{"id":21699,"date":"2020-01-28T16:10:02","date_gmt":"2020-01-28T10:40:02","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=21699"},"modified":"2021-07-02T15:26:25","modified_gmt":"2021-07-02T09:56:25","slug":"2nd-puc-basic-maths-previous-year-question-paper-june-2016","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/2nd-puc-basic-maths-previous-year-question-paper-june-2016\/","title":{"rendered":"2nd PUC Basic Maths Previous Year Question Paper June 2016"},"content":{"rendered":"<p>Students can Download 2nd PUC Basic Maths Previous Year Question Paper June 2016, Karnataka <a href=\"https:\/\/kseebsolutions.guru\/2nd-puc-basic-maths-model-question-papers-with-answers\/\">2nd PUC Maths Model Question Papers with Answers<\/a> helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.<\/p>\n<h2>Karnataka 2nd PUC Basic Maths Previous Year Question Paper June 2016<\/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 al the parts<\/li>\n<li>Part-A carries 10 marks\\, Parts &#8211; B carries 20 marks, Part &#8211; C carries 3 marks, Part &#8211; D carries 30 marks and Part &#8211; E carries 1 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;\">Answer All the ten questions: (10 \u00d7 1 = 10)<\/span><\/p>\n<p>Question 1.<br \/>\nFind x such that \\(\\left[ \\begin{matrix} 3 &amp; x \\\\ 4 &amp; 7 \\end{matrix} \\right] \\) is symmetric<br \/>\nAnswer:<br \/>\nX = 4<\/p>\n<p>Question 2.<br \/>\nFind n if <sup>n<\/sup>C<sub>8<\/sub> = <sup>n<\/sup>C<sub>7<\/sub><br \/>\nAnswer:<br \/>\n<sup>n<\/sup>C<sub>8<\/sub> = <sup>n<\/sup>C<sub>7<\/sub> \u21d2 <sup>n<\/sup>C<sub>8<\/sub> = <sup>n<\/sup>C<sub>7<\/sub> \u21d2 8 = n &#8211; 7 \u21d2 n = 15<\/p>\n<p>Question 3.<br \/>\nNegate the proposition &#8220;4 is an even integer or 7 is a prime number&#8221;.<br \/>\nAnswer:<br \/>\n4 is not an even integer and 7 is not a prime number.<\/p>\n<p>Question 4.<br \/>\nFind the value of x if 32 : x = 75 : 50.<br \/>\nAnswer:<br \/>\n\\(x=\\frac{32 \\times 50}{75}=\\frac{64}{3}\\)<\/p>\n<p>Question 5.<br \/>\nFind the income obtained by investing \u20b9 3,600 in 5% stock at 90.<br \/>\nAnswer:<br \/>\nIncome = \\(\\frac { 5 }{ 100 }\\) \u00d7 3600 = 180<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 6.<br \/>\nFind the value of 3 sin 10\u00b0 &#8211; 4 sin 10\u00b0.<br \/>\nAnswer:<br \/>\n3 sin 10\u00b0 &#8211; 4 sin 10\u00b0 = sin 3.10\u00b0 = sin 30\u00b0 = \\(\\frac { 1 }{ 2 }\\)<\/p>\n<p>Question 7.<br \/>\nIf x<sup>2<\/sup> + y<sup>2<\/sup> &#8211; 4x &#8211; 8y + k = 0 represents a point circle find k.<br \/>\nAnswer:<br \/>\nR = \\(\\sqrt{g^{2}+f^{2}-c}\\), g = -2, f = -4,c = k, r = 0.<br \/>\n\u2234 \\(\\sqrt{4+16-k}=0\\)<br \/>\n20 &#8211; k = 0 \u21d2 k = 20<\/p>\n<p>Question 8.<br \/>\nEvaluate \\(\\lim _{x \\rightarrow 0}(1+3 x)^{\\frac{1}{x}}\\)<br \/>\nAnswer:<br \/>\n\\(\\lim _{x \\rightarrow 0}(1+3 x)^{\\frac{1}{x}}=e^{3}\\)<\/p>\n<p>Question 9.<br \/>\nIf y = cos (x<sup>3<\/sup>) find \\(\\frac{\\mathrm{d} \\mathrm{y}}{\\mathrm{d} \\mathrm{x}}\\)<br \/>\nAnswer:<br \/>\nLet y = Cos(x<sup>3<\/sup>)<br \/>\n\u2234 \\(\\frac{\\mathrm{d} \\mathrm{y}}{\\mathrm{d} \\mathrm{x}}\\) = sin(x<sup>3<\/sup>).3x<sup>2<\/sup><\/p>\n<p>Question 10.<br \/>\nEvaluate : \u222b(x<sup>e<\/sup> + e<sup>x<\/sup> &#8211; log a)dx<br \/>\nAnswer:<br \/>\n\\(\\frac{x^{e+1}}{e+1}+e^{x}-\\log a \\cdot x+C\\)<\/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 \/>\nSolve using Cramer&#8217;r rule:<br \/>\n5x + 7y = 3<br \/>\n7x + 5y = 9<br \/>\nAnswer:<br \/>\n5x + 7y = 3<br \/>\n7x + 5y = 9<br \/>\n\u0394 = \\(\\left| \\begin{matrix} 5 &amp; 7 \\\\ 7 &amp; 5 \\end{matrix} \\right| \\) = 25 &#8211; 69 = -24 \u0394<sub>x<\/sub> = \\(\\left| \\begin{matrix} 3 &amp; 7 \\\\ 9 &amp; 5 \\end{matrix} \\right| \\) = 15 &#8211; 63 = -48 \u0394<sub>y<\/sub> = \\(\\left| \\begin{matrix} 5 &amp; 3 \\\\ 7 &amp; 9 \\end{matrix} \\right| \\) = 45 &#8211; 21 = 24<br \/>\n\u2234 x = \\(\\frac{\\Delta_{x}}{\\Delta}=\\frac{-48}{-24}\\) = 2 y = \\(\\frac{\\Delta_{y}}{\\Delta}=\\frac{24}{-24}\\) = -1<br \/>\n\u2234 x = 2, y = -1<\/p>\n<p>Question 12.<br \/>\nFind the number of parallelograms that can be formed form a set of 6 parallel lines intersecting another set of 4 parallel lines.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65907\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-1.