{"id":26949,"date":"2020-06-23T17:45:06","date_gmt":"2020-06-23T12:15:06","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=26949"},"modified":"2021-07-02T15:19:15","modified_gmt":"2021-07-02T09:49:15","slug":"2nd-puc-basic-maths-model-question-paper-2","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/2nd-puc-basic-maths-model-question-paper-2\/","title":{"rendered":"2nd PUC Basic Maths Model Question Paper 2 with Answers"},"content":{"rendered":"<p>Students can Download 2nd PUC Basic Maths Model Question Paper 2 with Answers, Karnataka <a href=\"https:\/\/kseebsolutions.guru\/2nd-puc-basic-maths-model-question-papers-with-answers\/\">2nd PUC Maths Model Question Papers with Answers<\/a> helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.<\/p>\n<h2>Karnataka 2nd PUC Basic Maths Model Question Paper 2 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 \/>\nWithout expanding evaluate: \\(\\left|\\begin{array}{cc}500 &amp; 503 \\\\506 &amp; 509\\end{array}\\right|\\)<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66285\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-1.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 1\" width=\"459\" height=\"90\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-1.png 459w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-1-300x59.png 300w\" sizes=\"(max-width: 459px) 100vw, 459px\" \/><\/p>\n<p>Question 2.<br \/>\nFind r if \\(^{15} \\mathrm{C}_{r+3}=^{15} \\mathrm{C}_{2 r-3}\\)<br \/>\nSolution:<br \/>\n\\(^{\\mathrm{n}} \\mathrm{C}_{\\mathrm{r}}=^{\\mathrm{n}} \\mathrm{C}_{\\mathrm{n}-\\mathrm{r}}\\)<br \/>\n\u21d2 r + (n &#8211; r) = n<br \/>\n\u21d2 (r + 3) + (2r &#8211; 3) = 15<br \/>\n\u21d2 3r = 15<br \/>\n\u21d2 r = 5<\/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 Model Question Paper 2 with Answers\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 3.<br \/>\nNegate: If Ramya study hard then she will get the rank.<br \/>\nSolution:<br \/>\np: Ramya study hard<br \/>\nq: She will get the Rank<br \/>\n~ (P \u2192 q) = P\u2227~q<br \/>\n&#8220;Ramya study hard and she will not get the rank:&#8221;<\/p>\n<p>Question 4.<br \/>\nIf a : b = 2 : 5 and b : c = 3 : 5 find a : c.<br \/>\nSolution:<br \/>\na : b = 2 : 5, b : c = 3 : 5<br \/>\n2 : 5 : 3 : 5<br \/>\nMultiply 1st ratio by 3 and 2nd ratio by 5<br \/>\na : b &amp; b : c<br \/>\n6 : 15 &amp; 15 : 25<br \/>\na : b : c = 6 : 15 : 25<br \/>\na : c = 6 : 25<\/p>\n<p>Question 5.<br \/>\nWhat rate of interest is realised by investing in 14.5% p.a at 81?<br \/>\nSolution:<br \/>\nFor face value \u20b9 100 Income = 145<br \/>\n\u20b9 81 \u2192 \\(\\frac{14.5 \\times 81}{100}\\) = \u20b9 11.75<\/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 Model Question Paper 2 with Answers\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 6.<br \/>\nFind the value of sin 70\u00b0 cos 20\u00b0 + cos 70\u00b0 sin 20\u00b0.<br \/>\nSolution:<br \/>\nSin 70\u00b0 cos 20\u00b0 + cos 70\u00b0 sin 20\u00b0<br \/>\n{\u2235 sin (A + B) = sin A cos B + cos A sin B [By compound angle formula]}<br \/>\nsin (A + B) = sin (70\u00b0 + 20\u00b0) = sin 90\u00b0 = 1<\/p>\n<p>Question 7.<br \/>\nFind the equation of the point circle with centre at (4, -3).<br \/>\nSolution:<br \/>\nPoint circle means radius = r = 0<br \/>\nCentre = (\u03b1, \u03b2) = (4, -3)<br \/>\nEquation of circle is (x &#8211; \u03b1)<sup>2<\/sup> + (y &#8211; \u03b2)<sup>2<\/sup> = r<sup>2<\/sup><br \/>\n(x &#8211; 4)<sup>2<\/sup> + (y + 3)<sup>2<\/sup> = 0<br \/>\nCircle equation is x<sup>2<\/sup> + y<sup>2<\/sup> &#8211; 8x + 6y + 25 = 0<\/p>\n<p>Question 8.<br \/>\nEvaluate \\(\\lim _{x \\rightarrow-4} \\frac{x^{4}-256}{x+4}\\)<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66286\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-2.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 2\" width=\"187\" height=\"62\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66287\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-3.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 3\" width=\"286\" height=\"94\" \/><\/p>\n<p>Question 9.<br \/>\nFind \\(\\frac{d y}{d x}\\) if \u221ax + \u221ay = \u221aa<br \/>\nSolut:<br \/>\n\u221ax + \u221ay = \u221aa<br \/>\nDifferentiate w.r.t x<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66288\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-4.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 4\" width=\"467\" height=\"85\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-4.png 467w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-4-300x55.png 300w\" sizes=\"(max-width: 467px) 100vw, 467px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 10.<br \/>\nEvaluate \\(\\int\\left(\\frac{1+x^{2}}{x}\\right) d x\\)<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66289\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-5.