{"id":27057,"date":"2020-06-24T15:23:43","date_gmt":"2020-06-24T09:53:43","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=27057"},"modified":"2021-07-02T15:19:15","modified_gmt":"2021-07-02T09:49:15","slug":"2nd-puc-basic-maths-previous-year-question-paper-june-2018","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/2nd-puc-basic-maths-previous-year-question-paper-june-2018\/","title":{"rendered":"2nd PUC Basic Maths Previous Year Question Paper June 2018"},"content":{"rendered":"<p>Students can Download 2nd PUC Basic Maths Model Question June 2018 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 June 2018 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 \/>\nIf A = \\(\\left[\\begin{array}{ccc}1 &amp; -5 &amp; 4 \\\\2 &amp; 3 &amp; 6\\end{array}\\right]\\) find 4A&#8217;.<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66242\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-1.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 1\" width=\"232\" height=\"93\" \/><\/p>\n<p>Question 2.<br \/>\nIf \\(^{n} C_{8}=^{n} C_{5}\\), find n.<br \/>\nSolution:<br \/>\nn = 8 + 5 = 13<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 3.<br \/>\nWrite symbolically &#8220;If two numbers are equal then their squares are equal&#8221;.<br \/>\nSolution:<br \/>\np \u2192 q<\/p>\n<p>Question 4.<br \/>\nFind third proportional of 7 and 28.<br \/>\nSolution:<br \/>\n7 : 28 : : 28 : x<br \/>\nx = \\(\\frac { 28\\times 28 }{ 7 }\\) = 112<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 5.<br \/>\nWhat income can be obtained from \u20b9 8,000 of 4% stock?<br \/>\nSolution:<br \/>\nFor 100 Rs. \u2192 Income 4 Rs.<br \/>\nfor 8000 Rs \u2192 \\(\\frac{8000 \\times 4}{100}\\) = Rs. 320<\/p>\n<p>Question 6.<br \/>\nWrite the formulae for learning index.<br \/>\nSolution:<br \/>\nIndex of learning = \\(\\frac{\\text { Log (learing ratio) }}{\\log 2}\\)<\/p>\n<p>Question 7.<br \/>\nFind cos 2A if sin A = \\(\\frac{1}{2}\\)<br \/>\nSolution:<br \/>\nCos 2A = 1 &#8211; 2sin<sup>2<\/sup> A = 1 &#8211; 2(\\(\\frac{1}{4}\\)) = \\(\\frac{1}{2}\\)<\/p>\n<p>Question 8.<br \/>\nEvaluate: \\(\\lim _{x \\rightarrow 0} \\frac{2}{x} \\log (1+x)\\)<br \/>\nSolution:<br \/>\n\\(2 \\lim _{x \\rightarrow 0} \\frac{\\log (1+x)}{x}\\) = 2 \u00d7 1 = 2.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 9.<br \/>\nIf y = sec (sec x) find \\(\\frac{d y}{d x}\\).<br \/>\nSolution:<br \/>\n\\(\\frac{d y}{d x}\\) = sec(sec x) . tan(sec x) = sec x . tan x<\/p>\n<p>Question 10.<br \/>\nEvaluate \\(\\int\\left(x^{a}+e^{x}-\\frac{1}{x}\\right) d x\\)<br \/>\nSolution:<br \/>\n\\(\\left[\\frac{x^{a+1}}{a+1}+e^{x}-\\log x\\right]+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 \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66243\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-2.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 2\" width=\"434\" height=\"66\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-2.png 434w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-2-300x46.png 300w\" sizes=\"(max-width: 434px) 100vw, 434px\" \/><br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66244\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-3.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 3\" width=\"453\" height=\"67\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-3.png 453w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-3-300x44.png 300w\" sizes=\"(max-width: 453px) 100vw, 453px\" \/><\/p>\n<p>Question 12.<br \/>\nIn how many ways can the letters of the word &#8216;HOPPER&#8217; be arranged?<br \/>\nSolution:<br \/>\nNo. of arrangements = \\(\\frac{6 !}{2 !}\\) = 6 \u00d7 5 \u00d7 4 \u00d7 3 = 360<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 13.<br \/>\nIf P(A) = \\(\\frac{1}{4}\\), P(B) = \\(\\frac{2}{5}\\), P(A\u222aB) = \\(\\frac{1}{2}\\), find P(A\/B).<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66245\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-4.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 4\" width=\"569\" height=\"148\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-4.png 569w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-4-300x78.