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 1\" width=\"402\" height=\"56\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-1.png 402w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-1-300x42.png 300w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 13.<br \/>\nWhat is the probability that there will be 53 Mondays in a randomly selected leap year?<br \/>\nAnswer:<br \/>\nEvery year has 52 complete weeks 8 = 364 days (52 \u00d7 7) A leap year has 366 days, in the remaining two days we have to see what is the probability I getting Monday, the two days may occur in any one of the following (Sunday, Monday) (Mon,Tue), (Wed, Thur) (Thur,Fri) (Fri, Satur) (Satur, Sun) Out of the 7 Possibilities, the first two cases have Monday<br \/>\n\u2234 P(53Mondays in a leap) = \\(\\frac { 2 }{ 7 }\\)<\/p>\n<p>Question 14.<br \/>\nWrite the converse and income of the statement &#8220;If Maths is easy then child is brave&#8221;.<br \/>\nAnswer:<br \/>\nConverse = (q \u2192 P) = If the child is brave then maths is easy<br \/>\nInverse = (~ P \u2192 ~q) = If maths is not easy then the child is not brave.<\/p>\n<p>Question 15.<br \/>\nDivide 6,000 in the ratio 3 : 4 : 5.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65906\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-2.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 2\" width=\"209\" height=\"48\" \/><br \/>\nII part = \\(\\frac{4}{12}\\) \u00d7 6000 = 2000<\/p>\n<p>III part = \\(\\frac{5}{12}\\) \u00d7 6000 = 2500<\/p>\n<p>Question 16.<br \/>\nA banker pays 2,380 on a bill of 2,500,73 days before the legally due date. Find the rate of discount charged by the banker.<br \/>\nAnswer:<br \/>\nF = \u20b9 2,500, discounted value = 2380, t = 73 days, t = \\(\\frac{73}{365}=\\frac{1}{5}\\) yr<br \/>\nDiscounted value = F (1 \u2013 tr}<br \/>\n2380 = 2500 \\(\\left(1-\\frac{1}{5} \\times r\\right)\\) \u21d2 \\(\\frac{2380}{2500}\\) = 1 &#8211; \\(\\frac{r}{5}\\) \u21d2 1 &#8211; 0.952<br \/>\n0.2r = 0.048<br \/>\nr = \\(\\frac{0.048}{0.2}\\) = 24 = 24%<\/p>\n<p>Question 17.<br \/>\nIf A + B + C = 180\u00b0 and tan A = 1, tan B=2, show that tan C = 3,<br \/>\nAnswer:<br \/>\nGiven A + B + C = 180\u00b0 \u21d2 A + B = 180 &#8211; C \u2234 tan(A + B) = tan (180 &#8211; C)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65905\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-3.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 3\" width=\"485\" height=\"43\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-3.png 485w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-3-300x27.png 300w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><\/p>\n<p>Question 18.<br \/>\nFind the focus and equation of the directrix of the parabol x<sup>2<\/sup> = &#8211; 16y<br \/>\nAnswer:<br \/>\nGiven x<sup>2<\/sup> = &#8211; 16y<br \/>\nCompare x<sup>2<\/sup> = -4ay \u21d2 4a = 16 \u21d2 a = 4<br \/>\nThe curve turns down words \u2234 focus S = (0,-4)<br \/>\nEquation of directrix is y = 4 or y &#8211; 4 = 0<\/p>\n<p>Question 19.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65904\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-4.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 4\" width=\"412\" height=\"76\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-4.png 412w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-4-300x55.png 300w\" sizes=\"(max-width: 412px) 100vw, 412px\" \/><br \/>\nAnswer:<br \/>\nGiven the function is continuous \\(\\lim _{x \\rightarrow 4}\\) f(x) = f(4)<br \/>\n\\(\\lim _{x \\rightarrow 4} \\frac{x^{4}-4^{4}}{x-4}=K\\) \u2234 k = 4.4<sup>+-1<\/sup> = 4.4<sup>3<\/sup> = 4<sup>4<\/sup> = 256<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 20.<br \/>\nIf y = x<sup>x<\/sup> find \\(\\frac{d y}{d x}\\)<br \/>\ndx<br \/>\nAnswer:<br \/>\nLet y = x<sup>x<\/sup><br \/>\nlog y = x.log x<br \/>\n\\(\\frac{1}{y} \\frac{d y}{d x}=x, \\frac{1}{x}+\\log x, 1 \\Rightarrow \\frac{d y}{d x}\\) = y (1 + log x) = x<sup>x<\/sup>(1 + logx)<\/p>\n<p>Question 21.<br \/>\nWhen brakes are applied to a moving car, the car travels a distance &#8216;s&#8217; feet in &#8216;t&#8217; secs is given by s = 20t &#8211; 40t<sup>2<\/sup>. When does the car stop?<br \/>\nAnswer:<br \/>\nGiven s = 20t &#8211; 40t<sup>2<\/sup><br \/>\nv = \\(\\frac{d s}{d t}\\) = 20 &#8211; 80t<br \/>\nThe car stops when the velocity = 0 \u21d2 20 &#8211; 80t = 0 \u21d2 t = \\(\\frac{1}{4}\\) sec<\/p>\n<p>Question 22.