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 5\" width=\"243\" height=\"143\" \/><\/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: (2 \u00d7 10 = 20)<\/span><\/p>\n<p>Question 11.<br \/>\nProve that if any two rows (or columns) of a determinant are interchanged then the value of the determinant changes only in sign.<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66290\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-6.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 6\" width=\"479\" height=\"358\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-6.png 479w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-6-300x224.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><\/p>\n<p>Question 12.<br \/>\nIf a convex polygon has 170 diagonals, find the number of sides of the polygon.<br \/>\nSolution:<br \/>\nNo. of diagonal = 170, No. of sides = n = ?<br \/>\nNo. of diagonal = \\(\\frac{n(n-3)}{2}\\)<br \/>\n170 = \\(\\frac{n^{2}-3 n}{2}\\)<br \/>\n\u21d2 n<sup>2<\/sup> &#8211; 3n = 340<br \/>\n\u21d2 n<sup>2<\/sup> &#8211; 3n &#8211; 34 = 0<br \/>\n\u21d2 n<sup>2<\/sup> &#8211; 20n + 17n &#8211; 340 = 0<br \/>\n\u21d2 n(n &#8211; 20) + 17(n &#8211; 20) = 0<br \/>\n\u21d2 n = 20 or n = -17<br \/>\nn = 20 sides [\u2235 n can not be -ve]<\/p>\n<p>Question 13.<br \/>\nIn a single throw of two dice, what is the probability of obtaining a total of 9?<br \/>\nSolution:<br \/>\nTotal probability = \\(\\frac{\\text { Favourable cases }}{\\text { Total No. of cases }}\\) = \\(\\frac{4}{36}\\)<br \/>\nP = \\(\\frac{1}{9}\\)<br \/>\nsum of = [(3 + 6), (6 + 3), (4 + 5), (5 + 4)] \u2192 4 cases<br \/>\n= [(3, 6) (6, 3), (4, 5), (5, 4)]<\/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 Model Question Paper 2 with Answers\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 14.<br \/>\nIf p, q, r are three propositions with truth values T, T, F respectively find the truth value of p \u2192 (~q \u2227 r).<br \/>\nSolution:<br \/>\np = T, q = T, r = F<br \/>\np \u2192 (~q \u2227 r) = T \u2192 (F \u2227 F) = T \u2192 (F) = F<\/p>\n<p>Question 15.<br \/>\nTwo numbers are in the ratio 3 : 5. If 9 is subtracted from each the new numbers are in the ratio 12 : 23. Find the smaller number.<br \/>\nSolution:<br \/>\nGiven ratio 3 : 5<br \/>\nThe two are 3x and 5y<br \/>\nGiven 9 is subtracted<br \/>\n\\(\\frac{3 x-9}{5 x-9}=\\frac{12}{23}\\)<br \/>\n\u21d2 23(3x &#8211; 9) =12(5x &#8211; 2)<br \/>\n\u21d2 69x &#8211; 207 = 60x &#8211; 108<br \/>\n\u21d2 (69x &#8211; 60x) = 207 &#8211; 108<br \/>\n\u21d2 9x = 99<br \/>\n\u21d2 x = 11<br \/>\n3x = 3 \u00d7 11 = 33 \u2192 1st no.<br \/>\n5x = 5 \u00d7 1 = 55 \u2192 2nd no.<\/p>\n<p>Question 16.<br \/>\nThe Banker&#8217;s gain on a certain Bill due six months hence is \u20b9 10 the rate of interest is 10% p.a. Find the face value of the Bill.<br \/>\nSolution:<br \/>\nBankers gain = Rs. 10<br \/>\nRate = 10% = 0.1, F = ?, t = \\(\\frac{6}{12}\\) = 0.5 yr<br \/>\nBG = TD (tr)<br \/>\n10 = T (0.5 \u00d7 0.1)<br \/>\n10 = TD(0.05)<br \/>\nTD = \\(\\frac{10}{0.05}\\)<br \/>\nAgain BG = BD &#8211; TD<br \/>\nBD = BG + TD = 10 + 200 = 210<br \/>\nBD = Ftr<br \/>\nF = BD\/tr<br \/>\nF = \\(\\frac{210}{t r}=\\frac{210}{0.5 \\times 0.1}=\\frac{210}{0.05}\\) = \u20b9 4200<\/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 Model Question Paper 2 with Answers\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 17.<br \/>\nIf sin \u03b8 = \\(\\frac{3}{5}\\) and \u03b8 is acute, find the value of sin3\u03b8.<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66291\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-7.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 7\" width=\"425\" height=\"133\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-7.png 425w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-7-300x94.png 300w\" sizes=\"(max-width: 425px) 100vw, 425px\" \/><\/p>\n<p>Question 18.<br \/>\nShow that sin (A + B) sin (A &#8211; B) = sin<sup>2<\/sup> A &#8211; sin<sup>2<\/sup> B.<br \/>\nSolution:<br \/>\nLHS = sin (A + B) . sin (A &#8211; B)<br \/>\n= (sin A cos B + cos A sin B) (sin A cos B &#8211; cos A sin B)<br \/>\n{\u2235 (a + b)(a &#8211; b) = a<sup>2<\/sup> &#8211; b<sup>2<\/sup>}<br \/>\n= sin<sup>2<\/sup> A cos<sup>2<\/sup> B &#8211; cos<sup>2<\/sup> A sin<sup>2<\/sup> B<br \/>\n= sin<sup>2<\/sup> A (1 &#8211; sin<sup>2 <\/sup>B) &#8211; (1 &#8211; sin<sup>2<\/sup> A)(sin<sup>2<\/sup> B)<br \/>\n= sin<sup>2<\/sup> A &#8211; sin<sup>2<\/sup> B<br \/>\n= RHS<\/p>\n<p>Question 19.<br \/>\nFind the equation of the parabola whose focus is (0, -6) and directrix y = 6.<br \/>\nSolution:<br \/>\nFocus (0, -6) = (0, a)<br \/>\nDirectrix y = 6 \u21d2 y = -a<br \/>\nComapare a = -6<br \/>\nthe required parabola equation is x<sup>2<\/sup> = 4ay<br \/>\nx<sup>2<\/sup> = 4(-6)y<br \/>\nx<sup>2<\/sup> = -24y<\/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 Model Question Paper 2 with Answers\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 20.