hat{j}-3 \\hat{k})=5\\) and \\(\\vec{r} \\cdot(3 \\hat{i}+3 \\hat{j}-5 \\hat{k})=3\\)<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63427\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q23.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q23\" width=\"241\" height=\"495\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q23.png 241w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q23-146x300.png 146w\" sizes=\"(max-width: 241px) 100vw, 241px\" \/><\/p>\n<p>Question 24.<br \/>\nA random variable X has the following probability distribution:<br \/>\nDetermine:<br \/>\n(i) k<br \/>\n(ii) P(X \u2265 2)<br \/>\nSolution:<br \/>\nThe probability distribution of X is<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63428\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q24.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q24\" width=\"234\" height=\"66\" \/><br \/>\n(i) We know that \\(\\sum_{i=1}^{n} p i=1\\)<br \/>\nTherefore 0.1 + k + 2k + 2k + k = 1<br \/>\n\u21d2 k = 0.15<\/p>\n<p>(ii) P(you study at least two hours) = P(X \u2265 2)<br \/>\n= P(X = 2) + P(X = 3) + P(X = 4)<br \/>\n= 2k + 2k + k<br \/>\n= 5k<br \/>\n= 5 \u00d7 0.15<br \/>\n= 0.75<br \/>\nP(you study exactuly two hours) = P(X = 2)<br \/>\n= 2k<br \/>\n= 2 \u00d7 0.15<br \/>\n= 0.3<br \/>\nP(you study at most two hours) = P(X \u2264 2)<br \/>\n= P(X = 0) + P(X = 1) + P(X = 2)<br \/>\n= 0.1 + k + 2k<br \/>\n= 0.1 + 3k<br \/>\n= 0.1 +3 \u00d7 0.15<br \/>\n= 0.55<\/p>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\">Part &#8211; C<\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"color: #0000ff;\">Answer any TEN questions: (10 \u00d7 3 = 30)<\/span><\/p>\n<p>Question 25.<br \/>\nShow that the relation R in the set A = {1, 2, 3, 4, 5} given by R = {(a, b) : |a &#8211; b| is even}, is an equivalence relation.<br \/>\nSolution:<br \/>\n|a &#8211; a| = |o| = 0 is even<br \/>\n(a, a) \u2208 R.<br \/>\n\u2234 R is reflexive.<br \/>\nLet (a, b) \u2208 R \u21d2 |a &#8211; b| is even<br \/>\n\u21d2 |-(a &#8211; b)| is even<br \/>\n\u21d2 |(b &#8211; a)| is even<br \/>\n\u21d2 (b, a) \u2208 R<br \/>\n\u2234 R is symmetric.<br \/>\nLet (a, b) \u2208 R and (b, c) \u2208 R<br \/>\n\u21d2 |a &#8211; b| is even and |b &#8211; c| is even<br \/>\n\u21d2 a &#8211; b is even<br \/>\n\u21d2 b &#8211; c is even<br \/>\n\u21d2 a &#8211; b + b &#8211; c is even<br \/>\n\u21d2 a &#8211; c is even<br \/>\n\u21d2 |a &#8211; c| is even<br \/>\n\u2234 (a, c) \u2208 R.<br \/>\n\u2234 R is transitive<br \/>\n\u2234 R is an equivalence relation.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 26.<br \/>\nProve that \\(2 \\tan ^{-1} \\frac{1}{2}+\\tan ^{-1} \\frac{1}{7}=\\tan ^{-1} \\frac{31}{17}\\) in the simplest form.<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63430\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q26.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q26\" width=\"415\" height=\"234\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q26.png 415w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q26-300x169.png 300w\" sizes=\"(max-width: 415px) 100vw, 415px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63429\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q26.1.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q26.1\" width=\"510\" height=\"111\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q26.1.png 510w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q26.1-300x65.png 300w\" sizes=\"(max-width: 510px) 100vw, 510px\" \/><\/p>\n<p>Question 27.<br \/>\nBy using elementary transformations, find the inverse of the matrix A = \\(\\left[\\begin{array}{ll}1 &amp; 3 \\\\2 &amp; 7\\end{array}\\right]\\)<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63432\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q27.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q27\" width=\"551\" height=\"140\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q27.png 551w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q27-300x76.png 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63431\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q27.1.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q27.1\" width=\"363\" height=\"135\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q27.1.png 363w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q27.1-300x112.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><\/p>\n<p>Question 28.<br \/>\nIf x = sin t, y = cos 2t then prove that \\(\\frac{d y}{d x}\\) = -4 sin t<\/p>\n<p>Question 29.