{"id":15408,"date":"2021-05-21T08:28:57","date_gmt":"2021-05-21T02:58:57","guid":{"rendered":"https:\/\/yanamtakshashila.com\/?p=15408"},"modified":"2021-07-07T12:17:24","modified_gmt":"2021-07-07T06:47:24","slug":"n-scheme-engineering-mathematics-ii-model-exam-question-paper-2021","status":"publish","type":"post","link":"https:\/\/yanamtakshashila.com\/?p=15408","title":{"rendered":"N-SCHEME-ENGINEERING MATHEMATICS-II MODEL EXAM QUESTION PAPER\/2021"},"content":{"rendered":"\n<p class=\"has-text-align-center\"><strong>MODEL EXAM QUESTION PAPER<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>40022 ENGINEERING MATHEMATICS &#8211; II<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>Time : 3.00 Hours&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;Date:&nbsp; 22-05-2021&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Max.Marks: 100<\/strong><\/p>\n\n\n\n<p>Note:<\/p>\n\n\n\n<p>1. Answer all question in PART A. Each question carries one mark.<\/p>\n\n\n\n<p>2. Answer any ten questions in PART B. Each question carries two marks.<\/p>\n\n\n\n<p>3. Answer all question by selecting either A or B. Each question carries fifteen marks.<\/p>\n\n\n\n<p>4. Clarkes Table and programmable calculators are not permitted.<\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;                                <u>PART \u2013 A<\/u>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;                 (5\u00d71=5)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/strong><\/p>\n\n\n\n<p>1.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Find the value of&nbsp; \u2018p\u2019if the pair of &nbsp;lines px<sup>2<\/sup>-5xy&nbsp; + 7y<sup>2<\/sup> =&nbsp; 0&nbsp; are perpendicular<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;to each&nbsp; Other.<\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[2.\\ Find\\  \\overrightarrow{a}\u00d7 \\overrightarrow{b}if\\  \\overrightarrow{a}= \\overrightarrow{i}+ \\overrightarrow{j}+ \\overrightarrow{k}\\ and \\overrightarrow{b}= 2\\overrightarrow{i}- \\overrightarrow{j}+ 3\\overrightarrow{k}\\ \\hspace{20cm}\\]<script src=\"https:\/\/yanamtakshashila.com\/wp-includes\/js\/dist\/hooks.min.js?ver=dd5603f07f9220ed27f1\" id=\"wp-hooks-js\"><\/script>\n<script src=\"https:\/\/yanamtakshashila.com\/wp-includes\/js\/dist\/i18n.min.js?ver=c26c3dc7bed366793375\" id=\"wp-i18n-js\"><\/script>\n<script id=\"wp-i18n-js-after\">\nwp.i18n.setLocaleData( { 'text direction\\u0004ltr': [ 'ltr' ] } );\n\/\/# sourceURL=wp-i18n-js-after\n<\/script>\n<script  async src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-MML-AM_CHTML\" id=\"mathjax-js\"><\/script>\n<\/div>\n\n\n\n<p>3.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Define vector Differential operator.<\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[4.\\ Evaluate: \\int(x^2 -x -1)\\ dx\\ \\hspace{30cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[5.\\ Evaluate: \\int_1^2 x^2\\ dx\\ \\hspace{30cm}\\]<\/div>\n\n\n\n<script async=\"\" src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script>\n<!