<br \/>\nFind the value of k if <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66292\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-8.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 8\" width=\"209\" height=\"107\" \/>\u00a0is continuous at x = 0.<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66293\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-9.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 9\" width=\"467\" height=\"197\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-9.png 467w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-9-300x127.png 300w\" sizes=\"(max-width: 467px) 100vw, 467px\" \/><\/p>\n<p>Question 21.<br \/>\nIf x = a sec \u03b8, y = b tan \u03b8 find \\(\\frac{d y}{d x}\\)<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66294\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-10.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 10\" width=\"485\" height=\"116\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-10.png 485w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-10-300x72.png 300w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><\/p>\n<p>Question 22.<br \/>\nFind a point on the parabola y<sup>2<\/sup> = 18x at which ordinate increases at twice the rate of the abscissa.<br \/>\nSolution:<br \/>\nGiven y<sup>2<\/sup> = 18x<br \/>\nordinate =y, abscissa = x,<br \/>\ngiven y = 2x<br \/>\n\u21d2 (2x)<sup>2<\/sup> = 18(2x)<br \/>\n\u21d2 4x<sup>2<\/sup> = 36x<br \/>\n\u21d2 4x(x &#8211; 9) = 0<br \/>\n\u2234 x = 0 or x = 9<br \/>\n\u2234 y = 0 or y = 18<br \/>\n\u2234 (0, 0) (9, 18) are the Two points on the parabola.<\/p>\n<p>Question 23.<br \/>\nFind two positive numbers whose sum is 14 and the sum of the squares of the numbers is minimum.<br \/>\nSolution:<br \/>\nLet the two true nos. are x and y<br \/>\nGiven that x + y = 14<br \/>\ny = 14 &#8211; x &#8230;&#8230;. (1)<br \/>\nSum of the square = s = x<sup>2<\/sup> + y<sup>2<\/sup> = x<sup>2<\/sup> + (14 &#8211; x)<sup>2<\/sup><br \/>\ns = x<sup>2<\/sup> + x<sup>2<\/sup> + 196 &#8211; 28x<br \/>\ns = 2x<sup>2<\/sup> &#8211; 28x + 196<br \/>\nLet f(x) = 2x<sup>2<\/sup> &#8211; 28x + 196<br \/>\nf'(x) = \\(\\frac{d s}{d x}\\) = 4x &#8211; 28 = 0<br \/>\n\u21d2 0 = 4x &#8211; 28<br \/>\n\u21d2 4x = 28<br \/>\n\u21d2 x = 7<br \/>\ny = 14 &#8211; 7 = 0<br \/>\nHerce the Two numbers are (7, 7)<\/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 Model Question Paper 2 with Answers\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 24.<br \/>\nIntegrate w.r.t x \\(\\int\\left(4 x^{2}-2 x+7\\right)^{3 \/ 2}(4 x-1) d x\\)<br \/>\nSolution:<br \/>\nput (4x<sup>2<\/sup> &#8211; 2x + 7) = t<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66295\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-11.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 11\" width=\"656\" height=\"213\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-11.png 656w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-11-300x97.png 300w\" sizes=\"(max-width: 656px) 100vw, 656px\" \/><\/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 (3 \u00d7 10 = 30)<\/span><\/p>\n<p>Question 25.<br \/>\nIf A = \\(\\left[\\begin{array}{ll}2 &amp; 3 \\\\4 &amp; 5\\end{array}\\right]\\) show that A<sup>2<\/sup> &#8211; 7A &#8211; 2I = 0. (I = Idtenity matrix of 2nd order)<br \/>\nSolution:<br \/>\nA<sup>2<\/sup> &#8211; 7A &#8211; 2I = 0<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66296\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-12.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 12\" width=\"447\" height=\"134\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-12.png 447w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-12-300x90.png 300w\" sizes=\"(max-width: 447px) 100vw, 447px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66297\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-13.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 13\" width=\"435\" height=\"138\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-13.png 435w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-13-300x95.png 300w\" sizes=\"(max-width: 435px) 100vw, 435px\" \/><\/p>\n<p>Question 26.<br \/>\nFind the adjoint of the matrix A = \\(\\left[\\begin{array}{ccc}\\cos \\theta &amp; -\\sin \\theta &amp; 0 \\\\\\sin \\theta &amp; \\cos \\theta &amp; 0 \\\\0 &amp; 0 &amp; 1\\end{array}\\right]\\)<br \/>\nSolution:<br \/>\nCofactor of A = \\(\\left[\\begin{array}{ccc}+(\\cos \\theta) &amp; -(\\sin \\theta) &amp; +(0) \\\\-(-\\sin \\theta) &amp; +(\\cos \\theta) &amp;-(0) \\\\+(0) &amp; -(0) &amp; +(1)\\end{array}\\right]\\)<br \/>\nMinor of cos \u03b8 = [cos \u03b8 &#8211; 0] = cos \u03b8<br \/>\n-sin \u03b8 = [sin \u03b8 &#8211; 0] = sin \u03b8<br \/>\n0 = [0 &#8211; 0] = 0<br \/>\nsin \u03b8 = [-sin \u03b8 &#8211; 0] = -sin \u03b8<br \/>\ncos \u03b8 = [cos \u03b8 &#8211; 0] = cos \u03b8<br \/>\n0 = [0 &#8211; 0] = 0<br \/>\n0 = [0 &#8211; 0] = 0<br \/>\n1 = [\u2234 cos<sup>2<\/sup> \u03b8 + sin<sup>2<\/sup> \u03b8] = 1<br \/>\nadjoint of A = Transpose of cofactor A = \\(\\left[\\begin{array}{ccc}\\cos \\theta &amp; \\sin \\theta &amp; 0 \\\\-\\sin \\theta &amp;\\cos \\theta &amp; 0 \\\\0 &amp; 0 &amp; 1\\end{array}\\right]\\)<\/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 Model Question Paper 2 with Answers\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 27.