<br \/>\nVerify Rolle&#8217;s theorem for the function f(x) = x<sup>2<\/sup> + 2, x \u2208 [-2, 2]<br \/>\nSolution:<br \/>\nThe function y = x<sup>2<\/sup> + 2 is Continuous in {-2, 2} and differentiable in (-2, 2). Also f(-2) = f(2) = 6 and hence the value of f(x) at -2 and 2 coincide.<br \/>\nRolle\u2019s theorem states that there is a point c \u2208 (-2, 2) where f'(c) = 0. Since f'(x) = 2x, we get c = 0. Thus at c = 0, we have f'(c) = 0 and c = 0 \u2208 (-2, 2).<\/p>\n<p>Question 30.<br \/>\nFind two numbers whose sum is 24 and whose product is as large as possible.<br \/>\nSolution:<br \/>\nLet one number be x. Then, the other number is (24 &#8211; x).<br \/>\n(\u2235 Sum of the two numbers is 24)<br \/>\nLet y denotes the product of the two numbers. Thus, we have<br \/>\ny = x(24 &#8211; x) = 24x &#8211; x<sup>2<\/sup><br \/>\nOn differentiating twice w.r.t. x, we get<br \/>\n\\(\\frac{d y}{d x}\\) = 24 &#8211; 2x and \\(\\frac{d^{2} y}{d x^{2}}\\) = -2<br \/>\nNow, put \\(\\frac{d y}{d x}\\) = 0<br \/>\n\u21d2 24 &#8211; 2x = 0<br \/>\n\u21d2 x = 12<br \/>\nAt x = 12, \\(\\frac{d^{2} y}{d x^{2}}\\) = -2 &lt; 0<br \/>\n\u2234 By second derivative test, x = 12 is the point of local mxima of y. Thus, the product of the number is maximum when the numbers are 12 and 24 &#8211; 12 = 12.<br \/>\nHence, the numbers are 12 and 12.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 31.<br \/>\nFind: \\(\\int \\frac{x d x}{(x+1)(x+2)}\\)<\/p>\n<p>Question 32.<br \/>\nFind: \u222be<sup>x<\/sup> sin x dx<br \/>\nSolution:<br \/>\nTake e<sup>x<\/sup> as the first function and sin x as second function. Then integrating by parts, we have<br \/>\nI = \u222be<sup>x<\/sup> sin x dx = e<sup>x<\/sup> (-cos x) + \u222be<sup>x<\/sup> cos x dx = -e<sup>x<\/sup> cos x + I<sub>1<\/sub> (say) &#8230;&#8230; (1)<br \/>\nTaking e<sup>x<\/sup> and cos x as the first and second functions, respectively, in I<sub>1<\/sub>, we get<br \/>\nI = e<sup>x<\/sup> sin x &#8211; \u222be<sup>x<\/sup> sin x dx<br \/>\nSubstituting the value of I<sub>1<\/sub> in (i), we get<br \/>\nI = -e<sup>x<\/sup> cos x + e<sup>x<\/sup> sin x &#8211; 1 or 2I = e<sup>x<\/sup> (sin x &#8211; cos x)<br \/>\nHence I = \u222be<sup>x<\/sup> sin x dx = \\(\\frac{e^{x}}{2}\\) (sin x &#8211; cos x) + C<\/p>\n<p>Question 33.<br \/>\nFind the area of the region bounded by the curve y = x<sup>2<\/sup> and the line y = 4.<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63434\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q33.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q33\" width=\"337\" height=\"239\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q33.png 337w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q33-300x213.png 300w\" sizes=\"(max-width: 337px) 100vw, 337px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63433\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q33.1.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q33.1\" width=\"275\" height=\"242\" \/><\/p>\n<p>Question 34.<br \/>\nForm the differential equation representing the family of curves y = a sin(x + b), where a, b are arbitrary constants.<\/p>\n<p>Question 35.<br \/>\nShow that the position vector of the point P, which divides the fine joining the points A and B having position vectors \\(\\vec{a}\\) and \\(\\vec{b}\\) internally in the ratio m : n is \\(\\frac{m \\vec{b}+n \\vec{a}}{m+n}\\)<\/p>\n<p>Question 36.<br \/>\nFind x such that the fojir points A(3, 2, 1) B(4, x, 5), C(4, 2, -2) and D(6, 5, -1) are coplanar.<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63435\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q36.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q36\" width=\"258\" height=\"231\" \/><\/p>\n<p>Question 37.<br \/>\nFind the equation of the plane through the intersection of the planes 3x &#8211; y + 2z &#8211; 4 = 0 and x + y + z &#8211; 2 = 0 and the point (2, 2, 1).<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 38.<br \/>\nA bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.<\/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 \/>\nLef R<sub>+<\/sub> be the set of all non-negative real numbers. Show that the function f : R<sub>+<\/sub> \u2192 [4, \u221e) given by f(x) = x<sup>2<\/sup> + 4 is invertible and write the inverse of f.<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63437\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q39.