-- Text & display ads -->\n<ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-9453835310745500\" data-ad-slot=\"6703350399\" data-ad-format=\"auto\" data-full-width-responsive=\"true\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n\n\n\n<a target=\"_blank\" href=\"https:\/\/shareasale.com\/r.cfm?b=1774718&amp;u=2863840&amp;m=16058&amp;urllink=&amp;afftrack=\" rel=\"noopener\"><img data-recalc-dims=\"1\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/static.shareasale.com\/image\/16058\/300X2501_01.gif?ssl=1\" border=\"0\" alt=\"Latest Collection\"><\/a>\n\n\n\n<p class=\"has-text-align-center\">                                          <strong><u>PART \u2013 <\/u>B&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;                 (10\u00d72=20)<\/strong> <\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[6.\\ Find\\ the\\ angle\\ between\\ the\\ lines\\ y = \\sqrt{3x}\\ and\\ x- y = 0\\ \\hspace{30cm}\\]<\/div>\n\n\n\n<p>7.  Find the equation of the circle passing through the point &nbsp;A (2, &#8211; 3) and having its centre at <\/p>\n\n\n\n<p>      C ( &#8211; 5 , 1). <\/p>\n\n\n\n<p>8.   Prove that the circles&nbsp; x<sup>2<\/sup>&nbsp; + &nbsp;&nbsp;y<sup>2<\/sup> &nbsp;&#8211; 4x&nbsp; + 6y + 4 = 0&nbsp; and <\/p>\n\n\n\n<p>       x<sup>2<\/sup>&nbsp; + &nbsp;&nbsp;y<sup>2<\/sup> &nbsp;+ 2x&nbsp; + 4y + 4 = 0 cut orthogonally. <\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[9.\\ Find\\ the\\ projection\\ of\\ the\\ vector\\ 3\\overrightarrow{i}+ 4\\overrightarrow{j}- 5\\overrightarrow{k} on\\  the\\ vector\\  \\overrightarrow{i}+ 2\\overrightarrow{j}+2\\overrightarrow{k}\\ \\hspace{30cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[10.\\ Find\\ the\\ value\\ of\\ m\\ if\\ the\\ vectors\\ 2\\overrightarrow{i}+ m\\overrightarrow{j}- 3\\overrightarrow{k} and\\  3\\overrightarrow{i}+ 1\\overrightarrow{j}+4\\overrightarrow{k} are\\ perpendicular\\ \\hspace{30cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[11.\\ Find\\ the\\ area\\ of\\ the\\ parellelogram\\ whose\\ adjacent\\ sides\\ are\\ 3\\overrightarrow{i}- \\overrightarrow{k} and\\  \\overrightarrow{i}+ \\overrightarrow{j}+\\overrightarrow{k}.\\ \\hspace{30cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[12.\\ Prove\\ that\\ the\\  vectors\\ 2\\overrightarrow{i}+ \\overrightarrow{j}+ \\overrightarrow{k},\\   3\\overrightarrow{i} + 4\\overrightarrow{j}+ \\overrightarrow{k}\\ and\\ \\overrightarrow{i} &#8211; 2\\overrightarrow{j}+ \\overrightarrow{k}\\ are\\ coplanar.\\ \\hspace{30cm}\\]<\/div>\n\n\n\n<p>13.  Find the unit normal to the surface xy +yz + zx= 3 at the point (1, 1, 1). <\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[14.\\ If\\  \\overrightarrow{F}=xyz\\overrightarrow{i} + 3x^2y\\overrightarrow{j} +(x y ^2- zy^3)\\overrightarrow{k}\\ then\\ find\\ curl\\ \\overrightarrow{F}\\ \\hspace{30cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[15.\\ Evaluate: \\int tan^2 x \\ dx\\ \\hspace{30cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[16.\\ Evaluate: \\int(2 sin x + 7)\\ dx\\ \\hspace{30cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[17.\\ Evaluate:\\ \\int \\frac{dx}{{\\sqrt{9 &#8211; x^2}}}\\ \\hspace{30cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[18.\\ Evaluate: \\int \\frac{cos^2 x}{ 1- sin x} \\ dx\\ \\hspace{30cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[19.\\ Evaluate:\\ \\int x\\ e^x\\ dx\\ \\hspace{30cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[20.\\ Evaluate: \\int_0^\\frac{\\pi}{2} sin^2 x\\ dx\\ \\hspace{30cm}\\]<\/div>\n\n\n\n<!