<br \/>\nThe radius of a sphere is increasing at the rate of 0.5 mts \/ sec. Find the rate of Increase of its volume when r=1.5 mts.<br \/>\nAnswer:<br \/>\nGiven \\(\\frac{d r}{d t}\\) = 0.5 mts \/ sec. \\(\\frac{d v}{d t}\\) = ? when r =1.5mts v = \\(\\frac{4}{3}\\)\u03c0r<sup>3<\/sup><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65903\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-5.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 5\" width=\"332\" height=\"46\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-5.png 332w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-5-300x42.png 300w\" sizes=\"(max-width: 332px) 100vw, 332px\" \/><\/p>\n<p>Question 23.<br \/>\nEvaluate : \\(\\int \\frac{e^{x}}{e^{x}-1} d x\\)<br \/>\nAnswer:<br \/>\n\\(\\int \\frac{e^{x}}{e^{x}-1} d x\\) = log (e<sup>x<\/sup>+ 1) + C \u2234 \\(\\int \\frac{f^{\\prime}(x)}{f(x)}\\) dx = log(f(x))<\/p>\n<p>Question 24.<br \/>\nEvaluate \\( \\int_{1}^{2}\\left(x+e^{x}\\right) d x\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65902\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-6.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 6\" width=\"452\" height=\"56\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-6.png 452w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-6-300x37.png 300w\" sizes=\"(max-width: 452px) 100vw, 452px\" \/><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\">Part &#8211; C<\/span><\/p>\n<p><span style=\"color: #0000ff;\">Answer any ten questions: (10 \u00d7 3 = 30)<\/span><\/p>\n<p>Question 25.<br \/>\nIf A = \\(\\left[ \\begin{matrix} 2 &amp; -1 \\\\ 1 &amp; 4 \\end{matrix} \\right] \\) and B = \\(\\left[ \\begin{matrix} -3 &amp; 2 \\\\ -1 &amp; 4 \\end{matrix} \\right] \\) show that (AB)&#8217; = B&#8217; A&#8217;.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65901\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-7.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 7\" width=\"785\" height=\"107\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-7.png 785w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-7-300x41.png 300w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-7-768x105.png 768w\" sizes=\"(max-width: 785px) 100vw, 785px\" \/><br \/>\nFrom 1 and 2 we get (AB)&#8217; = B&#8217;A&#8217;<\/p>\n<p>Question 26.<br \/>\nSolve for \\(\\left[ \\begin{matrix} x+2 &amp; 3 &amp; 4 \\\\ 2 &amp; x+3 &amp; 4 \\\\ 2 &amp; 3 &amp; x+4 \\end{matrix} \\right] =\\quad 0\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65900\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-8.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 8\" width=\"498\" height=\"187\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-8.png 498w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-8-300x113.png 300w\" sizes=\"(max-width: 498px) 100vw, 498px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 27.<br \/>\nFind the number of permutations of the letters of the word Engineering How many of these<br \/>\n(a) Begin with GRIN<br \/>\n(b) Have all 3 E&#8217;s together?<br \/>\nAnswer:<br \/>\nThe word has 11 letters, E = 3, N = 3, G = 2, I = 2<br \/>\nTotal permutations \\(\\frac{11 !}{3 !, 3 !, 2 ! 2 !}\\)<br \/>\n(a) Permutations word which begin with GRIN = \\(\\frac{7 !}{3 ! 2 !}\\)<br \/>\n(b) All 3E&#8217;s are together Consider 3E as one unit remaining letters = 8 + 1 = 9<br \/>\nN = 3,G = 2, 1 &#8211; 2 No of permutation = \\(\\frac{9 !}{3 ! 2 ! 2 !}\\)<\/p>\n<p>Question 28.<br \/>\nOne Card is randomly drawn from a pack of 52 cards, Find the probability that<br \/>\n(a) Card is either black or jack<br \/>\n(b) Card is red<br \/>\n(c) Card is diamond.<br \/>\nAnswer:<br \/>\nTotally there are 52 cards and any one can be drawn<br \/>\n\u2234 Total no cases = n = 52<\/p>\n<p>(a) There are 26 black cards and 2 jack totally = 28 cards \u2234 no of favourable case = m = 28<br \/>\n\u2234 P(black or jack) = \\(\\frac{28}{52}\\)<\/p>\n<p>(b) There are 26 red cards<br \/>\n\u2234 m = 26,<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65899\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-9.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 9\" width=\"184\" height=\"54\" \/><\/p>\n<p>(C) There are 13 diamonds cards<br \/>\n\u2234 m = 13,<br \/>\nP(getting diamond) = \\(\\frac{13}{52}=\\frac{1}{4}\\)<\/p>\n<p>Question 29.