{"id":14413,"date":"2021-04-28T11:41:19","date_gmt":"2021-04-28T06:11:19","guid":{"rendered":"https:\/\/yanamtakshashila.com\/?p=14413"},"modified":"2021-05-06T21:08:04","modified_gmt":"2021-05-06T15:38:04","slug":"diploma-continuous-assessment-test-2-april-2021","status":"publish","type":"post","link":"https:\/\/yanamtakshashila.com\/?p=14413","title":{"rendered":"Diploma Continuous Assessment  Test -2\/ April \u2013 2021"},"content":{"rendered":"\n<p><strong>Course: First year Diploma course in Engineering &amp; Technology<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-left\"><strong>Subject &amp; Code : Engineering Mathematics \u2013 II (40022)<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-left\"><strong>Time : 2 Hours&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Date:&nbsp; 27-04-2021&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: 50<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong><u>PART \u2013 A<\/u><\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>&nbsp;Answer all questions&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ( 6\u00d71=6 marks)<\/strong><\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[1.\\ Evaluate:\\ [\\overrightarrow{i} + \\overrightarrow{j}\\ \\overrightarrow{j} + \\overrightarrow{k}\\ \\overrightarrow{k} + \\overrightarrow{i}]\\ \\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> Soln: <\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\overrightarrow{a}= \\overrightarrow{i}\\ + \\overrightarrow{j}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\overrightarrow{b}= \\overrightarrow{j}\\ + \\overrightarrow{k}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\overrightarrow{c}= \\overrightarrow{k} + \\overrightarrow{i}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[ [\\overrightarrow{a}\\   \\overrightarrow{b}    \\overrightarrow{c}] =\\begin{vmatrix}\n1 &amp; 1 &amp; 0\\\\\n0 &amp; 1 &amp; 1\\\\\n1 &amp; 0 &amp; 1 \\\\\n\\end{vmatrix}\\]<\/div>\n\n\n\n<p class=\"has-text-align-center\"> =&nbsp;&nbsp;&nbsp; 1&nbsp; ( 1 &#8211; 0 )&nbsp; &#8211; 1 ( 0 &#8211; 1 )&nbsp; + 0 (&nbsp; 0 &#8211; 1 ) <\/p>\n\n\n\n<p class=\"has-text-align-center\"> =&nbsp;&nbsp; 1 ( 1 )&nbsp; -1 (- 1 ) +&nbsp; 0 <\/p>\n\n\n\n<p class=\"has-text-align-center\"> =&nbsp;&nbsp; 1 + 1 <\/p>\n\n\n\n<p class=\"has-text-align-center\"> =&nbsp;&nbsp; 2 <\/p>\n\n\n\n<script async=\"\" src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-9453835310745500\" crossorigin=\"anonymous\"><\/script>\n<!-- sidebar ad 1 -->\n<ins class=\"adsbygoogle\" style=\"display:inline-block;width:326px;height:280px\" data-ad-client=\"ca-pub-9453835310745500\" data-ad-slot=\"6703350399\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n\n\n\n<p class=\"has-text-align-left\">2. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Define vector Differential operator.<\/p>\n\n\n\n<p>Soln:<\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[The\\ vector\\ differential\\ operator\\ &#8216;DEL&#8217;\\ denoted\\ as\\ &#8216;\\nabla&#8217;\\ is\\ defined\\ by\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\nabla = \\frac{\\partial}{\\partial\\ x}\\overrightarrow{i} + \\frac{\\partial}{\\partial\\ y}\\overrightarrow{j} + \\frac{\\partial}{\\partial\\ z}\\overrightarrow{k}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\overrightarrow{i},\\ \\overrightarrow{j},\\ \\overrightarrow{k}\\ are\\ unit\\ vectors\\ in\\ x,\\ y,\\ z\\ directions\\]<\/div>\n\n\n\n<script async src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script>\n<ins class=\"adsbygoogle\"\n     style=\"display:block; text-align:center;\"\n     data-ad-layout=\"in-article\"\n     data-ad-format=\"fluid\"\n     data-ad-client=\"ca-pub-9453835310745500\"\n     data-ad-slot=\"2812384453\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[3.