<br \/>\nIn how many ways 3 boys and 5 girls can be arranged in a row so that no two boys are together?<br \/>\nSolution:<br \/>\nNo two boys together, first we have to arrange 5 girls in \\(^{5} \\mathrm{P}_{5}\\) = 5!<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66298\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-14.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 14\" width=\"225\" height=\"34\" \/><br \/>\nThere are 6 place between 5 girls where we can arrange 3 boys = \\(^6 \\mathbf{P}_{3}\\) ways<br \/>\nTotal no. of arrangement = 5! \u00d7 \\(^{6} \\mathrm{P}_{3}\\)<\/p>\n<p>Question 28.<br \/>\nIf A and B are events with P(A) = \\(\\frac{5}{8}\\), P(B) = \\(\\frac{3}{8}\\) and P(A\u222aB) = \\(\\frac{3}{4}\\). find (i) P(B\/A) (ii) P(A\/B)<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66299\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-15.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 15\" width=\"541\" height=\"334\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-15.png 541w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-15-300x185.png 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/p>\n<p>Question 29.<br \/>\nTwo trains 130m and 80m long are running in opposite directions and are at the rate of 75km\/hr and 33km\/hr respectively. From the moment they meet find the time of the two trains cross each other?<br \/>\nSolution:<br \/>\nIf they are running in opposite directions, their relative speed will be 75 + 33 = 118 km per hour.<br \/>\nTime Taken = \\(\\frac{\\text { Distance travelled }}{\\text { speed }}\\) = \\(\\frac{210}{118}\\) = 1.78 hour<\/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 Model Question Paper 2 with Answers\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 30.<br \/>\nA banker pays \u20b9 2380 on a bill of \u20b9 2500, 73 days before the legally due date. Find the rate of discount charged by the banker.<br \/>\nSolution:<br \/>\nF = \u20b9 2500<br \/>\nDiscount value of the bill = \u20b9 2380<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66300\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-16.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 16\" width=\"325\" height=\"61\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-16.png 325w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-16-300x56.png 300w\" sizes=\"(max-width: 325px) 100vw, 325px\" \/><br \/>\nBD = F &#8211; DVB = \u20b9 2500 &#8211; \u20b9 2380 = \u20b9 120<br \/>\nFtr = BD<br \/>\nFtr = 120<br \/>\nr = \\(\\frac{120}{\\mathrm{Ft}}\\)<br \/>\nRate of discount = r = \\(\\frac{120}{2500 \\times 0.2}=\\frac{12}{500}\\) = 0.24 of 24%<\/p>\n<p>Question 31.<br \/>\nFind the interest earned on \u20b9 4897.50 cash invested in 15% stock at 81.5 the brokerage given is 0.125.<br \/>\nSolution:<br \/>\nEach stock value = 81.5<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66301\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-17.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 17\" width=\"333\" height=\"252\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-17.png 333w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-17-300x227.png 300w\" sizes=\"(max-width: 333px) 100vw, 333px\" \/><\/p>\n<p>Question 32.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66302\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-18.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 18\" width=\"365\" height=\"55\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-18.png 365w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-18-300x45.png 300w\" sizes=\"(max-width: 365px) 100vw, 365px\" \/><br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66303\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-19.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 19\" width=\"319\" height=\"410\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-19.png 319w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-19-233x300.png 233w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><\/p>\n<p>Question 33.<br \/>\nFind the co-ordinates of the vertex, focus and equation of directrix of the parabola 5x<sup>2<\/sup> + 24y = 0.<br \/>\nSolution:<br \/>\nGiven parabola 5x<sup>2<\/sup> + 24y = 0<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66304\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-20.