<br \/>\nWalking 4 kmph a student reaches his college 5 minutes late and if he walks at 5 kmph, he reaches \\(2 \\frac{1}{2}\\) minutes early. What is the distance from his house to the college?<br \/>\nAnswer:<br \/>\nLet the distance from his house to the college = x km<br \/>\nTime taken to Cover x kns at 4km ph = \\(\\frac{x}{4}\\) hr<sup>5<\/sup><br \/>\nTime to cover 5 km ph = \\(\\frac{x}{5}\\) hrs<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65898\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-10.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 10\" width=\"564\" height=\"112\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-10.png 564w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-10-300x60.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 30.<br \/>\nA bill for \u20b9 12,900 was drawn on 3 Feb, 2014 at 6 months and discounted on 13 March 2014 at 8% p.a. For what sum was the bill discounted ?<br \/>\nAnswer:<br \/>\nF = 12,900, bill period = 6 months, Drawn date = 03 &#8211; 2 &#8211; 14<br \/>\n\u2234 LDD = DD + BP + Grace period<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65897\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-11.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 11\" width=\"309\" height=\"102\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-11.png 309w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-11-300x99.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><br \/>\nDate of discount 13-3-2014. This means, the no of days from 13-2-2014 to 06-08-14 becomes the unexpired period<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65896\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-12.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 12\" width=\"242\" height=\"169\" \/><br \/>\n\u2234 t = 145 days = \\(\\frac{146}{365}\\) year, r = 80% = 0.08, DV = ?<br \/>\nBD = Ftr = 12,900 \u00d7 \\(\\frac{146}{365}\\) \u00d7 0.08 = 412.8<br \/>\n\u2234 Discounted value = 12,900 &#8211; 412.8 = 12,487.20<\/p>\n<p>Question 31.<br \/>\nPrathik sells out \u20b9 6,000 of 7.5% stock at 108 and reinvests the proceeds in 9% stock. If Prathik&#8217;s income increase by \u20b9 270, at what price did Prathik buy 9% stock?<br \/>\nAnswer:<br \/>\nTo calculate income<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65895\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-13.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 13\" width=\"133\" height=\"83\" \/><br \/>\nIncome = \\(\\frac{6000 \\times 7.5}{10}\\) = 459.0 = \u20b9 450<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65894\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-14.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 14\" width=\"335\" height=\"154\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-14.png 335w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-14-300x138.png 300w\" sizes=\"(max-width: 335px) 100vw, 335px\" \/><br \/>\nFor 9% stock given income increase by \u20b9 270<br \/>\n\u2234 New income = 450 + 270 = \u20b9 270.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 32.<br \/>\nA furniture dealer sold furniture for \u20b9 21,000 and added 5% sales tax to the quoted price. The customers agree to buy it for \u20b9 21,000 including sales tax. Find the discount he received.<br \/>\nAnswer:<br \/>\nDiscount = 5% 21,00 = \\(\\frac{5}{10}\\) \u00d7 21,000 = 1050<\/p>\n<p>Question 33.<br \/>\nProve that \\(\\frac{\\cos 75^{\\circ}+\\cos 15^{\\circ}}{\\sin 75^{\\circ}-\\sin 15^{\\circ}}=\\sqrt{3}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65893\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-15.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 15\" width=\"589\" height=\"85\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-15.png 589w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-15-300x43.png 300w\" sizes=\"(max-width: 589px) 100vw, 589px\" \/><\/p>\n<p>Question 34.<br \/>\nFind equation of the parabola given that its vertex is (0,0) axis is Y-axis and passed through (-1,-3).<br \/>\nAnswer:<br \/>\nGiven v = (0,0) and axis is y-axis<br \/>\nThe parabola is of the form x<sup>2<\/sup> = 4ay or x<sup>2<\/sup> = -4ay<br \/>\nBut this equation passes through (-1,-0) which is in III qhadrant.<br \/>\n\u2234 The curve turn down words and is of the form x<sup>2<\/sup> = &#8211; 4ay, But it passes through (-1,-3)<br \/>\n\u2234 (-1)<sup>2<\/sup> = -4a(-3) \u21d2 1 = 12a \u21d2 a = \\(\\frac{1}{12}\\)<br \/>\n\u2234 The required equation is x<sup>2<\/sup> = -4 . \\(\\frac{1}{12}\\)y \u21d2 x<sup>2<\/sup> = \\(\\frac{-1}{3}\\) or 3x<sup>2<\/sup> + y = 0<\/p>\n<p>Question 35.