{"id":50724,"date":"2024-10-18T18:58:33","date_gmt":"2024-10-18T13:28:33","guid":{"rendered":"https:\/\/yanamtakshashila.com\/?p=50724"},"modified":"2024-11-27T10:04:38","modified_gmt":"2024-11-27T04:34:38","slug":"board-exam-april-2024-applied-mathematics-1-practical-question-paper-for-civil-branch","status":"publish","type":"post","link":"https:\/\/yanamtakshashila.com\/?p=50724","title":{"rendered":"BOARD EXAM &#8211; November 2024 &#8211; APPLIED MATHEMATICS &#8211; 1 (Model) PRACTICAL QUESTION PAPER FOR CIVIL BRANCH"},"content":{"rendered":"\n<p class=\"has-text-align-center\">DR.B.R.AMBEDKAR POLYTECHNIC COLLEGE &#8211; YANAM<\/p>\n\n\n\n<p class=\"has-text-align-center\">BASIC ENGINEERING<\/p>\n\n\n\n<p class=\"has-text-align-center\">BOARD PRACTICAL EXAMINATION &#8211; APRIL 2024<\/p>\n\n\n\n<p>Scheme: R 2023&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;                       APPLIED MATHEMATICS &#8211; 1&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; Marks: 100<\/p>\n\n\n\n<p>Time&nbsp; &nbsp; : 3 Hrs &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;                                   Date: 04-05-2024<\/p>\n\n\n\n<h5 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-e5977051260d5f9ddc729feb1c9853fe\">Ex &#8211; 1<\/h5>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\text{To draw the graph of given equations of the circles}\\ x^2\\ +\\ y^2\\ -\\ 4x\\ -\\ 6y\\ +\\ 8\\ =\\ 0\\ \\hspace{7cm}\\]\\[and\\ x^2\\ +\\ y^2\\ -\\ 10x\\ -\\ 6y\\ +\\ 14\\ =\\ 0\\]<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<div class=\"wp-block-mathml-mathmlblock\">\\[i).\\ \\text{Graph the equations of the circles in the Cartesian plane}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[ii).\\ \\text{To determine the coordinates of the centres and radii&nbsp; of the circles and mark them on the graph.}\\ \\hspace{5cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[iii).\\ \\text{To determine the distance between the centres of the circles.}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[iv).\\ \\text{Verify whether any of the relationships}\\ C_1\\ C_2\\ =\\ r_1\\ +\\ r_2\\  or\\ C_1\\ C_2\\ =\\ r_1\\ -\\ r_2\\  holds\\ or\\ not\\ \\hspace{4cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color {blue} {Soln:}\\ \\hspace{20cm}\\]<\/div>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-1 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img data-recalc-dims=\"1\" fetchpriority=\"high\" decoding=\"async\" width=\"630\" height=\"840\" data-attachment-id=\"52634\" data-permalink=\"https:\/\/yanamtakshashila.com\/?attachment_id=52634\" data-orig-file=\"https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0665-rotated.jpg?fit=3024%2C4032&amp;ssl=1\" data-orig-size=\"3024,4032\" 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https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0675-rotated.jpg?resize=274%2C365&amp;ssl=1 274w, https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0675-rotated.jpg?resize=768%2C1024&amp;ssl=1 768w, https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0675-rotated.jpg?resize=1152%2C1536&amp;ssl=1 1152w, https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0675-rotated.jpg?resize=1536%2C2048&amp;ssl=1 1536w, https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0675-rotated.jpg?resize=900%2C1200&amp;ssl=1 900w, https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0675-rotated.jpg?resize=600%2C800&amp;ssl=1 600w, https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0675-rotated.jpg?resize=450%2C600&amp;ssl=1 450w, https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0675-rotated.jpg?resize=300%2C400&amp;ssl=1 300w, https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0675-rotated.jpg?resize=150%2C200&amp;ssl=1 150w, https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0675-rotated.jpg?resize=1200%2C1600&amp;ssl=1 1200w, https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0675-rotated.jpg?w=2000&amp;ssl=1 2000w, https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0675-rotated.jpg?w=3000&amp;ssl=1 3000w\" sizes=\"(max-width: 630px) 100vw, 