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Question 14.<br \/>\nIf (~p \u2228 q) \u2228~r is a false proposition, then find the truth values of p, q and r.<br \/>\nSolution:<br \/>\nF \u2228 F = F<br \/>\n~p \u2228 q is false<br \/>\np = T and q = F and r = T<\/p>\n<p>Question 15.<br \/>\nDivide \u20b9 6,000 in ratio 3 : 4 : 5.<br \/>\nSolution:<br \/>\nIst part = \\(\\frac{3}{12}\\) \u00d7 6000 = 15000<br \/>\nIInd part = \\(\\frac{4}{12}\\) \u00d7 6000 = 2000<br \/>\nIIIrd part = \\(\\frac{5}{12}\\) \u00d7 6000 = 2500<\/p>\n<p>Question 16.<br \/>\nT.D on a bill was \u20b9 100 and BG was \u20b9 10. What is the face value of the bill?<br \/>\nSolution:<br \/>\nGiven T.D = 100, B.G = 10, F = ?<br \/>\nBD &#8211; TD = BG<br \/>\n\u21d2 B.D = BG + TD = 100 + 10 = 110<br \/>\nF = \\(\\frac{B D \\times T D}{B . G}\\) = \\(\\frac{110 \\times 100}{10}\\)<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 17.<br \/>\nProve that (sin A + cos A)<sup>2<\/sup> = 1 + sin 2A.<br \/>\nSolution:<br \/>\nL.H.S = sin<sup>2<\/sup> A + cos<sup>2<\/sup> A + 2 sinA . cosA<br \/>\n= 1 + sin 2A<br \/>\n= R.H.S<\/p>\n<p>Question 18.<br \/>\nProve that: \\(\\frac{\\sin x-\\sin y}{\\sin x+\\sin y}=\\tan \\left(\\frac{x-y}{2}\\right) \\cot \\left(\\frac{x+y}{2}\\right)\\)<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66246\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-5.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 5\" width=\"454\" height=\"101\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-5.png 454w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-5-300x67.png 300w\" sizes=\"(max-width: 454px) 100vw, 454px\" \/><\/p>\n<p>Question 19.<br \/>\nFind the equation of the parabola given that vertex (0, 0) and directrix x = -5.<br \/>\nSolution:<br \/>\nThe curve turns right side and a = 5.<br \/>\ny<sup>2<\/sup> = 20x is equation of the parabola.<\/p>\n<p>Question 20.<br \/>\nFind the value of K, if the function <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66247\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-6.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 6\" width=\"188\" height=\"84\" \/>\u00a0is continuous at x = 0.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 21.<br \/>\nFind \\(\\frac{d y}{d x}\\) if y = xx.<br \/>\nSolution:<br \/>\nTaking log<sup>m<\/sup> both sides<br \/>\nlog y = log x<sup>x<\/sup><br \/>\nlog y = x log x<br \/>\ndiff w.t.r x<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66248\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-7.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 7\" width=\"278\" height=\"128\" \/><\/p>\n<p>Question 22<br \/>\nIf the displacement \u2018s\u2019 at any time \u2018t\u2019 is given by s = \\(\\sqrt{1-t}\\). Show that the velocity is inversely proportional to the displacement.<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66249\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-8.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 8\" width=\"397\" height=\"196\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-8.png 397w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-8-300x148.png 300w\" sizes=\"(max-width: 397px) 100vw, 397px\" \/><\/p>\n<p>Question 23.<br \/>\nEvaluate : \\(\\int \\frac{3 x^{8}}{1+x^{9}} d x\\)<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66250\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-9.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 9\" width=\"229\" height=\"61\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 24.<br \/>\nEvaluate : \\(\\int_{0}^{\\pi \/ 4} \\sec ^{2} 3 x \\cdot d x\\)<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66251\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-10.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 10\" width=\"510\" height=\"74\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-10.png 510w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-10-300x44.png 300w\" sizes=\"(max-width: 510px) 100vw, 510px\" \/><\/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 \/>\nProve that A<sup>2<\/sup> &#8211; 4A &#8211; 5I = 0, where I = \\(\\left[\\begin{array}{lll} 1 &amp; 0 &amp; 0 \\\\0 &amp; 1 &amp; 0 \\\\0 &amp; 0 &amp; 1\\end{array}\\right]\\) is the unit matrix and A = <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66252\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-11.