<br \/>\nIf x = \\(\\frac{1-t^{2}}{1+t^{2}}\\) y = \\(\\frac{2 t}{1+t^{2}}\\) find \\(\\frac{\\mathrm{dy}}{\\mathrm{dt}}\\)<br \/>\nAnswer:<br \/>\nDifferentiate both w.r.tt<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65892\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-16.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 16\" width=\"615\" height=\"139\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-16.png 615w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-16-300x68.png 300w\" sizes=\"(max-width: 615px) 100vw, 615px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65891\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-17.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 17\" width=\"335\" height=\"85\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-17.png 335w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-17-300x76.png 300w\" sizes=\"(max-width: 335px) 100vw, 335px\" \/><br \/>\nIf the total cost function is given by C(x) = 350 + 12x + \\(\\frac{x^{2}}{4}\\) and revenue function is given by R(x) = 75x &#8211; 2x<sup>2<\/sup>, find the level of output at which profit is maximum.<br \/>\nProfit function = TR &#8211; TC = 75x &#8211; 2x &#8211; 350 &#8211; 12x &#8211; \\(\\frac{x^{2}}{4}\\) p(x) = -2x<sup>2<\/sup> &#8211; x<sup>2<\/sup> + 63x &#8211; 350<br \/>\nFor maximum profit differentiate w.r.t x \\(\\frac{d}{d x}\\) P(x) = 0<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65890\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-18.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 18\" width=\"361\" height=\"49\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-18.png 361w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-18-300x41.png 300w\" sizes=\"(max-width: 361px) 100vw, 361px\" \/><br \/>\n126 = 9x \u21d2 x = \\(\\frac{126}{9}\\) = 14 \u2234 x = 14<\/p>\n<p>Question 37.<br \/>\nEvaluate \u222bx<sup>2<\/sup> log xdx<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65889\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-19.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 19\" width=\"588\" height=\"47\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-19.png 588w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-19-300x24.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 38.<br \/>\nEvaluate \\(\\int \\frac{1+\\cos x}{1-\\cos x} d x\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65888\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-20.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 20\" width=\"534\" height=\"138\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-20.png 534w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-20-300x78.png 300w\" sizes=\"(max-width: 534px) 100vw, 534px\" \/><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\">Part &#8211; D<\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"color: #0000ff;\">Answer any six questions: (6 \u00d7 5 = 30)<\/span><\/p>\n<p>Question 39.<br \/>\nFind the term independent of x in \\(\\left(x^{3}-\\frac{3}{x^{2}}\\right)^{15}\\)<br \/>\nAnswer:<br \/>\nT<sub>r+1<\/sub> = <sup>n<\/sup>C<sub>r<\/sub> x<sup>n-r<\/sup> a<sup>r<\/sup><br \/>\nHere x \u2192 x<sup>3<\/sup>a \u2192 \\(\\frac{-3}{x^{2}}\\) n \u2192 15<br \/>\nT<sub>r+1<\/sub> = <sup>15<\/sup>C<sub>r<\/sub> (x<sup>3<\/sup>)<sup>15 &#8211; r<\/sup> \\(\\left(\\frac{-3}{x^{2}}\\right)\\) = <sup>15C<sub>r . <\/sub><\/sup>x<sup>45 &#8211; 3r<\/sup> (-3)<sup>r<\/sup> . x<sup>-2r<\/sup><br \/>\nT<sub>r+1<\/sub> = <sup>15<\/sup>C<sub>r<\/sub>(-3)<sup>r<\/sup> . x<sup>45 &#8211; 5r<\/sup><br \/>\nTo find the term independent of x equate the power of x = 0<br \/>\n\u21d2 45 &#8211; 5r = 0 \u21d2 45 = 5r = 0 \u21d2 r = 9<br \/>\nT<sub>9+1<\/sub> = <sup>15<\/sup>C<sub>9<\/sub>(-3)<sup>9<\/sup> . x<sup>0<\/sup> = <sup>15<\/sup>C<sub>9<\/sub>(-3)<sup>9<\/sup><br \/>\nT<sub>10<\/sub> = 3<sup>9<\/sup>, <sup>15<\/sup>C<sub>9<\/sub> is the term independent of x<\/p>\n<p>Question 40.<br \/>\nResolve into partial fractions \\(\\frac{3 x+2}{(x-2)(x+3)^{2}}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65887\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-21.