-- admitad.banner: hjdpvbg24h109003a688aadae9dc1a Magzter2 [CPS] IN -->\n<a target=\"_blank\" rel=\"nofollow noopener\" href=\"https:\/\/ad.admitad.com\/g\/hjdpvbg24h109003a688aadae9dc1a\/?i=4\"><img fetchpriority=\"high\" decoding=\"async\" width=\"728\" height=\"90\" border=\"0\" src=\"https:\/\/ad.admitad.com\/b\/hjdpvbg24h109003a688aadae9dc1a\/\" alt=\"Magzter2 [CPS] IN\"><\/a>\n<!-- \/admitad.banner -->\n\n\n\n<p class=\"has-text-align-center\">                                                 <strong><u>PART \u2013 <\/u>C&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;                 (5\u00d715=75)<\/strong> <\/p>\n\n\n\n<p class=\"has-text-align-left\"> 21 A). i)  Prove that the circles &nbsp;x2&nbsp; + &nbsp;&nbsp;y2 &nbsp;+ 2x&nbsp; &#8211;&nbsp; 4y&nbsp; &#8211; 3 = 0 and x2&nbsp; + &nbsp;&nbsp;y2&nbsp; &#8211; 8x&nbsp; +&nbsp; 6y&nbsp; +7 = 0 touch each&nbsp; other.                        ( 7 )<\/p>\n\n\n\n<p>           ii)  Find K if&nbsp;&nbsp; 2x<sup>2<\/sup>&nbsp; &#8211;&nbsp; 7xy&nbsp; + 3y<sup>2<\/sup> + 5x &#8211; 5y + k= 0&nbsp; represents a pair of  straight lines.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;                                                         ( 8 )<\/p>\n\n\n\n<p class=\"has-text-align-center\">(or)<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; B)&nbsp; i.&nbsp;&nbsp;&nbsp;Find vertex, focus , equation of directrix&nbsp; and latus rectum for&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;                                                                             ( 7 )<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; y<sup>2<\/sup> + 8x \u2013 6y + 1 = 0.<\/p>\n\n\n\n<p>            ii.    The slope of one of the lines ax<sup>2<\/sup>&nbsp; +&nbsp; 2hxy&nbsp; + by<sup>2<\/sup> =&nbsp; 0 is thrice that of the                                                                           (8)&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;other. Show that 3h<sup>2<\/sup>= 4ab<\/p>\n\n\n\n<p>22  A)  i.     Prove that the points  whose position&nbsp; vectors&nbsp; are <\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[3\\overrightarrow{i}\\ &#8211; \\overrightarrow{j}+ 6\\overrightarrow{k},  5\\overrightarrow{i}\\ &#8211; 2\\overrightarrow{j}+ 7\\overrightarrow{k} and\\ 6\\overrightarrow{i}\\ -5 \\overrightarrow{j}+ 2\\overrightarrow{k}\\  form\\  a\\ right\\   angled\\ triangle\\ \\hspace{4cm}\\ (7)\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\hspace{-1cm}\\ ii.\\ Find\\ the\\ projection\\ of\\ the\\ vector\\ 3\\overrightarrow{i}+ \\overrightarrow{j}- 2\\overrightarrow{k} on\\  7\\overrightarrow{i}+ \\overrightarrow{j}+2\\overrightarrow{k}. Also\\ find\\ the\\ angle\\ between\\ them\\ \\hspace{1cm}\\ (8)\\]<\/div>\n\n\n\n<p class=\"has-text-align-center\">(or) <\/p>\n\n\n\n<p>    B)&nbsp;&nbsp; i.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; A particle acted on by the&nbsp; forces<\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\hspace{-2cm}\\ 3\\overrightarrow{i}+ 2\\overrightarrow{j}- 3\\overrightarrow{k} and\\  \\overrightarrow{i}+ 7\\overrightarrow{j}+7\\overrightarrow{k} acting\\ on\\ the\\ particle\\ \\hspace{11cm}\\ (7)\\] <\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[displaces\\ the\\ particle\\ from\\ the\\  point\\  \\overrightarrow{i}+ 2\\overrightarrow{j}+ 3\\overrightarrow{k} to\\  the\\ point\\  3\\overrightarrow{i}- 5\\overrightarrow{j}+4\\overrightarrow{k}.  