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 11\" width=\"85\" height=\"88\" \/><\/p>\n<p>Question 26.<br \/>\nProve that \\(\\left[\\begin{array}{ccc}1 &amp; 1 &amp; 1 \\\\a &amp; b &amp; c \\\\b c &amp; c a &amp; a b\\end{array}\\right]\\) = (a &#8211; b)(b &#8211; c)(c &#8211; a)<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66253\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-12.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 12\" width=\"580\" height=\"231\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-12.png 580w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-12-300x119.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66254\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-13.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 13\" width=\"445\" height=\"152\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-13.png 445w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-13-300x102.png 300w\" sizes=\"(max-width: 445px) 100vw, 445px\" \/><\/p>\n<p>Question 27.<br \/>\nIf a convex polygon has 170 diagonals, find the number of sides of the polygon.<br \/>\nSolution:<br \/>\n170 = \\(n C_{2}\\) &#8211; n<br \/>\n\u21d2 170 = \\(\\frac{n(n-1)}{2}\\) &#8211; n<br \/>\n\u21d2 340 = n<sup>2<\/sup> &#8211; 3n<br \/>\n\u21d2 n<sup>2<\/sup> &#8211; 3n &#8211; 340 = 0<br \/>\n\u21d2 (n &#8211; 20)(n + 17) = 0<br \/>\n\u21d2 n = 20<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 28.<br \/>\nA bag contains 10 gold and 8 silver coins. Two successive drawings of 4 coins are made. Find the probability that the first drawing will get 4 gold and second 4 silver coins if coins are replaced before the second trial.<br \/>\nSolution:<br \/>\n4 coins can be drawn from 18 coins in \\(^{18} \\mathrm{C}_{4}\\) ways.<br \/>\n4 goldcoins can be drawn in \\(^{10} \\mathrm{C}_{4}\\) ways.<br \/>\nP(4 gold coins in Ist draw) = \\(\\frac{_{10 \\mathrm{C}_{4}}}{18 \\mathrm{C}_{4}}\\)<br \/>\nSince 4 coins are replaced in the second draw again 4 coins are drawn from 18 coins in \\(^{18} \\mathrm{C}_{4}\\) ways.<br \/>\nSilver coins can be selected in \\(^{8} \\mathrm{C}_{4}\\) ways.<br \/>\nP (4 silver coins in II draw) = \\(\\frac{^{8} C_{4}}{^{18} C_{4}}\\)<br \/>\nP (4 gold and 4 silver) = \\(\\frac{^{10} \\mathrm{C}_{4}}{^{18} \\mathrm{C}_{4}} \\times \\frac{^{8} \\mathrm{C}_{4}}{^{18} \\mathrm{C}_{4}}\\)<\/p>\n<p>Question 29.<br \/>\n5 men each working 9 hours a day can finish a work in 30 days. How many men are required to finish eight times the work in 25 days, each working 8 hours a day?<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66255\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-14.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 14\" width=\"270\" height=\"176\" \/><br \/>\nmore men fewer hours \u2192 Inverse proposition<br \/>\nmore men fewer days \u2192 Inverse proposition<br \/>\nmore work, more men \u2192 Direct proportion<br \/>\nx = \\(\\frac{5 \\times 9 \\times 30 \\times 8}{8 \\times 25 \\times 1}\\) = 54 men<br \/>\n54 men are required to finish the work.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 30.<br \/>\nBanker&#8217;s gain on a bill due after 6 months at 4% p.a is \u20b9 24. Find TD, BD and bill amount.<br \/>\nSolution:<br \/>\nGiven B.G = 20, t = 6 months = \\(\\frac {1}{2}\\) yr, r = 4% = 0.04<br \/>\n(i) B.G = T.D. tr<br \/>\n20 = TD (0.5 \u00d7 0.04)<br \/>\nTD = \\(\\frac{20}{0.020}\\) = Rs. 1000<br \/>\n(ii) B.D = T.D + B.G = 1000 + 20 = 1020<br \/>\n(iii) F = \\(\\frac{B . D \\times T . D}{B . G}\\) = \\(\\frac{1020 \\times 100}{20}\\) = 51000<\/p>\n<p>Question 31.<br \/>\nPrashanth sold 25 Biocon shares when the market price was \u20b9 400 per share. He then bought 10 Reliance shares which were selling at \u20b9 800 per share. Brokerage for each transaction was 0.25%. The balance amount he gave to his daughter Sonu for shopping. How much did Sonu receive?