630px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"630\" height=\"840\" data-attachment-id=\"52644\" data-permalink=\"https:\/\/yanamtakshashila.com\/?attachment_id=52644\" data-orig-file=\"https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0676-rotated.jpg?fit=3024%2C4032&amp;ssl=1\" data-orig-size=\"3024,4032\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;1.6&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;iPhone 13&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1732676504&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;5.1&quot;,&quot;iso&quot;:&quot;125&quot;,&quot;shutter_speed&quot;:&quot;0.02&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"IMG_0676\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0676-rotated.jpg?fit=630%2C840&amp;ssl=1\" data-id=\"52644\" src=\"https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0676.jpg?resize=630%2C840&#038;ssl=1\" alt=\"\" class=\"wp-image-52644\" srcset=\"https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0676-rotated.jpg?resize=630%2C840&amp;ssl=1 630w, https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0676-rotated.jpg?resize=274%2C365&amp;ssl=1 274w, https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0676-rotated.jpg?resize=768%2C1024&amp;ssl=1 768w, https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0676-rotated.jpg?resize=1152%2C1536&amp;ssl=1 1152w, https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0676-rotated.jpg?resize=1536%2C2048&amp;ssl=1 1536w, https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0676-rotated.jpg?resize=900%2C1200&amp;ssl=1 900w, https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0676-rotated.jpg?resize=600%2C800&amp;ssl=1 600w, 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data-permalink=\"https:\/\/yanamtakshashila.com\/?attachment_id=52651\" data-orig-file=\"https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0677-rotated.jpg?fit=3024%2C4032&amp;ssl=1\" data-orig-size=\"3024,4032\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;1.6&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;iPhone 13&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1732676512&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;5.1&quot;,&quot;iso&quot;:&quot;125&quot;,&quot;shutter_speed&quot;:&quot;0.02&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"IMG_0677\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0677-rotated.jpg?fit=630%2C840&amp;ssl=1\" data-id=\"52651\" src=\"https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0677.jpg?resize=630%2C840&#038;ssl=1\" alt=\"\" class=\"wp-image-52651\" srcset=\"https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0677-rotated.jpg?resize=630%2C840&amp;ssl=1 630w, https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0677-rotated.jpg?resize=274%2C365&amp;ssl=1 274w, https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0677-rotated.jpg?resize=768%2C1024&amp;ssl=1 768w, https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0677-rotated.jpg?resize=1152%2C1536&amp;ssl=1 1152w, https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0677-rotated.jpg?resize=1536%2C2048&amp;ssl=1 1536w, https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0677-rotated.jpg?w=2000&amp;ssl=1 2000w, https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2024\/10\/IMG_0677-rotated.jpg?w=3000&amp;ssl=1 3000w\" sizes=\"(max-width: 630px) 100vw, 630px\" \/><\/figure>\n<\/figure>\n\n\n<p><iframe width=\"747\" height=\"467\" src=\"https:\/\/www.youtube.com\/embed\/e89syWjNNvo?list=PLQIom4Rz29vyp5ZiCGuc0-zCEqs8Pvslf\" title=\"Draw the two equations of circles and find their centres and radii using GeoGebra classic 5\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen=\"\"><\/iframe><\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\"><\/div>\n\n\n\n<ol class=\"wp-block-list\"><\/ol>\n\n\n\n<h5 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-4cdf7a59cac671110e1234dc3a91e8e9\">Ex -2&nbsp;<\/h5>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\text{A pair of super gear consists of }\\ Z_p\\ =)\\ \\text{20 teeth pinion meshing with}\\ (Z_g\\ =)\\ 120\\ teeth\\ gear.\\ \\hspace{3cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\text{Let the module be (m =) 4mm.}\\ \\hspace{5cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[i).\\ \\text{Calculate the pitch circle diameters of the pinion and the gear using the formulae}\\ d_p\\ =\\ m\\ Z_p\\hspace{5cm}\\]\\[and\\ d_g\\ =\\ m\\ Z_g\\ \\hspace {10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[ii).