\\ If\\  \\overrightarrow{F}=xyz\\overrightarrow{i} + 3x^2y\\overrightarrow{j} + (xy^2 &#8211; zy^3)\\overrightarrow{k}, then\\ find\\ div\\ \\overrightarrow{F}\\ \\hspace{20cm}\\] <\/div>\n\n\n\n<p>Soln:<\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[Let\\  \\overrightarrow{F}=xyz\\overrightarrow{i} + 3x^2y\\overrightarrow{j} + (xy^2 &#8211; zy^3)\\overrightarrow{k}\\] <\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\nabla\\ . \\overrightarrow{F} = \\frac{\\partial {F_1}}{\\partial\\ x} + \\frac{\\partial {F_2}}{\\partial\\ y} + \\frac{\\partial {F_3}}{\\partial\\ z}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[ = \\frac{\\partial }{\\partial\\ x} {(xyz)}+ \\frac{\\partial}{\\partial\\ y} {(3x^2y)}+ \\frac{\\partial}{\\partial\\ z} {(xy^2-xy^3)}\\]<\/div>\n\n\n\n<p class=\"has-text-align-center\"> =&nbsp;&nbsp; yz&nbsp; + 3x<sup>2<\/sup> ( 1 )&nbsp; + ( 0 &#8211; y<sup>3<\/sup> ) <\/p>\n\n\n\n<p class=\"has-text-align-center\"> =&nbsp; yz&nbsp; + 3x<sup>2<\/sup> &#8211; y<sup>3<\/sup> <\/p>\n\n\n\n<script async src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script>\n<!-- Ad1 -->\n<ins class=\"adsbygoogle\"\n     style=\"display:block\"\n     data-ad-client=\"ca-pub-9453835310745500\"\n     data-ad-slot=\"8240817448\"\n     data-ad-format=\"auto\"\n     data-full-width-responsive=\"true\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[ 4.\\ Evaluate: \\int(x^2 -x -1)\\ dx\\ \\hspace{20cm}\\] <\/div>\n\n\n\n<p>Soln: <\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\int(x^2 -x -1)\\ dx = \\frac{x^3}{3} &#8211; \\frac{x^2}{2} &#8211; x + c\\]<\/div>\n\n\n\n<script async src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script>\n<ins class=\"adsbygoogle\"\n     style=\"display:block\"\n     data-ad-format=\"autorelaxed\"\n     data-ad-client=\"ca-pub-9453835310745500\"\n     data-ad-slot=\"3040040190\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[5.\\ Evaluate\\ :\\ \\int\\ \\frac{2x}{1 + x^2}\\ dx\\ \\hspace{20cm}\\]<\/div>\n\n\n\n<p>Soln:  <\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[put\\   u\\ =\\ 1 + x^2\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\frac{du}{dx}= \\ 2x\\]<\/div>\n\n\n\n<p class=\"has-text-align-center\"> du\u00a0 = 2 dx <\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\int\\ \\frac{2x}{1 + x^2}\\ dx= \\int\\ \\frac{du}{u}\\]<\/div>\n\n\n\n<p class=\"has-text-align-center\"> =\u00a0 log u + c <\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[= log(1 + x^2) + c\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\int\\ \\frac{2x}{1 + x^2}\\ dx= log(1 + x^2) + c\\]<\/div>\n\n\n\n<script async src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script>\n<ins class=\"adsbygoogle\"\n     style=\"display:block\"\n     data-ad-format=\"fluid\"\n     data-ad-layout-key=\"-6t+ed+2i-1n-4w\"\n     data-ad-client=\"ca-pub-9453835310745500\"\n     data-ad-slot=\"9770958327\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[6.\\ Evaluate:\\ \\int \\frac{dx}{x^2 + 16}\\ \\hspace{20cm}\\]<\/div>\n\n\n\n<p>Soln:<\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[W.K.T\\  \\int \\frac{dx}{x^2 + a^2} = \\frac{1}{a}\\ {tan}^{-1} (\\frac{x}{a}) +c\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\int \\frac{dx}{x^2 + 16} = \\int \\frac{dx}{x^2 + 4^2}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[ = \\frac{1}{4}\\ {tan}^{-1} (\\frac{x}{4}) +c\\]<\/div>\n\n\n\n<script async src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script>\n<!