<br \/>\nSolution:<br \/>\nAmount received by selling Biocon shares = 25 \u00d7 400 = \u20b9 10,000.<br \/>\nBrokerage = \\(\\frac {0.25}{100}\\) \u00d7 10,000 = \u20b9 25<br \/>\nNet Amount Received = 10,000 &#8211; 25 = \u20b9 9,975<br \/>\nAmount paid for Reliance shares = 800 \u00d7 10 = \u20b9 8, 000<br \/>\nBrokerage = \\(\\frac {0.25}{100}\\) \u00d7 8000 = \u20b9 20<br \/>\nNet Amount paid = 8000 + 20 = \u20b9 8020<br \/>\nBalance Amount = 9975 &#8211; 8020 = \u20b9 1955<br \/>\nAmount paid to Sonu for shopping is \u20b9 1955.<\/p>\n<p>Question 32.<br \/>\nA colour TV is marked for sale for \u20b9 17,600 which include sales tax at 10%. Calculate the sales tax in \u20b9?<br \/>\nSolution:<br \/>\nS.P = \u20b9 17,600, S.T% = 10%, S.T. = ?<br \/>\nLet M.P = x<br \/>\nTotal amount to be paid (S.P) = M.P + ST% of M.P<br \/>\n17,600 = x + 10% of x<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66256\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-15.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 15\" width=\"249\" height=\"179\" \/><br \/>\nS.T = S.P &#8211; M.P = 17,600 &#8211; 16,000 = \u20b9 1,600.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 33.<br \/>\nIf one end of the diameter of the circle x<sup>2<\/sup> + y<sup>2<\/sup> + 2x + 6y &#8211; 22 = 0 is (3, -7). Find the co-ordinates of the other end point.<br \/>\nSolution:<br \/>\nCentre of the given circle = (-1, -3)<br \/>\nOneendisgivenas A(3, -7)<br \/>\nLet the other end be B(x, y) = ?<br \/>\nW.K.T. centre = mid point of the diameter<br \/>\n\u21d2 (-1, -3) = \\(\\left(\\frac{3+x}{2}, \\frac{-7+y}{2}\\right)\\)<br \/>\n\u21d2 3 + x = -2, -7 + y = -6<br \/>\n\u21d2 x = -5, y = 1<br \/>\nThe other end of the diameter = B(-5, 1).<\/p>\n<p>Question 34.<br \/>\nDifferentiate \u201csin x\u201d from the first circles.<br \/>\nSolution:<br \/>\nLet y = f(x) = sin x, then<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66257\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-16.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 16\" width=\"269\" height=\"68\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66258\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-17.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 17\" width=\"274\" height=\"405\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-17.png 274w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-17-203x300.png 203w\" sizes=\"(max-width: 274px) 100vw, 274px\" \/><\/p>\n<p>Question 35.<br \/>\nFind the maxima and minima of the function f(x) = 3x<sup>3<\/sup> &#8211; 9x<sup>2<\/sup> &#8211; 27x + 30<br \/>\nSolution:<br \/>\nGiven f(x) = 3x<sup>3<\/sup> &#8211; 9x<sup>2<\/sup> &#8211; 27x + 30 &#8230;&#8230;.. (1)<br \/>\nf'(x) = 9x<sup>2<\/sup> &#8211; 18x &#8211; 27 &#8230;&#8230;.. (2)<br \/>\nf&#8221;(x) = 18x &#8211; 18 &#8230;&#8230;. (3)<br \/>\nfor a function to be maximum or minimum f'(x) = 0<br \/>\n\u21d2 9x<sup>2<\/sup> &#8211; 18x &#8211; 27 = 0<br \/>\n\u21d2 x<sup>2<\/sup> &#8211; 2x &#8211; 3 = 0<br \/>\n\u21d2 (x &#8211; 3)(x + 1) = 0<br \/>\n\u21d2 x = 3 or -1<br \/>\nCase I: Put x = 3 in Eqn. (3).<br \/>\nf&#8221;(x) = 18 \u00d7 3 &#8211; 18 = 36 &gt; 0<br \/>\nf(x) is minimum at x = -1 and minimum value is given by<br \/>\nf(3) = 3(3)<sup>3<\/sup> &#8211; 9(3)<sup>2<\/sup> &#8211; 27(3) + 30 = -51<br \/>\nCase II :<br \/>\nPut x = -1 in equation (3)<br \/>\nf&#8221;(-1) = 18(-1) &#8211; 18 = -36 &lt; 0<br \/>\nf(x) is maximum, at x = -1 and maximum value is given by<br \/>\nf(-1) = 3(-1)<sup>3<\/sup> &#8211; 9(-1)<sup>2<\/sup> &#8211; 27(-1) + 30 = -3 &#8211; 9 + 27 + 30 = 45<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 36.<br \/>\nA man 2 mt. height walks at a uniform speed of 6 km\/hr away from the lamp post 6 mt high. Find the rate at which the<br \/>\n(i) length of his shadow increase<br \/>\n(ii) Rate at which the tip of the shadow is moving.<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66259\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-18.