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 21\" width=\"284\" height=\"49\" \/><br \/>\n3x + 2 = A(x +3 )<sup>2<\/sup> + B(x &#8211; 2)(x &#8211; 3) + C(x &#8211; 2)<br \/>\nPut x = 2,6 + 2 = A (2 + 3))<sup>2<\/sup> \u21d2 A = \\(\\frac { 8 }{ 25 }\\)<br \/>\nPut x = -3 -9 + 2 = 0 + 0 + C(-5)<br \/>\n-7 = -5C \u21d2 C = 715<br \/>\nPut x = 0 we get B = \\(-\\frac { 8 }{ 25 }\\)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65886\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-22.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 22\" width=\"333\" height=\"53\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-22.png 333w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-22-300x48.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=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 41.<br \/>\nVerify whether the proposition ~(p \u2228 q) \u2192 (~P \u2227 ~q) is a tautology contradiction or neither.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65885\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-23.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 23\" width=\"536\" height=\"156\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-23.png 536w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-23-300x87.png 300w\" sizes=\"(max-width: 536px) 100vw, 536px\" \/><\/p>\n<p>Question 42.<br \/>\nTwo taps can separately fill a tank in 12 minutes and 15 minutes respectively. The tank when full can be emptied by a drain tap in 20 minutes. When the tank was empty all the three taps were opened simultaneously. In what time will the tank be filled up?<br \/>\nAnswer:<br \/>\n1<sup>st<\/sup> tap can fill \\(\\frac{1}{12}^{\\text {th }}\\) tank in 1 min 2nd tap can fill \\(\\frac{1}{15}^{\\text {th }}\\) tank in 1 min<br \/>\nDrain pipe drain out = \\(\\frac{1}{20}^{\\text {th }}\\) tank in 1 min<br \/>\n\u2234 In 1 min = \\(\\frac{1}{12}+\\frac{1}{15}-\\frac{1}{20}=\\frac{15+12-9}{180}=\\frac{18}{180}=\\frac{1}{10}\\) of tank will get filled<br \/>\n\u2234 The tank will get filled in 10 minutes.<\/p>\n<p>Question 43.<br \/>\nABC company required 1000 hours to produce first 30 engines. If the learning effect is 90%, find the total labour cost at \u20b9 20 per hour to produce total of 120 engines.<br \/>\nAnswer:<br \/>\nAssume 1 lot = 30 engines<br \/>\n\u2234 120 engines = 4 lots<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65884\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-24.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 24\" width=\"683\" height=\"136\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-24.png 683w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-24-300x60.png 300w\" sizes=\"(max-width: 683px) 100vw, 683px\" \/><br \/>\nThe total no of hrs to produce 4 lots = 3240<br \/>\nThe lab cost at 20 per hour = 3240 \u00d7 20 = \u20b9 64,800<\/p>\n<p>Question 44.<br \/>\nSolve the L.P.P graphically<br \/>\nMaximize Z = 2x + 3y<br \/>\nSubject to constraints x + y \u2264 400, 2x + y \u2264 400, x,y \u2265 0.<br \/>\nAnswer:<br \/>\nConsider<br \/>\nX + y = 400 2x + y = 600<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65883\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-25.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 25\" width=\"307\" height=\"169\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-25.png 307w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-25-300x165.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><br \/>\nPoint of intersection of x + y = 400 &amp; 2x + y = 600<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65882\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-26.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 26\" width=\"396\" height=\"229\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-26.png 396w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-26-300x173.png 300w\" sizes=\"(max-width: 396px) 100vw, 396px\" \/><br \/>\nFunction is maximum at the point A (0.400) and maximum value = 1200<\/p>\n<p>Question 45.<br \/>\nThe angles of elevation of the top of a tower the base and the top of a building are 60\u00b0 and 30\u00b0. 3x + 5y \u2264 15, 5x + 2y \u2264 10 and x \u2265 0, y \u2265 0.<br \/>\nAnswer:<br \/>\nLet AB = Building &amp; CD is the tower. From the rt angled \u2206 ACD<br \/>\nWe have tan 60 = \\(\\frac { h }{ x }\\)<br \/>\n\u221a3 = \\(\\frac { h }{ x }\\) \u21d2 x = \u221a3(h -20)<br \/>\nFrom 1 and 2 wet \u221a3(h &#8211; 20) = \\(\\frac{\\mathrm{h}}{\\sqrt{3}}\\) \u21d2 3(h &#8211; 20) = h \u21d2 3h &#8211; 60 = h \u21d2 3h &#8211; 60 = h \u21d2 2h = 60 \u21d2 h = 30 mts<br \/>\n\u2234 Height of the tower = 30mts<\/p>\n<p>Question 46.