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q39\" width=\"683\" height=\"338\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q39.png 683w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q39-300x148.png 300w\" sizes=\"(max-width: 683px) 100vw, 683px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63436\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q39.1.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q39.1\" width=\"559\" height=\"257\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q39.1.png 559w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q39.1-300x138.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 40.<br \/>\nIf A = \\(\\left[\\begin{array}{rrr}0 &amp; 6 &amp; 7 \\\\-6 &amp; 0 &amp; 8 \\\\7 &amp; -8 &amp; 0\\end{array}\\right]\\), B = \\(\\left[\\begin{array}{lll}0 &amp; 1 &amp; 1 \\\\1 &amp; 0 &amp; 2 \\\\1 &amp; 2 &amp; 0\\end{array}\\right]\\), C = \\(\\left[\\begin{array}{c}2 \\\\-2 \\\\3\\end{array}\\right]\\), calculate AC, BC and (A + B)C. Also verify that (A + B)C = AC + BC.<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63440\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q40.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q40\" width=\"385\" height=\"209\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q40.png 385w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q40-300x163.png 300w\" sizes=\"(max-width: 385px) 100vw, 385px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63438\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q40.1.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q40.1\" width=\"414\" height=\"307\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q40.1.png 414w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q40.1-300x222.png 300w\" sizes=\"(max-width: 414px) 100vw, 414px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63439\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q40.2.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q40.2\" width=\"635\" height=\"259\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q40.2.png 635w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q40.2-300x122.png 300w\" sizes=\"(max-width: 635px) 100vw, 635px\" \/><\/p>\n<p>Question 41.<br \/>\nSolve the following system of linear equations by matrix method.<br \/>\nx &#8211; y + 2z = 7, 3x + 4y &#8211; 5z = -5 and 2x &#8211; y + 3z = 12.<\/p>\n<p>Question 42.<br \/>\nIf y = (tan<sup>-1<\/sup> x)<sup>2<\/sup>. Show that (x<sup>2<\/sup> + 1)<sup>2<\/sup> y<sub>2<\/sub> + 2x(x<sup>2<\/sup> + 1) y<sub>1<\/sub> = 2.<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63441\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q42.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q42\" width=\"675\" height=\"312\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q42.png 675w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q42-300x139.png 300w\" sizes=\"(max-width: 675px) 100vw, 675px\" \/><\/p>\n<p>Question 43.<br \/>\nSand is pouring from a pipe at the rate of 12 cm<sup>3<\/sup>\/s. The falling sand forms a cone on the ground is such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm?<br \/>\nSolution:<br \/>\nLet r be the radius, h be the height and V be the volume of the sand cone at any time t.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63442\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q43.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q43\" width=\"593\" height=\"346\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q43.png 593w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q43-300x175.png 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><br \/>\nHence, when the height of the sand cone is 4 cm, its height is increasing at the rate of \\(\\frac{1}{48 \\pi}\\) cm\/s.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 44.<br \/>\nFind the integral of \\(\\frac{1}{x^{2}+a^{2}}\\) with respect to x and hence find \\(\\int \\frac{1}{x^{2}-6 x+13} d x\\)<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63443\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q44.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q44\" width=\"525\" height=\"379\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q44.png 525w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q44-300x217.png 300w\" sizes=\"(max-width: 525px) 100vw, 525px\" \/><\/p>\n<p>Question 45.<br \/>\nUsing integration find the area of the region bounded by the triangle whose vertices are (1, 0), (2, 2) and (3, 1).