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 18\" width=\"301\" height=\"254\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-18.png 301w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-18-300x253.png 300w\" sizes=\"(max-width: 301px) 100vw, 301px\" \/><br \/>\nGiven the rate of man walking \\(\\frac{d x}{d t}\\) = 6 km\/hr<br \/>\nRate of shadow length increase = \\(\\frac{d y}{d t}\\) = ?<br \/>\nRate of tip of the shadow increasing = \\(\\frac{d z}{d t}\\) = ?<br \/>\n\u2206ABE and \u2206CDE are similar<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66260\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-19.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 19\" width=\"315\" height=\"153\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-19.png 315w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-19-300x146.png 300w\" sizes=\"(max-width: 315px) 100vw, 315px\" \/><br \/>\nRate of increase of length of shadow = \\(\\frac{d y}{d t}=\\frac{6}{2}\\) = 3 km\/hr<br \/>\nAgain Z = x + y<br \/>\nDifferentiate w.r. to x.<br \/>\n\\(\\frac{d z}{d t}=\\frac{d x}{d t}+\\frac{d y}{d t}\\) = 6 + 3 = 9 km\/hr<br \/>\nRate at which tip of shadow is moving = 9 km\/hr<\/p>\n<p>Question 37.<br \/>\nEvaluate : \u222bx cos x dx<br \/>\nSolution:<br \/>\n\u222bx(sinx) &#8211; \u222bsin x dx<br \/>\n= x sin x &#8211; (-cos x) + C<br \/>\n= x sin x + cos x + C<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 38.<br \/>\nEvaluate:\\(\\int \\frac{1}{1+\\cos x} d x\\)<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66261\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-20.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 20\" width=\"115\" height=\"76\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66262\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-21.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 21\" width=\"228\" height=\"171\" \/><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\">Part &#8211; D<\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\">IV. Answer any six questions: (6 \u00d7 5 = 30)<\/span><\/p>\n<p>Question 39.<br \/>\nFind the coefficient of x<sup>5<\/sup> in the expansion of \\(\\left(x+\\frac{1}{x^{2}}\\right)^{17}\\)<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66263\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-22.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 22\" width=\"339\" height=\"361\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-22.png 339w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-22-282x300.png 282w\" sizes=\"(max-width: 339px) 100vw, 339px\" \/><\/p>\n<p>Question 40.<br \/>\nResolve into partial fractions: \\(\\frac{3 x+2}{(x-2)(x+3)^{2}}\\)<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66264\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-23.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 23\" width=\"391\" height=\"329\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-23.png 391w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-23-300x252.png 300w\" sizes=\"(max-width: 391px) 100vw, 391px\" \/><\/p>\n<p>Question 41.<br \/>\nProve that ~(p \u2192 q) = p\u2227~ q<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66265\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-24.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 24\" width=\"400\" height=\"187\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-24.png 400w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-24-300x140.png 300w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/p>\n<p>Question 42.<br \/>\nA jar contains two liquids A and B in the ratio 7 : 5 when 9 litres of the mixture is drawn and the jar is filled with the same quantity of B, the ratio of A and B becomes 7 : 9. Find the quantity of A in the jar initially.<br \/>\nSolution:<br \/>\nLet the quantities of the two liquids be 7x and 5x, 9 litres are drawn and the jar is filled with the same quantity of B i.e. 5.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66266\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-25.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 25\" width=\"221\" height=\"230\" \/><br \/>\nInitial quantity Of liquid A = 7x = 7 \u00d7 \\(\\frac{2}{7}\\) = 2 litres<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 43.