<br \/>\nFind the equation of circle passing through points (5,3) (1,5) (3,-1)<br \/>\nAnswer:<br \/>\nLet the required equation of the circle is<br \/>\nx<sup>2<\/sup> + y<sup>2<\/sup> + 2gx + 2fg + c = 0<br \/>\nBut this eqn passes through the points<br \/>\n(5,3) 10g + 6f + C + 34 = 0<br \/>\n(1,5) 2g + 10 f + C + 26 = 0<br \/>\n(3,-1) 6g &#8211; 2f + C + 10 = 0<br \/>\nSolving 2,3 and 4 we get<br \/>\n2 &#8211; 3 \u21d2 2g &#8211; f + 2 = 0<br \/>\n3 &#8211; 4 \u21d2 g &#8211; 3f &#8211; 4 = 0<br \/>\nAgain solving we get y = -2, f = -2, c = -2<br \/>\nThis the required egn of the circle is x<sup>2 <\/sup>+ y<sup>2<\/sup> &#8211; 4x &#8211; 4y -2 = 0<\/p>\n<p>Question 47.<br \/>\nIf y = \\((x+\\sqrt{1+x^{2}})^{m}\\) prove that (1 + x<sup>2<\/sup>)y<sub>2<\/sub> + xy<sub>1<\/sub> &#8211; m<sup>2<\/sup>y=0<br \/>\nAnswer:<br \/>\nGiven y = \\((x+\\sqrt{1+x^{2}})^{m}\\)<br \/>\nDiff. w.r.tx<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65881\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-27.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 27\" width=\"553\" height=\"135\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-27.png 553w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-27-300x73.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><br \/>\n\\(\\sqrt{1+x^{2}} y_{1}\\) = my S.BS<br \/>\n(1 + x<sup>2<\/sup>)y<sup>2<\/sup><sub>1<\/sub> = m<sup>2<\/sup>y<sup>2<\/sup><br \/>\nAgain differentiate w.r.t.x (1 + x<sup>2<\/sup>).2y<sub>1<\/sub>y<sub>2<\/sub> + y<sup>2<\/sup><sub>1<\/sub> (2x) = m<sup>2<\/sup>.2yy<sub>1<\/sub> \u00f7 2y<sub>1<\/sub> \u2234 (1 + x<sup>2<\/sup>).y<sub>2<\/sub> + xy<sub>1<\/sub> &#8211; m<sup>2<\/sup>y = 0<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 48.<br \/>\nFind the area enclosed between parabola y<sup>2<\/sup> = x and the line x + y = 2.<br \/>\nAnswer:<br \/>\nGiven y<sup>2<\/sup> = x and x + y = 2<br \/>\n\u21d2 (2 &#8211; x)<sup>2<\/sup> = x \u2234 y = 2 &#8211; x<br \/>\n\u21d2 4 + x<sup>2<\/sup> &#8211; 4x &#8211; x = 0 \u21d2 x<sup>2<\/sup> &#8211; 5x &#8211; 4 = 0 \u21d2 x = 4 or<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65880\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-28.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 28\" width=\"445\" height=\"115\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-28.png 445w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-28-300x78.png 300w\" sizes=\"(max-width: 445px) 100vw, 445px\" \/><\/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 questions: (1 \u00d7 10 = 10)<\/span><\/p>\n<p>Question 49.<br \/>\n(a) A school wants to award to award its students for the values of leadership, good behavior and hard work with a total cash award of \u20b9 6,000. Three times the award money for hard work added to that given for leadership amounts to 11,000. The award money for leadership and hard work together is double the one given for good behavior. Calculate the award money given for each value, using matrix method.<br \/>\nAnswer:<br \/>\nLet the values of punctuality, good behavior and hard work be denoted by x,y &amp; z respectively<br \/>\nx + y + z = 6000<br \/>\nx + oy + 3z = 11,000<br \/>\nx + z = 2y or x &#8211; 2y + z = 0<br \/>\nThe given equations in matrix form is \\(\\left[ \\begin{matrix} 1 &amp; 1 &amp; 1 \\\\ 1 &amp; 0 &amp; 3 \\\\ 1 &amp; -2 &amp; 1 \\end{matrix} \\right] \\left[ \\begin{matrix} x \\\\ y \\\\ z \\end{matrix} \\right] \\left[ \\begin{matrix} 6000 \\\\ 11,000 \\\\ 0 \\end{matrix} \\right] \\)<br \/>\nA x = B<br \/>\n\u21d2 X = A<sup>-1<\/sup>B<br \/>\nWhere A = \\(\\left[ \\begin{matrix} 1 &amp; 1 &amp; 1 \\\\ 1 &amp; 0 &amp; 3 \\\\ 1 &amp; -2 &amp; 1 \\end{matrix} \\right] \\)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65879\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-29.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 29\" width=\"458\" height=\"184\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-29.png 458w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-29-300x121.png 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nX = \u20b9 500, y = \u20b9 2000, z = \u20b9 3500.