<br \/>\nSolution:<br \/>\nArea = Area of \u2206ABD + Area of trapezium BDEC &#8211; Area of \u2206AEC<br \/>\nNow equation of the sides AB, BD and CA are given by<br \/>\ny = 2(x &#8211; 1), y = 4 &#8211; x, y = \\(\\frac{1}{2}\\)(x &#8211; 1) respectively<br \/>\nHence, area of \u2206<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63445\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q45.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q45\" width=\"641\" height=\"214\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q45.png 641w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q45-300x100.png 300w\" sizes=\"(max-width: 641px) 100vw, 641px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63444\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q45.1.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q45.1\" width=\"278\" height=\"251\" \/><\/p>\n<p>Question 46.<br \/>\nFind the general solution of the differential equation x \\(\\frac{d y}{d x}\\) + 2y = x<sup>2<\/sup> log x.<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63447\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q46.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q46\" width=\"458\" height=\"307\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q46.png 458w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q46-300x201.png 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63446\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q46.1.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q46.1\" width=\"169\" height=\"191\" \/><\/p>\n<p>Question 47.<br \/>\nDerive the equation of the line in space passing through two given points, both in vector and Cartesian form.<br \/>\nSolution:<br \/>\nVector Form<br \/>\nLet \\(\\overrightarrow { a }\\) and \\(\\overrightarrow { b }\\) be the position vectors of two points A (x<sub>1<\/sub>, y<sub>1<\/sub>, z<sub>1<\/sub>) and B(x<sub>2<\/sub>, y<sub>2<\/sub>, z<sub>2<\/sub>) respectively that are lying on a line.<br \/>\nLet \\(\\overrightarrow { r }\\) be the position vector of an arbitrary point P(x, y, z), then P is a point on the line if and only if \\(\\overrightarrow{\\mathrm{AP}}=\\overrightarrow{\\mathrm{r}}-\\overrightarrow{\\mathrm{a}}\\) and \\(\\overrightarrow{\\mathrm{AB}}=\\overrightarrow{\\mathrm{b}}-\\overrightarrow{\\mathrm{a}}\\) are collinear vectors. Therefore, P is on the line if and only<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63450\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q47.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q47\" width=\"360\" height=\"198\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q47.png 360w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q47-300x165.png 300w\" sizes=\"(max-width: 360px) 100vw, 360px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63448\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q47.1.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q47.1\" width=\"511\" height=\"221\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q47.1.png 511w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q47.1-300x130.png 300w\" sizes=\"(max-width: 511px) 100vw, 511px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63449\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q47.2.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q47.2\" width=\"322\" height=\"227\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q47.2.png 322w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q47.2-300x211.png 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><\/p>\n<p>Question 48.<br \/>\nIf a fair coin is tossed 10 times, find the probability of<br \/>\n(i) exactly six heads<br \/>\n(ii) at least six heads.<br \/>\nSolution:<br \/>\nLet X denote the number of heads in an experiment of 10 trials.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63451\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q48.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q48\" width=\"701\" height=\"292\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q48.png 701w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q48-300x125.png 300w\" sizes=\"(max-width: 701px) 100vw, 701px\" \/><\/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 question: (1 \u00d7 10 = 10)<\/span><\/p>\n<p>Question 49(a).<br \/>\nProve that \\(\\int_{0}^{a} f(x) d x=\\int_{0}^{1} f(a-x) d x\\) and hence evaluate \\(\\int_{0}^{a} \\frac{\\sqrt{x}}{\\sqrt{x}+\\sqrt{a-x}} d x\\)<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63453\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q49a.