<br \/>\nXYZ company supplies water tankers to the Government. The first water tanker takes 20,000 labour hours. The government auditors suggest that there should be a 90% learning effect rate. The management expects an order of 8 water tankers in the next year. What will be the labour cost the company will incur at the rate of \u20b9 20 per hour?<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66267\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-26.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 26\" width=\"659\" height=\"154\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-26.png 659w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-26-300x70.png 300w\" sizes=\"(max-width: 659px) 100vw, 659px\" \/><br \/>\nTotal labour hrs produced = 1,16,640<br \/>\nTotal labour cost produced for 8 water tankers at the rate of 20\/- hr = 1,16,640 \u00d7 20 = 23,32800<\/p>\n<p>Question 44.<br \/>\nSolve the following L.P.P graphically maximise z = 60x + 15y subject to the constraints x + y \u2264 50, 3x + y \u2264 90, x \u2265 0, y \u2265 0.<br \/>\nSolution:<br \/>\nConsider x + y = 50<br \/>\nPut x = 0, y = 50, (0, 50)<br \/>\nPut y = 0, x = 50 (50, 0)<br \/>\n3x + y = 90<br \/>\nx = 0, y = 90, (0, 90)<br \/>\ny = 0, x = 30 (30, 0)<br \/>\nOABC is the feasible region.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66268\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-27.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 27\" width=\"467\" height=\"194\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-27.png 467w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-27-300x125.png 300w\" sizes=\"(max-width: 467px) 100vw, 467px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66269\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-28.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 28\" width=\"440\" height=\"415\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-28.png 440w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-28-300x283.png 300w\" sizes=\"(max-width: 440px) 100vw, 440px\" \/><\/p>\n<p>Question 45.<br \/>\nProve that sin 20\u00b0 sin 40\u00b0 sin 60\u00b0 sin 80\u00b0 = \\(\\frac{3}{16}\\)<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66270\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-29.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 29\" width=\"487\" height=\"271\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-29.png 487w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-29-300x167.png 300w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66271\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-30.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 30\" width=\"333\" height=\"119\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-30.png 333w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-30-300x107.png 300w\" sizes=\"(max-width: 333px) 100vw, 333px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 46.<br \/>\nFind the equation of the circle passing through the points (1, 2) and (2, 1) and has its centre on the y-axis.<br \/>\nSolution:<br \/>\nLet the required equation of the circle be x<sup>2<\/sup> + y<sup>2<\/sup> + 2gx + 2fy + c = 0<br \/>\nIt passes through the points (1, 2) and (2, 1) and the centre lies on y-axis<br \/>\n\u21d2 g = 0 &#8230;&#8230;. (1)<br \/>\n(1, 2) \u21d2 12 + 22 + 2g(1) + 2f(2) + C = 0<br \/>\n\u21d2 4f + c + 5 = 0 &#8230;&#8230;..(2)<br \/>\n(2, 1) \u21d2 22 + 12 + 2g(2) + 2f(1) + c = 0<br \/>\n\u21d2 2f + c + 5 = 0 &#8230;&#8230;.. (3)<br \/>\nEqn. (3) &#8211; Eqn. (2) gives 2f = 0 \u21d2 f = 0<br \/>\nput g = 0 and f = 0 in eqn (3) gives c = -5 \u21d2 c = -5<br \/>\nthe required equation of the circle is x<sup>2<\/sup> + y<sup>2<\/sup> + 2(0)x + 2(0)y &#8211; 5 = 0<br \/>\n\u21d2 x<sup>2<\/sup> + y<sup>2<\/sup> &#8211; 5 = 0<\/p>\n<p>Question 47.<br \/>\nIf y = (x<sup>2<\/sup> + a<sup>2<\/sup>)<sup>6<\/sup> prove that (x<sup>2<\/sup> + a<sup>2<\/sup>)y<sub>2<\/sub> &#8211; 10xy<sub>1<\/sub> &#8211; 12y = 0<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66272\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-31.