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 20\" width=\"297\" height=\"336\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-20.png 297w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-20-265x300.png 265w\" sizes=\"(max-width: 297px) 100vw, 297px\" \/><\/p>\n<p>Question 34.<br \/>\nRaju goes to purchase a motorcycle which is priced \u20b9 35,640 including 10% on sales tax however the actual rate of sales tax at the time of purchase is 7%. Find the extra profit made by the shop keeper if he still charges the original listed price.<br \/>\nSolution:<br \/>\nLet the marked price = \u20b9 x<br \/>\nS.P = \u20b9 35,640<br \/>\nS.T = 10%<br \/>\nTotal amount to be paid = M.P + ST% of MP<br \/>\n35,640 = x + 10% of x<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66305\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-21.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 21\" width=\"267\" height=\"216\" \/><br \/>\nAt the time of purchase the S.T is 7%<br \/>\nRaju paid at the purchase time = \\(\\frac{32400 \\times 7}{100}\\) = 2,268<br \/>\nSP = 32,400 + 2,268 = \u20b9 34,557<br \/>\nProfit by the shop keeper = (35,640) &#8211; (34,668) = \u20b9 972<\/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 Model Question Paper 2 with Answers\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 35.<br \/>\nA circular plate of metal is heated so that its radius increases at the rate of 0.1 mm per minute. At what rate is the plate&#8217;s area increasing when the radius is 25 cm.<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66306\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-22.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 22\" width=\"356\" height=\"255\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-22.png 356w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-22-300x215.png 300w\" sizes=\"(max-width: 356px) 100vw, 356px\" \/><\/p>\n<p>Question 36.<br \/>\nThe cost function C = 500x &#8211; 20x<sup>2<\/sup> + \\(\\frac{x^{3}}{3}\\) where x stands for output. Calculate the output when the marginal cost is equal to average cost.<br \/>\nSolution:<br \/>\nC = 500x &#8211; 20x<sup>2<\/sup> + \\(\\frac{x^{3}}{3}\\)<br \/>\nMarginal cost = Average cost,<br \/>\nx = ?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66307\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-23.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 23\" width=\"476\" height=\"305\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-23.png 476w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-23-300x192.png 300w\" sizes=\"(max-width: 476px) 100vw, 476px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66308\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-24.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 24\" width=\"214\" height=\"198\" \/><\/p>\n<p>Question 37.<br \/>\nEvaluate \\(\\int \\frac{1}{e^{x}+e^{-x}} d x\\)<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66309\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-25.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 25\" width=\"514\" height=\"175\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-25.png 514w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-25-300x102.png 300w\" sizes=\"(max-width: 514px) 100vw, 514px\" \/><\/p>\n<p>Question 38.<br \/>\nEvaluate: \\(\\int_{0}^{\\pi \/ 2} \\sin 5 x \\cdot \\cos 3 x d x\\)<br \/>\nSolution:<br \/>\n\\(\\int_{0}^{\\pi \/ 2} \\sin 5 x \\cdot \\cos 3 x d x\\)<br \/>\nBy using transformation formulae of production in to sum is<br \/>\nsin A cos B = \\(\\frac{1}{2}\\) (sin (A + B) + sin (A &#8211; B))<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66310\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-26.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 26\" width=\"651\" height=\"209\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-26.png 651w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-26-300x96.png 300w\" sizes=\"(max-width: 651px) 100vw, 651px\" \/><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\">Part &#8211; D<\/span><\/p>\n<p><span style=\"color: #0000ff;\">IV. Answer any SIX questions: (5 \u00d7 6 = 30)<\/span><\/p>\n<p>Question 39.<br \/>\nFind the coefficient of x<sup>-11<\/sup> in the expansion of \\(\\left(\\sqrt{x}-\\frac{2}{x}\\right)^{17}\\)<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66311\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-27.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 27\" width=\"510\" height=\"239\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-27.png 510w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-27-300x141.png 300w\" sizes=\"(max-width: 510px) 100vw, 510px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66312\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-28.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 28\" width=\"465\" height=\"294\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-28.png 465w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-28-300x190.png 300w\" sizes=\"(max-width: 465px) 100vw, 465px\" \/><\/p>\n<p>Question 40.