Find\\ the\\ total\\ work\\ done\\ by\\ the\\ forces.\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\hspace{-1cm}\\ ii.\\ Find\\ the\\ moment\\ of\\ the\\ force\\ 3\\overrightarrow{i}+\\overrightarrow{k}\\ acting\\ through\\ the\\ point\\ \\overrightarrow{i}+2\\overrightarrow{j}-\\overrightarrow{k} about\\ the\\ point\\  2\\overrightarrow{i}+ \\overrightarrow{j}-2\\overrightarrow{k}.\\ \\hspace{1cm}\\ (8)\\]<\/div>\n\n\n\n<p>23. A)&nbsp;&nbsp; i.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Show that the points whose position vectors<\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[4\\overrightarrow{i}+ 5\\overrightarrow{j}+ \\overrightarrow{k},\\  &#8211; \\overrightarrow{j}- \\overrightarrow{k},\\  3\\overrightarrow{i} + 9\\overrightarrow{j}+ 4\\overrightarrow{k}\\ \\hspace{15cm}\\ (7)\\]\\[and\\ -4\\overrightarrow{i} + 4\\overrightarrow{j}+ 4\\overrightarrow{k}\\ lie\\  on\\  the\\ same\\ plane.\\ (or)\\ Coplanar.\\]<\/div>\n\n\n\n<p class=\"has-text-align-left\">          ii.     Find the acute angle between the surface xy<sup>2<\/sup>z = 4 and&nbsp; x<sup>2<\/sup> + y<sup>2 <\/sup>+ z<sup>2<\/sup> =6&nbsp; at the point (2, 1, 1).                                                       (8)   <\/p>\n\n\n\n<p class=\"has-text-align-center\">     (or) <\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\hspace{-2cm}\\ B)\\ i.\\ If\\  \\overrightarrow{F}=( 2x + 2y + 2z)\\overrightarrow{i} &#8211; (xy + yz + zx)\\overrightarrow{j} + 3xyz\\overrightarrow{k}\\ then\\ find\\ \\nabla\\ \u00d7 \\overrightarrow{F}\\ and\\ \\nabla\\ \u00d7 ( \\nabla\\ \u00d7 \\overrightarrow{F})\\ \\hspace{5cm}\\ (7)\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\hspace{-2cm}\\ ii.\\ If\\ \\overrightarrow{a} = 2\\overrightarrow{i} &#8211; \\overrightarrow{j}+ 2\\overrightarrow{k},\\  \\overrightarrow{b} = \\overrightarrow{i} +\\overrightarrow{j}+ \\overrightarrow{k},\\   \\overrightarrow{c} = \\overrightarrow{i}+2\\overrightarrow{j} +3\\overrightarrow{k}\\}\\ and\\ \\overrightarrow{d} = \\overrightarrow{i}-\\overrightarrow{j} &#8211; \\overrightarrow{k}\\ \\hspace{5cm}\\ (8)\\]\\[find\\ (\\overrightarrow{a} \u00d7 \\overrightarrow{ b} ) . (\\overrightarrow{c} \u00d7 \\overrightarrow{ d} )\\]<\/div>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;24. A)&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Evaluate<\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[a)\\ \\hspace{1cm}\\ (i)\\ \\hspace{1cm}\\ \\int ( sin x + cos x ) ^ 2\\ dx\\ \\hspace{5cm}\\  (ii)\\ \\hspace{1cm}\\ \\int {\\sqrt{9x^2 +16}}\\ dx\\ \\hspace{5cm}\\ (7)\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[b)\\ \\hspace{1cm}\\ (i)\\ \\hspace{1cm}\\ \\int \\frac{cos^2 x}{ 1- sin x} \\ dx\\ \\hspace{5cm}\\  (ii)\\ \\hspace{1cm}\\  \\int \\frac{dx}{(3x + 2)^2 + 16}\\ dx\\ \\hspace{5cm}\\ (8)\\]<\/div>\n\n\n\n<p class=\"has-text-align-center\"> (or)  <\/p>\n\n\n\n<p>            B)&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Evaluate <\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[a)\\ \\hspace{1cm}\\ (i)\\ \\hspace{1cm}\\ \\int\\ \\frac{2ax + b}{{\\sqrt{(ax^2 + bx + c)}}}\\ dx\\ \\hspace{5cm}\\  (ii)\\ \\hspace{1cm}\\ \\int cos^3 x \\ dx\\ \\hspace{5cm}\\ (7)\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[b)\\ \\hspace{1cm}\\ (i)\\ \\hspace{1cm}\\ \\int sin 5x\\  cos 2x\\ dx\\ \\hspace{5cm}\\  (ii)\\ \\hspace{1cm}\\  \\int \\frac{dx}{4 + 9 x^2}\\ \\hspace{5cm}\\ (8)\\]<\/div>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp; 25. A)&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Evaluate &nbsp;<\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[a)\\ \\hspace{1cm}\\ (i)\\ \\hspace{1cm}\\ \\int x^2\\ sin\\ 2x\\ dx\\ \\hspace{5cm}\\  (ii)\\ \\hspace{1cm}\\ \\int x^n\\ log\\ x\\ dx\\ \\hspace{5cm}\\ (7)\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[b)\\ \\hspace{1cm}\\ (i)\\ \\hspace{1cm}\\ \\int x^2\\ cos\\ 5x\\ dx\\ \\hspace{5cm}\\  (ii)\\ \\hspace{1cm}\\  \\int x^3\\ e^{2x}\\ dx\\ \\hspace{5cm}\\ (8)\\]<\/div>\n\n\n\n<p class=\"has-text-align-center\"> (or) <\/p>\n\n\n\n<p>            B)&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Evaluate  <\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[a)\\ \\hspace{1cm}\\ (i)\\ \\hspace{1cm}\\ \\int x^3\\ log\\ x\\ dx\\ \\hspace{5cm}\\  (ii)\\ \\hspace{1cm}\\ \\int_0^\\frac{\\pi}{2} sin^3 x\\ dx\\ \\hspace{5cm}\\ (7)\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[b)\\ \\hspace{1cm}\\ (i)\\ \\hspace{1cm}\\ \\int x^3\\ e^{-x}\\ dx\\ \\hspace{5cm}\\  (ii)\\ \\hspace{1cm}\\  \\int_0^\\frac{\\pi}{2} \\frac{sin\\ x}{sin\\ x + cos\\ x}\\ dx \\hspace{5cm}\\ (8)\\]<\/div>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <\/p>\n\n\n\n<a target=\"_blank\" href=\"https:\/\/shareasale.com\/r.cfm?b=167780&amp;u=2863840&amp;m=17801&amp;urllink=&amp;afftrack=\" rel=\"noopener\"><img data-recalc-dims=\"1\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/static.shareasale.com\/image\/17801\/250x250_28.gif?ssl=1\" border=\"0\" alt=\"BurkeDecor.com\"><\/a>\n\n\n\n<p> <\/p>\n\n\n\n<p>            <\/p>\n","protected":false},"excerpt":{"rendered":"<p>MODEL EXAM QUESTION PAPER 40022 ENGINEERING MATHEMATICS &#8211; II Time : 3.00 Hours&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;Date:&nbsp; 22-05-2021&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Max.Marks: 100 Note: 1. Answer all question in PART A. Each question carries one mark. 2. Answer any ten questions in PART B. Each question carries two marks. 3. Answer all question by selecting either A or B. Each question [&hellip;]<\/p>\n","protected":false},"author":187055548,"featured_media":20254,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"_wpas_customize_per_network":false,"jetpack_post_was_ever_published":false},"categories":[711787927],"tags":[],"class_list":["post-15408","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-n-2021-model-exam"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>N-SCHEME-ENGINEERING MATHEMATICS-II MODEL EXAM QUESTION PAPER\/2021 - YANAMTAKSHASHILA<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/yanamtakshashila.com\/?p=15408\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"N-SCHEME-ENGINEERING MATHEMATICS-II MODEL EXAM QUESTION PAPER\/2021 - YANAMTAKSHASHILA\" \/>\n<meta property=\"og:description\" content=\"MODEL EXAM QUESTION PAPER 40022 ENGINEERING MATHEMATICS &#8211; II Time : 3.00 Hours&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;Date:&nbsp; 22-05-2021&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Max.Marks: 100 Note: 1. 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