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 31\" width=\"353\" height=\"207\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-31.png 353w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-31-300x176.png 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66273\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-32.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 32\" width=\"308\" height=\"150\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-32.png 308w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-32-300x146.png 300w\" sizes=\"(max-width: 308px) 100vw, 308px\" \/><\/p>\n<p>Question 48.<br \/>\nFind the area bounded by the parabola y<sup>2<\/sup> = 4x and the line y = 2x &#8211; 4.<br \/>\nSolution:<br \/>\nThe given parabola is y<sup>2<\/sup> = 4x &#8230;&#8230;&#8230; (1)<br \/>\nThe given line is y = 2x &#8211; 4 and x = \\(\\frac{y+4}{2}\\) &#8230;&#8230;. (2)<br \/>\nSolving (1) and (2) we get \\(\\frac{y^{2}}{4}=\\frac{y+4}{2}\\)<br \/>\n\u21d2 y<sup>2<\/sup> &#8211; 2y &#8211; 8 = 0<br \/>\n\u21d2 (y + 2)(y &#8211; 4) = 0<br \/>\n\u21d2 y = -2 or 4<br \/>\nThe points of intersection are A(1, 2) and B(4, 4)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66274\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-33.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 33\" width=\"376\" height=\"372\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-33.png 376w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-33-300x297.png 300w\" sizes=\"(max-width: 376px) 100vw, 376px\" \/><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\">Part &#8211; E<\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"color: #0000ff;\">V. Answer any one questions. (1 \u00d7 10 = 10)<\/span><\/p>\n<p>Question 49.<br \/>\n(a) Transport corporation operates bus service between two villages. Date regarding the passenger traffic during the first three days of the week is given below&#8217; along with the total revenue. The data does not include bus fare charged per child, senior citizen and adults.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66275\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-34.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 34\" width=\"652\" height=\"185\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-34.png 652w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-34-300x85.png 300w\" sizes=\"(max-width: 652px) 100vw, 652px\" \/><br \/>\nFind the bus fare charged per child, senior citizen and per adult by using matrix method.<br \/>\nSolution:<br \/>\nLet x, y &amp; z denote the raters of commission in Rupees\/unit for the child, senior citizen and per adult respectively. Then the data given can be expressed as a system of linear equations.<br \/>\n100x + 100y + 200z = 900<br \/>\n300x + 200y + 100z = 1000<br \/>\n100x + 200y + 300z = 1400<br \/>\nor<br \/>\nx + y + 2z = 9<br \/>\n3x + 2y + z = 10<br \/>\nx + 2y + 3z = 14<br \/>\nSolve these equations by Matrix Method.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66276\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-35.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 35\" width=\"475\" height=\"289\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-35.png 475w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-35-300x183.png 300w\" sizes=\"(max-width: 475px) 100vw, 475px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66277\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-36.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 36\" width=\"427\" height=\"410\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-36.png 427w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-36-300x288.png 300w\" sizes=\"(max-width: 427px) 100vw, 427px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66278\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-37.