-- sidebar ad 1 -->\n<ins class=\"adsbygoogle\"\n     style=\"display:inline-block;width:326px;height:280px\"\n     data-ad-client=\"ca-pub-9453835310745500\"\n     data-ad-slot=\"6703350399\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n\n\n\n<p class=\"has-text-align-center\"> <strong><u>PART \u2013 A<\/u><\/strong> <\/p>\n\n\n\n<p class=\"has-text-align-center\"> <strong>Answer all questions\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 ( 7\u00d72=14 marks)<\/strong> <\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[7.\\ 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{20cm}\\]<\/div>\n\n\n\n<p>Soln: <\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\overrightarrow{a}= 2\\overrightarrow{i}+ \\overrightarrow{j}+ \\overrightarrow{k}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\overrightarrow{b}= 3\\overrightarrow{i}+ 4\\overrightarrow{j}+ \\overrightarrow{k}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\overrightarrow{c}= \\overrightarrow{i}- 2\\overrightarrow{j}+ \\overrightarrow{k}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[ [\\overrightarrow{a}\\   \\overrightarrow{b}    \\overrightarrow{c}] =\\begin{vmatrix}\n2 &amp; 1 &amp; 1\\\\\n3 &amp; 4 &amp; 1\\\\\n1 &amp; -2 &amp; 1\\\\\n\\end{vmatrix}\\]<\/div>\n\n\n\n<p class=\"has-text-align-center\"> =\u00a0\u00a0\u00a0 2\u00a0 ( 4 + 2 )\u00a0 &#8211; 1 (3 &#8211; 1 )\u00a0 + 1 ( -6 &#8211; 4 ) <\/p>\n\n\n\n<p class=\"has-text-align-center\"> =\u00a0\u00a0 2 ( 6 )\u00a0 &#8211; 1 (2 ) +\u00a0 1 ( &#8211; 10 ) <\/p>\n\n\n\n<p class=\"has-text-align-center\"> =\u00a0\u00a0 12 &#8211; 2\u00a0 &#8211;\u00a0 10\u00a0\u00a0 =\u00a0\u00a0\u00a0 10\u00a0 &#8211;\u00a0 10 <\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[ [\\overrightarrow{a}\\   \\overrightarrow{b}    \\overrightarrow{c}] = 0\\]<\/div>\n\n\n\n<p> The given points are coplanar. <\/p>\n\n\n\n<script async src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script>\n<ins class=\"adsbygoogle\"\n     style=\"display:block; text-align:center;\"\n     data-ad-layout=\"in-article\"\n     data-ad-format=\"fluid\"\n     data-ad-client=\"ca-pub-9453835310745500\"\n     data-ad-slot=\"2812384453\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n\n\n\n<p>8.   Find the unit normal to the surface xy +yz + zx= 3 at the point (1, 1, 1). <\/p>\n\n\n\n<p>Soln:<\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\phi(x,y,z)\\ = c\\ (being\\ constant)\\ represents\\ a\\ surface\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[then\\ unit\\ normal\\ to\\ the\\ surface\\ \\phi\\ at\\ the\\ point\\  (x,y,z)\\ is\\ \\frac{\\nabla\\phi}{|\\nabla\\phi|}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[Here\\ \\phi = xy +yz + zx\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\nabla\\ \\phi=(\\frac{\\partial\\ \\phi}{\\partial\\ x})\\overrightarrow{i} + (\\frac{\\partial\\ \\phi}{\\partial\\ y})\\overrightarrow{j} + (\\frac{\\partial\\ \\phi}{\\partial\\ z})\\overrightarrow{k}&#8212;&#8212;&#8212;&#8212;(1)\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\frac{\\partial\\ \\phi}{\\partial\\ x} = y \\frac{\\partial}{\\partial\\ x}(x) + 0 + z \\frac{\\partial}{\\partial\\ x}(x)\\]<\/div>\n\n\n\n<p class=\"has-text-align-center\"> = y ( 1 )\u00a0 + z ( 1 )<\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\frac{\\partial\\ \\phi}{\\partial\\ x} = y + z\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\frac{\\partial\\ \\phi}{\\partial\\ y} = x \\frac{\\partial}{\\partial\\ y}(y) + z \\frac{\\partial}{\\partial\\ y}(y) + 0\\]<\/div>\n\n\n\n<p class=\"has-text-align-center\">  = x ( 1 )\u00a0 + z ( 1 ) <\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\frac{\\partial\\ \\phi}{\\partial\\ y} = x + z\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\frac{\\partial\\ \\phi}{\\partial\\ z} = 0 + y \\frac{\\partial}{\\partial\\ z}(z) + x \\frac{\\partial}{\\partial\\ z}(z)\\]<\/div>\n\n\n\n<p class=\"has-text-align-center\"> = y ( 1 )\u00a0 + x ( 1 ) <\/p>\n\n\n\n<p> Equation (1) becomes <\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\nabla\\ \\phi=(y + z)\\overrightarrow{i} + (x + z)\\overrightarrow{j} + (y + x)\\overrightarrow{k}\\]<\/div>\n\n\n\n<p> At the point (1,1, 1),  <\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\nabla\\ \\phi=(1 + 1)\\overrightarrow{i} + (1 + 1)\\overrightarrow{j} + (1 + 1)\\overrightarrow{k}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\nabla\\ \\phi= 2\\overrightarrow{i} + 2\\overrightarrow{j} + 2\\overrightarrow{k}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[|\\nabla\\phi| =  \\sqrt{(2)^2 + (2)^2 + (2)^2 }\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[= \\sqrt{(4 + 4 + 4) }\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[= 2\\sqrt{3}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[unit\\ normal\\ to\\ the\\ surface\\ \\phi\\ at\\ the\\ point\\  (1,1,1)\\ =\\ \\frac{\\nabla\\phi}{|\\nabla\\phi|}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[  = \\frac{2\\overrightarrow{i}+ 2\\overrightarrow{j}+ 2\\overrightarrow{k}}{2\\sqrt{3}}\\]<\/div>\n\n\n\n<script async src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script>\n<!-- Ad1 -->\n<ins class=\"adsbygoogle\"\n     style=\"display:block\"\n     data-ad-client=\"ca-pub-9453835310745500\"\n     data-ad-slot=\"8240817448\"\n     data-ad-format=\"auto\"\n     data-full-width-responsive=\"true\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n","protected":false},"excerpt":{"rendered":"<p>Course: First year Diploma course in Engineering &amp; Technology Subject &amp; Code : Engineering Mathematics \u2013 II (40022) Time : 2 Hours&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Date:&nbsp; 27-04-2021&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: 50 PART \u2013 A &nbsp;Answer all questions&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ( 6\u00d71=6 marks) Soln: =&nbsp;&nbsp;&nbsp; 1&nbsp; ( 1 &#8211; 0 )&nbsp; &#8211; 1 ( 0 &#8211; 1 )&nbsp; + 0 (&nbsp; 0 [&hellip;]<\/p>\n","protected":false},"author":187055548,"featured_media":0,"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":[711787912,711787911],"tags":[],"class_list":["post-14413","post","type-post","status-publish","format-standard","hentry","category-n-2021-ca-ii","category-n-internals-2021"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Diploma Continuous Assessment Test -2\/ April \u2013 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=14413\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Diploma Continuous Assessment Test -2\/ April \u2013 2021 - YANAMTAKSHASHILA\" \/>\n<meta property=\"og:description\" content=\"Course: First year Diploma course in Engineering &amp; Technology Subject &amp; Code : Engineering Mathematics \u2013 II (40022) Time : 2 Hours&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Date:&nbsp; 27-04-2021&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. 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