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>(b). A company produces two products P and Q. Each P require 4 hours of grinding and 2 hours of polishing and each Q requires 2 hours of grinding and 5 hours of polishing. The total available hours for grinding is 20 and for polishing is 24. Profit per unit of P is 6 and that of Q is \u20b9 8. Formulate the L.P.P<br \/>\nAnswer:<br \/>\nLet x be the units of P manufactured and y be the units of Q manufactured<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65878\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-30.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 30\" width=\"603\" height=\"110\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-30.png 603w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-30-300x55.png 300w\" sizes=\"(max-width: 603px) 100vw, 603px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65877\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-31.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 31\" width=\"116\" height=\"82\" \/><br \/>\nMaximize z = 6x + 8y<br \/>\nSubject to constraints<\/p>\n<p>Question 50.<br \/>\n(a). Prove that \\(\\lim _{\\theta \\rightarrow 0} \\frac{\\sin \\theta}{\\theta}=1\\), where \u03b8 is in radius.<br \/>\nAnswer:<br \/>\nLet &#8216;O&#8217; the centre of unit circle, assume that is measured in positive radians.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65876\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-32.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 32\" width=\"597\" height=\"41\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-32.png 597w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-32-300x21.png 300w\" sizes=\"(max-width: 597px) 100vw, 597px\" \/><br \/>\nFrom the figure, we have area of \u2206AOB = area of sector AOB = area of \u2206AOD<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65875\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-33.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 33\" width=\"266\" height=\"49\" \/><br \/>\n\u2234 Area of sector = \\(\\frac { 1 }{ 2 }\\) (radius)<sup>2<\/sup> \u00d7 angle in radians<br \/>\nFrom the triangle DOA, tan \u03b8 = \\(\\frac{\\mathrm{DA}}{\\mathrm{OA}}\\) [\u2234 DA = r tan\u03b8]<br \/>\nFrom the triangle BOC, sin \u03b8 = \\(\\frac{\\mathrm{BC}}{\\mathrm{OB}}\\) [\u2234 BC = r sin \u03b8]<br \/>\n(1) becomes<br \/>\n\u21d2 BC \u2264 \u03b8 \u2264 DA<br \/>\n\u21d2 sin \u03b8 \u2264 \u03b8 \u2264 tan \u03b8<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65874\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-34.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 34\" width=\"240\" height=\"244\" \/><br \/>\nDividing by sin \u03b8<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65873\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-35.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper June 2016 - 35\" width=\"394\" height=\"419\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-35.png 394w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-June-2016-35-282x300.png 282w\" sizes=\"(max-width: 394px) 100vw, 394px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>(b). Find the value of (1.1)<sup>5<\/sup> using binomial theorem upto 4 decimal places.<br \/>\nAnswer:<br \/>\n(1.1)<sup>5<\/sup> = (1 + 0.1)<sup>5<\/sup><br \/>\n= 1<sup>5<\/sup> + <sup>5<\/sup>C<sub>1<\/sub> (0.1) + <sup>5<\/sup>C<sub>2<\/sub>(0.1)<sup>2<\/sup> + <sup>5<\/sup>C<sub>3<\/sub> (0.1)<sup>3<\/sup> + <sup>5<\/sup>C<sub>4<\/sub>(0.1)<sup>4<\/sup> + <sup>5<\/sup>C<sub>5<\/sub>(0.1)<sup>5<\/sup><br \/>\n= 1 + 5(0.1) + 10(0.1) + 10(0.001) + 1(0.00001)<br \/>\n= 1 + 0.5 + 0.1 + 0.01 + 0.005 + 0.00001<br \/>\n(1.1)<sup>5<\/sup> = 1.61051<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Students can Download 2nd PUC Basic Maths Previous Year Question Paper June 2016, Karnataka 2nd PUC Maths Model Question Papers with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations. Karnataka 2nd PUC Basic Maths Previous Year Question Paper June 2016 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\/21699"}],"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=21699"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/21699\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=21699"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=21699"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=21699"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}