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 37\" width=\"303\" height=\"138\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-37.png 303w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-37-300x137.png 300w\" sizes=\"(max-width: 303px) 100vw, 303px\" \/><\/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 40 metres from the bank, he finds the angle to be 30\u00b0. Find the height of the tree and the breadth of the river.<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66279\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-38.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 38\" width=\"234\" height=\"232\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-38.png 234w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-38-150x150.png 150w\" sizes=\"(max-width: 234px) 100vw, 234px\" \/><br \/>\nLet AB = height of the tree = h<br \/>\nBreadth of the river = x mts<br \/>\nFrom \u2206AQB, tan 60\u00b0 = \\(\\frac{\\mathrm{AB}}{\\mathrm{QB}}\\)<br \/>\n\u21d2 \u221a3 = \\(\\frac{h}{x}\\)<br \/>\n\u21d2 h = x\u221a3 &#8230;&#8230; (1)<br \/>\nFrom \u2206APB, tan 30\u00b0 = \\(\\frac{\\mathrm{AB}}{\\mathrm{PB}}\\)<br \/>\n\u21d2 \\(\\frac{1}{\\sqrt{3}}=\\frac{h}{40+x}\\)<br \/>\n\u21d2 40 + x = \u221a3.h<br \/>\n\u21d2 40 + x = 3x<br \/>\n\u21d2 40 = 2x<br \/>\n\u21d2 x = 20 mts<br \/>\nh = x\u221a3 = 20\u221a3 mts<br \/>\nHence height of tree = 20\u221a3 mts, Breadth of the river = 20 mts<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 50.<br \/>\n(a) If the angle q is measured in radians then prove that \\(\\lim _{\\theta \\rightarrow 0} \\frac{\\sin \\theta}{\\theta}=1\\)<br \/>\nSolution:<br \/>\nLet &#8216;O&#8217; the centre of unit circle, assume that \u03b8 is measured in positive radians<br \/>\nLet \u2220AOB = \u03b8c, from A, draw AD is \u22a5 to OA, meeting OB produced to D, therefore OA = OB = radians<br \/>\nFrom the diagram we have area of \u2206AOB = area of sector AOB = area of \u2206AOD<br \/>\narea of \u2206AOB \u2264 area of sector \u2206AOB \u2264 area of \u2206AOD<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66280\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-39.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 39\" width=\"234\" height=\"332\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-39.png 234w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-39-211x300.png 211w\" sizes=\"(max-width: 234px) 100vw, 234px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66281\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-40.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 40\" width=\"300\" height=\"264\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66282\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-41.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 41\" width=\"413\" height=\"385\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-41.png 413w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-41-300x280.png 300w\" sizes=\"(max-width: 413px) 100vw, 413px\" \/><\/p>\n<p>(b) Using binomial theorem find the value of (1.01)<sup>5<\/sup> corrected up to four.<br \/>\nSolution:<br \/>\n(1 .01)<sup>5<\/sup><br \/>\n= (1 + 0.1)<sup>5<\/sup><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66283\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-42.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2018 - 42\" width=\"538\" height=\"45\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-42.png 538w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2018-42-300x25.png 300w\" sizes=\"(max-width: 538px) 100vw, 538px\" \/><br \/>\n= 1 + 5(0.01) + 10(0.001) + 10(0.000001) + Neglect the next terms<br \/>\n= 1 + 0.05 + 0.001 + 0.00001<br \/>\n= 1.0510 correct upto 4 decimals<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Students can Download 2nd PUC Basic Maths Model Question June 2018 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 June 2018 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\/27057"}],"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=27057"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/27057\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=27057"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=27057"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=27057"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}