<br \/>\nResolve \\(\\frac{2 x^{2}+16 x+29}{(x+3)^{2}(x+4)}\\) into partial fractions.<br \/>\nSolution:<br \/>\n\\(\\frac{2 x^{2}+16 x+29}{(x+3)^{2}(x+4)}=\\frac{A}{(x+4)}+\\frac{B}{(x+3)}+\\frac{C}{(x+2)^{2}(x+3)^{2}}\\)<br \/>\n2x<sup>2<\/sup> + 16x + 29 = A(x + 3)<sup>2<\/sup> + B(x + 4)(x + 3) + C(x + 4)<br \/>\nput x = -4<br \/>\n2(-4)<sup>2<\/sup> + 16(-4) + 29 = A(-4 + 3)<sup>2<\/sup> + 0 + 0<br \/>\n\u21d2 32 &#8211; 64 + 29 = A(1) + 0 + 0<br \/>\n\u21d2 -2 = A<br \/>\n\u21d2 A = -2<br \/>\nPut x = -3<br \/>\n2(-3)<sup>2<\/sup> + 16(-3) + 29 = 0 + 0 + C(-3 + 4)<br \/>\n\u21d2 18 &#8211; 48 + 29 = C(1)<br \/>\n\u21d2 -1 = C<br \/>\n\u21d2 C = -1<br \/>\nEquate the coefficient of x<sup>2<\/sup> on both side<br \/>\n2 = A + B<br \/>\n\u21d2 2 = -2 + B<br \/>\n\u21d2 B = 4<br \/>\n\\(\\frac{2 x^{2}+16 x+29}{(x+4)(x+3)^{2}}=\\frac{-2}{(x+4)}+\\frac{4}{(x+3)}-\\frac{1}{(x+3)^{2}}\\) are partial fractions<\/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 Model Question Paper 2 with Answers\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 41.<br \/>\nProve that, ~(p \u2194 q) = (p \u2227 ~q) \u2228 (q \u2227 ~p).<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66313\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-29.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 29\" width=\"689\" height=\"158\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-29.png 689w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-29-300x69.png 300w\" sizes=\"(max-width: 689px) 100vw, 689px\" \/><br \/>\nLHS = RMS from 6th column and 9th column<\/p>\n<p>Question 42.<br \/>\nIf 15 men working 12 hours per day perform the job in 16 days how long will it take for 21 men working 10 hours daily to do the same job?<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66314\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-30.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 30\" width=\"236\" height=\"85\" \/><br \/>\nMore men \u2192 less days (Inverse propertion)<br \/>\n15 : 21 = x : 16 &#8230;.(1)<br \/>\nMore hours \u2192 Less days (Inverse proportion)<br \/>\n12 : 10 = x : 16 &#8230;&#8230;(2)<br \/>\nFrom (1) and (2)<br \/>\n(15 \u00d7 12) : (21 \u00d7 10) = x : 16<br \/>\n\u21d2 \\(\\frac{180}{210}\\) = \\(\\frac{x}{16}\\)<br \/>\n\u21d2 7x = 96<br \/>\n\u21d2 x = \\(\\frac{96}{7}\\) = 13.7 days<\/p>\n<p>Question 43.<br \/>\nThe time required to produce the first unit of a product is 1000 hours. If the manufactures experience 80% learning effect. Calculate the cumulative average time per unit and the total time taken to produce altogether 8 units. Also, find the labour charges for the production of 8 units at the rate of \u20b9 10 per hour.<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66315\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-31.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 31\" width=\"653\" height=\"277\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-31.png 653w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-31-300x127.png 300w\" sizes=\"(max-width: 653px) 100vw, 653px\" \/><br \/>\nTotal labour hours to produce 8 unit = 4096 hr<br \/>\nTotal labour cost at \u20b9 10\/hr = 4096 \u00d7 10 = \u20b9 40,960<\/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 Model Question Paper 2 with Answers\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 44.<br \/>\nSolve L.P.P graphically, maximize z = 4x + 3y subject to the constraints x + 2y \u2264 5, x + y \u2264 3, 3x + y \u2264 7, x, y \u2265 0.<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66316\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-32.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 32\" width=\"556\" height=\"368\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-32.png 556w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-32-300x199.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><br \/>\nat A(0, 2.5), z = 4(0) + 3(2.5) = 7.5<br \/>\nat B (1, 2), z = 4(1) + 3(2) = 10<br \/>\nat C (2, 1), z = 4(2) + 3(1) = 11<br \/>\nat D (3, 0), z = 4(3)+ 3(0) = 12<br \/>\nz is maximise at D (3, 0)<br \/>\n\u2234 x = 3, y = 0<\/p>\n<p>Question 45.<br \/>\nThe angle of elevation of an object from a point 100 m above a lake is 30\u00b0 and angle of depression of its image in the lake is 45\u00b0. Find the height of the object above the lake.<br \/>\nSolution:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66317\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-33.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 33\" width=\"332\" height=\"230\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-33.png 332w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-33-300x208.png 300w\" sizes=\"(max-width: 332px) 100vw, 332px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66318\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-34.