\\ \\text{Calculate the distance between the centres of the pinion and the gear using the formula}\\ \\hspace{5cm}\\]\\[\\frac{1}{2}(d_p\\ +\\ d_g)\\ \\hspace {10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[iii).\\ \\text{Draw two externally touching circles to represent pinion and gear with appropriate centres and}\\ \\hspace{5cm}\\]\\[radii\\ \\frac{1}{2}\\ d_p\\ and \\ \\frac{1}{2}\\ d_g.\\ \\text{Calculate the distance between the centres of the circles from the graph}\\ \\hspace {2cm}\\]\\[\\text{and verify that it is equal to}\\ \\frac{1}{2}(d_p\\ +\\ d_g)\\ \\hspace {10cm}\\]<\/div>\n\n\n\n<ol class=\"wp-block-list\">\n<li><\/li>\n<\/ol>\n\n\n\n<h5 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-9125b4b92a66093b6bd3996292c44519\">Ex &#8211; 3<\/h5>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\text{Do the following activities for the given image of a parabolic shaped satellite dish antenna.}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[i).\\ \\text{Draw a parabola which fits the given image of the dish antenna.}\\ \\hspace{8cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[ii).\\ \\text{Write the equation of the parabola.}\\ \\hspace{14cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[iii).\\ \\text{Find the vertex, focus, directrix and latus-rectum and mark them on the graph.}\\ \\hspace{7cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[iv).\\ \\text{How far from the vertex should the receiver of the antenna be placed?}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<ol class=\"wp-block-list\">\n<li><\/li>\n<\/ol>\n\n\n\n<h5 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-36632d3f3a0ac0084ab93d94d52a7b2d\">Ex &#8211; 4<\/h5>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\text{Do the following actives for the given image of a parabolic shaped fly-over bridge..}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[i).\\ \\text{Draw a parabola which fits the given bridge.}\\ \\hspace{13cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[ii).\\ \\text{Write the equation of the parabola.}\\ \\hspace{15cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[iii).\\ \\text{Find the vertex, focus, directrix and lotus &#8211; rectum and mark them on the graph.}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<ol class=\"wp-block-list\">\n<li><\/li>\n<\/ol>\n\n\n\n<h5 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-b7f8abfd4061266304522ce7beebab3e\">Ex &#8211; 5<\/h5>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\text{Do the following actives.}\\ \\hspace{15cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[i).\\ \\text{Graph the polynomial function}\\ \ud835\udc53(\ud835\udc65) =\\ x^2\\  -\\ 5x\\ +\\ 6.\\ \\hspace{12cm}\\]\\[\\text{Find the value of \ud835\udc53(\ud835\udc65) at \ud835\udc65 = 5 and the limit of \ud835\udc53(\ud835\udc65) at \ud835\udc65 = 5.}\\ \\hspace {8cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[ii).\\ \\text{Graph the rational function}\\ f(\ud835\udc65) =\\ \\frac{x^2\\  -\\ 5x\\ +\\ 6}{x\\ -\\ 2}.\\ \\hspace{12cm}\\]\\[\\text{Find the value of \ud835\udc53(\ud835\udc65) at \ud835\udc65 = 4 and the limit of \ud835\udc53(\ud835\udc65) at \ud835\udc65 = 4.}\\ \\hspace {8cm}\\]<\/div>\n\n\n\n<script async src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-9453835310745500\"\n     crossorigin=\"anonymous\"><\/script>\n<!-- 350 x 250 ad -->\n<ins class=\"adsbygoogle\"\n     style=\"display:block\"\n     data-ad-client=\"ca-pub-9453835310745500\"\n     data-ad-slot=\"3583972194\"\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<h5 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-0012278cf444e9bc078fb9168292497c\">Ex &#8211; 6<\/h5>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\text{Two parallel straights of V = 20m apart are to be connected by reverse curve consisting}\\ \\hspace{7cm}\\]\\[\\text{of arcs of same radius.&nbsp; The distance between the end points of the curve is L = 200m.}\\ \\hspace{3cm}\\] <\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[i).\\ \\text{Find the approximate value of the common radius..}\\ \\hspace{12cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[ii).\\ \\text{Find the length of the whole curve.