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q49(a)\" width=\"386\" height=\"176\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q49a.png 386w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q49a-300x137.png 300w\" sizes=\"(max-width: 386px) 100vw, 386px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63452\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q49a.1.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q49(a).1\" width=\"389\" height=\"310\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q49a.1.png 389w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q49a.1-300x239.png 300w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><\/p>\n<p>Question 49(b).<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63456\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q49b.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q49(b)\" width=\"529\" height=\"95\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q49b.png 529w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q49b-300x54.png 300w\" sizes=\"(max-width: 529px) 100vw, 529px\" \/><br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63455\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q49b.1.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q49(b).1\" width=\"553\" height=\"367\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q49b.1.png 553w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q49b.1-300x199.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 50(a).<br \/>\nSolve the following problem graphically:<br \/>\nMinimise and Maximise: z = 3x + 9y<br \/>\nSubject to the constraints:<br \/>\nx + 3y \u2264 60, x + y \u2265 10, x \u2264 y, x \u2265 0, y \u2265 0.<br \/>\nSolution:<br \/>\nLet us graph the feasible region of the system of linear inequalities (2) to (5).<br \/>\nThe coordinates of the corner point A, B, C and D are (0, 10), (5, 5), (15, 15) and (0, 20) respectively.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63458\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q50a.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q50(a)\" width=\"414\" height=\"213\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q50a.png 414w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q50a-300x154.png 300w\" sizes=\"(max-width: 414px) 100vw, 414px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63457\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q50a.1.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q50(a).1\" width=\"393\" height=\"302\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q50a.1.png 393w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q50a.1-300x231.png 300w\" sizes=\"(max-width: 393px) 100vw, 393px\" \/><br \/>\nWe now find the minimum and maximum value of Z. From the table, we find that the minimum value of Z is 60 at point B (5, 5) of the feasible region.<br \/>\nThe maximum value of Z on the feasible region occurs at the two comer points C(15, 15) and D(0, 20) and it is 180 in each case.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 50(b).<br \/>\nFind the relationship between a and b so that function f defined by <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63460\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q50b.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q50(b)\" width=\"204\" height=\"61\" \/>\u00a0is continuous at x = 3.<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-63459\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q50b.1.png\" alt=\"2nd PUC Maths Previous Year Question Paper March 2018 Q50(b).1\" width=\"355\" height=\"184\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q50b.1.png 355w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Maths-Previous-Year-Question-Paper-March-2018-Q50b.1-300x155.png 300w\" sizes=\"(max-width: 355px) 100vw, 355px\" \/><br \/>\n3a + 1 = 3b + 3 = 3a + 1<br \/>\n\u21d2 3a + 1 = 3b + 3<br \/>\n\u21d2 3a = 3b + 3 &#8211; 1<br \/>\n\u21d2 3a = 3b + 2<br \/>\n\u21d2 a = b + \\(\\frac{2}{3}\\)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Students can Download 2nd PUC Maths Previous Year Question Paper March 2018, 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 Maths Previous Year Question Paper March 2018 Time: 3 Hrs 15 Min 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\/27329"}],"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=27329"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/27329\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=27329"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=27329"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=27329"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}