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 34\" width=\"220\" height=\"268\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66319\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-35.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 35\" width=\"598\" height=\"143\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-35.png 598w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-35-300x72.png 300w\" sizes=\"(max-width: 598px) 100vw, 598px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66320\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-36.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 36\" width=\"379\" height=\"135\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-36.png 379w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-36-300x107.png 300w\" sizes=\"(max-width: 379px) 100vw, 379px\" \/><\/p>\n<p>Question 46.<br \/>\nFind the equation of the circle possing through the points (1, 1), (2, -1) and (3, 2).<br \/>\nSolution:<br \/>\nLet the equation of circle be x<sup>2<\/sup> + y<sup>2<\/sup> + 2gx + 2fy + C = 0 &#8230;&#8230;. (1)<br \/>\nThis equation passes through (1, 1) (2, -1) and (3, 2)<br \/>\nat (1, 1), 1 + 1 + 2g + 2f + C = 0<br \/>\n2g + 2f + C + 2 = 0 &#8230;&#8230; (2)<br \/>\nat (2, -1), 4 + 1 + 4g &#8211; 2f + C = 0<br \/>\n4g &#8211; 2f + C + 5 = 0 &#8230;&#8230; (3)<br \/>\nat (3, 2), 9 + 4 + 6g + 4f + C = 0<br \/>\n6g + 4f + C + 13 = 0 &#8230;&#8230; (4)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66321\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-37.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 37\" width=\"544\" height=\"501\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-37.png 544w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-37-300x276.png 300w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><br \/>\n(1) becomes x<sup>2<\/sup> + y<sup>2<\/sup> &#8211; 5x &#8211; y + 4 = 0 is the circle equation<\/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 Model Question Paper 2 with Answers\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 47.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66322\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-38.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 38\" width=\"502\" height=\"58\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-38.png 502w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-38-300x35.png 300w\" sizes=\"(max-width: 502px) 100vw, 502px\" \/><br \/>\nSolution:<br \/>\nGiven<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66323\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-39.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 39\" width=\"331\" height=\"312\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-39.png 331w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-39-300x283.png 300w\" sizes=\"(max-width: 331px) 100vw, 331px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66324\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-40.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 40\" width=\"340\" height=\"422\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-40.png 340w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-40-242x300.png 242w\" sizes=\"(max-width: 340px) 100vw, 340px\" \/><\/p>\n<p>Question 48.<br \/>\nFind the area enclosed between the curves y<sup>2<\/sup> = 4x and x<sup>2<\/sup> = 4<br \/>\nSolution:<br \/>\nx<sup>2<\/sup> = 4y \u21d2 y = \\(\\frac{x^{2}}{4}\\)<br \/>\ny<sup>2<\/sup> = 4x<br \/>\n\u21d2 \\(\\left(\\frac{x^{2}}{4}\\right)^{2}\\) = 4x<br \/>\n\u21d2 x<sup>4<\/sup> = 64<br \/>\n\u21d2 x(x<sup>3<\/sup> &#8211; 4<sup>3<\/sup>) = 0<br \/>\n\u21d2 x = 0 or x = 4 are limits of integration<br \/>\nRequired Area<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66325\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-41.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 41\" width=\"246\" height=\"357\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-41.png 246w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-41-207x300.png 207w\" sizes=\"(max-width: 246px) 100vw, 246px\" \/><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\">Part &#8211; E<\/span><\/p>\n<p><span style=\"color: #0000ff;\">V. Answer any one question: (1 \u00d7 10 = 10)<\/span><\/p>\n<p>Question 49.<br \/>\n(a) Salesman Venki has the following record of sales during 3 months of July, August and September for three products. A, B, C which have different rates of commission.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66326\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-42.