}\\ \\hspace{13cm}\\]<\/div>\n\n\n\n<ol class=\"wp-block-list\">\n<li><\/li>\n<\/ol>\n\n\n\n<h5 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-72062c555ea831469ce0d8455b76993c\">Ex &#8211; 7<\/h5>\n\n\n\n<p>Do the following activities.<\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[i).\\ \\text{Graph the functions c (constant)},\\ x^n,\\ n\\ \\in\\ R,\\ sin\\ x.\\ \\ \\hspace{10cm}\\]\\[\\text{Find their indefinite integrals.}\\ \\hspace {8cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[ii).\\ \\text{Evaluate the definite integral},\\ \\int_a^b\\ f(x)\\ dx\\ and\\ \\hspace{10cm}\\]\\[\\text{relate it to the area under the curve y = f(x) between x-axis, x = a and x = b.}\\ \\hspace {2cm}\\]<\/div>\n\n\n\n<p>Ex &#8211; 8<\/p>\n\n\n\n<p>Do the following activities for the given image of a closed irregular plane figure.<\/p>\n\n\n\n<p>i) Mark the required number of points on the boundary of the figure.<\/p>\n\n\n\n<p>ii) Draw the boundary of the figure by joining the points.<\/p>\n\n\n\n<p>iii) Divide the figure into trapeziums using the points on the boundary.<\/p>\n\n\n\n<p>iv) Calculate the approximate area of the figure.<\/p>\n\n\n\n<p>Ex &#8211; 9<\/p>\n\n\n\n<p>1. To find the mean <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/bbdaff1b-9ec0-46fb-867c-0ae78ea98696\" alt=\"equation_29.pdf\"> for the following data of size 43, 45, 47, 44, 41, 46, 48, 47, 45, 48, 45, 42, 41, 49, 42, 46, 44, 49, 47, 49, 41, 50, 45, 45, 49, 42, 46, 49, 47, 46, 45, 45, 49, 41, 45, 49, 50, 43, 45, 47, 40, 45, 48, 43, 42, 46, 43, 45, 46, 42.&nbsp;<\/p>\n\n\n\n<p>2. To find the variance <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/57cfd430-dc17-4c8b-bd81-d76f06a1bc35\" alt=\"equation_30.pdf\"> and standard deviation <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/fffbcfef-a37f-42f2-b00d-9d770cff98dd\" alt=\"equation_31.pdf\"> for the given data.<\/p>\n\n\n\n<p>3. To fit the normal curve f(x) = N(<img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/dae252c5-b2aa-4679-aabd-63993b6909aa\" alt=\"equation_32.pdf\">, <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/15335359-6d4e-4e4e-9548-bdebf8d704b8\" alt=\"equation_33.pdf\">) = <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/ea8a3f95-6c38-4191-bc48-bc1411ab0bec\" alt=\"equation_34.pdf\">&nbsp; <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/2a09734e-29a3-4f06-a0ca-1ab13ec27ab5\" alt=\"equation_35.pdf\">,&nbsp; &#8211; <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/cba30036-b189-4cfa-8ee6-6781e107d73d\" alt=\"equation_36.pdf\"> &lt; x &lt; <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/3b7bcb44-d650-44e7-b9e9-ef49c3e2ca7f\" alt=\"equation_37.pdf\"><\/p>\n\n\n\n<p>4. To calculate the probability p = P(44 &lt; X &lt; 47) using the formula <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/da3928ac-e773-4c5d-80aa-8f0252fbced7\" alt=\"equation_38.pdf\"><\/p>\n\n\n\n<p>5. To calculate the probability <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/7ffffe63-6079-4635-9e8a-abed89121343\" alt=\"equation_39.pdf\"> = P(44 &lt; X &lt; 47) using the probability calculator and verify that <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/17ec89ff-ddcc-4f24-b940-865bef2e65ab\" alt=\"equation_40.pdf\"> = p&nbsp; approximately.<\/p>\n\n\n\n<p>6. To calculate the number of data points in the interval (44, 47) using the formula n = <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/e4686b1d-32a9-47a8-b7aa-9f28f14fe6a4\" alt=\"equation_41.pdf\"> and verify it with the given data.<\/p>\n\n\n\n<p>Ex: 10&nbsp;<\/p>\n\n\n\n<p>Consider the 4 samples each of size 5 taken from the production lot of a machine.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong>Sample&nbsp;<\/strong> <strong>Number<\/strong><\/td><td><img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/9cd7e2a9-efbc-4c44-890c-8475260b0d38\" alt=\"equation_42.pdf\"><\/td><td><img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/c3a6fc00-e372-40df-9417-60cd4f0e9077\" alt=\"equation_43.pdf\"><\/td><td><img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/cbb40666-ede4-487f-ac6a-670625a77852\" alt=\"equation_44.pdf\"><\/td><td><img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/96fb0085-aa8f-4894-8bcb-eeb6e05bdd21\" alt=\"equation_45.pdf\"><\/td><td><img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/7a5f78b0-47e3-4ef9-bde1-37ac9471fd16\" alt=\"equation_46.pdf\"><\/td><\/tr><tr><td><img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/b190a4e0-9ec5-42eb-8d09-2359630d1ede\" alt=\"equation_47.pdf\"><\/td><td>6.35<\/td><td>6.40<\/td><td>6.32<\/td><td>6.37<\/td><td>6.42<\/td><\/tr><tr><td><img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/ba456ce2-8aa6-44c5-8491-1088f62f2428\" alt=\"equation_48.pdf\"><\/td><td>6.34<\/td><td>6.40<\/td><td>6.34<\/td><td>6.36<\/td><td>6.39<\/td><\/tr><tr><td><img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/3fa8a247-cb26-4b3e-986b-d5acf463c728\" alt=\"equation_49.pdf\"><\/td><td>6.42<\/td><td>6.64<\/td><td>6.35<\/td><td>6.59<\/td><td>6.72<\/td><\/tr><tr><td><img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/75b82698-8724-4204-b4eb-1da5650da807\" alt=\"equation_50.pdf\"><\/td><td>6.38<\/td><td>6.48<\/td><td>6.44<\/td><td>6.58<\/td><td>6.39<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>1. To calculate the sample means <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/473ac2ad-fa19-4c9e-b7b3-235733d5db96\" alt=\"equation_51.pdf\">,&nbsp; <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/8072631b-9a90-4c3d-b095-7d97cc33c52c\" alt=\"equation_52.pdf\">,&nbsp; <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/0254986f-eb30-4e3d-ba3e-034b6556651f\" alt=\"equation_53.pdf\">,&nbsp; <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/ff38511b-9cd0-45be-8b13-ecbfd016a102\" alt=\"equation_54.pdf\">&nbsp; and the mean of the sample means&nbsp;<\/p>\n\n\n\n<p><img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/4bf498fa-af94-4faf-b7da-a807b55e1559\" alt=\"equation_55.pdf\"> .<\/p>\n\n\n\n<p>2. To calculate the sample variances <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/31e10bd7-3932-49cf-90e8-657f2f3739ae\" alt=\"equation_56.pdf\">, <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/59fce4d3-f394-41a8-8d23-56e0d492ce05\" alt=\"equation_57.pdf\">, <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/2a6fd69d-feb9-4b70-b0c0-08b882513c18\" alt=\"equation_58.pdf\">, <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/8d5b90ff-3d95-4b39-a7ed-5a4fd408b0f9\" alt=\"equation_59.pdf\"> and <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/e1d00e43-5228-4360-b7a1-750c760318b0\" alt=\"equation_60.pdf\"> = <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/d0179707-a369-4b45-bdbc-099abc53ec1f\" alt=\"equation_61.pdf\"><\/p>\n\n\n\n<p>3. To determine the central line CL = <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/df82c4e2-03a3-48d4-86fd-79799196a491\" alt=\"equation_62.pdf\">,&nbsp; lower control limit LCL = <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/c5c8c0b5-2212-45fa-8b44-4beb43c9f3b1\" alt=\"equation_63.pdf\">&nbsp; &#8211;&nbsp; <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/5f875ebe-b368-44cd-aa27-ca3251da3ee7\" alt=\"equation_64.pdf\">&nbsp; and<\/p>\n\n\n\n<p>upper control limit UCL = <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/555e839a-72f6-4066-abeb-0cadecea45bc\" alt=\"equation_65.pdf\">&nbsp; +&nbsp; <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/ee364153-7936-4dd2-8800-b45691092d3e\" alt=\"equation_66.pdf\"><\/p>\n\n\n\n<p>4. To draw the <img decoding=\"async\" src=\"blob:https:\/\/yanamtakshashila.com\/57af0a05-6510-4f7d-9449-5a975a0a66c4\" alt=\"equation_67.pdf\"> chart and determine the out &#8211; of &#8211; control signals.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>DR.B.R.AMBEDKAR POLYTECHNIC COLLEGE &#8211; YANAM BASIC ENGINEERING BOARD PRACTICAL EXAMINATION &#8211; APRIL 2024 Scheme: R 2023&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; APPLIED MATHEMATICS &#8211; 1&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; Marks: 100 Time&nbsp; &nbsp; : [&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":"set","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":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2},"_wpas_customize_per_network":false,"jetpack_post_was_ever_published":false},"categories":[711788743],"tags":[],"class_list":["post-50724","post","type-post","status-publish","format-standard","hentry","category-applied-mathematics-i"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - 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