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 42\" width=\"487\" height=\"146\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-42.png 487w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-42-300x90.png 300w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><br \/>\nUsing matrix method, find out the rates of commission on items A, B and C received by Venki. (6)<br \/>\nSolution:<br \/>\nConsider, 100x + 100y + 100z = 700<br \/>\n200x + 300y + 200z = 1700<br \/>\n400x + 900y + 100z = 3700<br \/>\n\u00f7 by 100<br \/>\nx + y + z = 7<br \/>\n2x + 3y + 2z = 17<br \/>\n4x + 9y + z = 37<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66327\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-43.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 43\" width=\"424\" height=\"257\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-43.png 424w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-43-300x182.png 300w\" sizes=\"(max-width: 424px) 100vw, 424px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66328\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-44.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 44\" width=\"522\" height=\"452\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-44.png 522w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-44-300x260.png 300w\" sizes=\"(max-width: 522px) 100vw, 522px\" \/><\/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 Model Question Paper 2 with Answers\" width=\"172\" height=\"16\" \/><\/p>\n<p>(b) Find the value of (0.98)3 using binomial theorem up to 5 places of decimals. (4)<br \/>\nSolution:<br \/>\n(0.98)<sup>3<\/sup> = (1 &#8211; 0.02)<sup>3<\/sup><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66329\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-45.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 45\" width=\"624\" height=\"143\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-45.png 624w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-45-300x69.png 300w\" sizes=\"(max-width: 624px) 100vw, 624px\" \/><\/p>\n<p>Question 50.<br \/>\n(a) Prove that \\(\\lim _{\\theta \\rightarrow 0} \\frac{\\sin \\theta}{\\theta}=1\\) and hence deduce that \\(\\lim _{\\theta \\rightarrow 0} \\frac{\\tan \\theta}{\\theta}=1\\). (\u03b8 in radian) (6)<br \/>\nSolution:<br \/>\nLet \u2018O\u2019 the centre of unit circle, assume that \u03b8 is measured in positive radians<br \/>\nLet \u2220AOB = \u03b8<sup>c<\/sup>, from A, draw AD is \u22a5 to OA, meeting OB produced to D, therefore OA = OB = radians<br \/>\nFrom the diagram, we have an 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-66330\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-46.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 46\" width=\"234\" height=\"331\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-46.png 234w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-46-212x300.png 212w\" sizes=\"(max-width: 234px) 100vw, 234px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66331\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-47.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 47\" width=\"296\" height=\"259\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66332\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-48.png\" alt=\"2nd PUC Basic Maths Model Question Paper 2 with Answers - 48\" width=\"414\" height=\"383\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-48.png 414w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/06\/2nd-PUC-Basic-Maths-Model-Question-Paper-2-with-Answers-48-300x278.png 300w\" sizes=\"(max-width: 414px) 100vw, 414px\" \/><\/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 Model Question Paper 2 with Answers\" width=\"172\" height=\"16\" \/><\/p>\n<p>(b) A company produces two types of leather belts A and B. A is of superior quality and B is of inferior quality. The respective profits are \u20b9 10 and \u20b9 5 per belt. The supply of raw material is sufficient for making 850 belts per day. For belt A, a special type of buckle is required and 500 are available per day. There are 700 buckles available for belt B per day. Belt A needs twice as much time as that required for belt B and the company can produce 500 belts if all of them were of the type A. Formulate an L.P.P model for the above problem. (4)<br \/>\nSolution:<br \/>\nObjective function max z = 10x + 5y<br \/>\nSubject to constrains<br \/>\n2x + y = 500<br \/>\nx \u2265 0, y \u2265 0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Students can Download 2nd PUC Basic Maths Model Question Paper 2 with Answers, Karnataka 2nd PUC Maths Model Question Papers with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations. Karnataka 2nd PUC Basic Maths Model Question Paper 2 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\/26949"}],"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=26949"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/26949\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=26949"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=26949"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=26949"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}