{"id":666,"date":"2023-08-10T09:39:18","date_gmt":"2023-08-10T09:39:18","guid":{"rendered":"https:\/\/iitmadrasstudentscommunity.me\/?page_id=666"},"modified":"2023-08-12T12:25:37","modified_gmt":"2023-08-12T06:55:37","slug":"maths-week-9-graded-assignments-iit-madras","status":"publish","type":"page","link":"https:\/\/iitmadrasstudentscommunity.me\/maths-week-9-graded-assignments-iit-madras\/","title":{"rendered":"Maths Week 9 Graded Assignments IIT Madras"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"666\" class=\"elementor elementor-666\" data-elementor-post-type=\"page\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-dd3c6c2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"dd3c6c2\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-72baf95\" data-id=\"72baf95\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-483fb8f elementor-widget elementor-widget-text-editor\" data-id=\"483fb8f\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<p><em>Maths week 9 graded assignment Complete\u00a0 Questions Discussed In This Blog We Hope This Might Help You All In Matching Answers . Or For Some Others Reasons Not Able To Complete Graded Assignments &#8211; Best Of Luck <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/14.0.0\/svg\/1f91e.svg\" alt=\"\ud83e\udd1e\" \/>\u00a0<b>Check Below For Answers Link<\/b><\/em><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-c679303 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c679303\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-de8e3ac\" data-id=\"de8e3ac\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ec3b916 elementor-widget elementor-widget-text-editor\" data-id=\"ec3b916\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div style=\"margin: 0px; padding: 0px;\"><div id=\"1JE3n9dorwhE\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: #e1e1e1 1px 1px 1px;\"><div id=\"1JE3n9dorwhE.0.6725429545140224\" class=\"qt-mc-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><p>1. Match the functions in Column A with the corresponding (signed) area between its graph and the interval\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">[\u22121,1]<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">[<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">]<\/span><\/span><\/span><\/span><\/span>\u00a0on the X-axis in column B and the images of their graphs and the highlighted region corresponding to the area computed in Column C, given in Table M2W3G1.<br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/><img decoding=\"async\" class=\"yui-img\" style=\"margin: 0px; padding: 0px; vertical-align: middle;\" title=\"\" src=\"https:\/\/backend.seek.onlinedegree.iitm.ac.in\/21t3_ma1003\/assets\/img\/T3W3GA-1.jpg\" alt=\"\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"qt-choices\" style=\"margin: 16px 0px 0px; padding: 0px;\"><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><p><input id=\"1JE3n9dorwhE.0.6725429545140224.0\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"1JE3n9dorwhE.0.6725429545140224\" type=\"checkbox\" data-index=\"0\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"1JE3n9dorwhE.0.6725429545140224.0\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"1JE3n9dorwhE.0.6725429545140224.0\">i)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a0b)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a01), iii)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a0a)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a02).<\/label><\/label><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><p><input id=\"1JE3n9dorwhE.0.6725429545140224.1\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"1JE3n9dorwhE.0.6725429545140224\" type=\"checkbox\" data-index=\"1\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><span style=\"color: #0000ff;\"><strong><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"1JE3n9dorwhE.0.6725429545140224.1\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"1JE3n9dorwhE.0.6725429545140224.1\">i)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a0b)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a03), ii)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a0c)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a01).<\/label><\/label><\/strong><\/span><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><p><input id=\"1JE3n9dorwhE.0.6725429545140224.2\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"1JE3n9dorwhE.0.6725429545140224\" type=\"checkbox\" data-index=\"2\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><strong><span style=\"color: #0000ff;\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"1JE3n9dorwhE.0.6725429545140224.2\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"1JE3n9dorwhE.0.6725429545140224.2\">ii)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a0c)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a01), iii)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a0a)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a02).<\/label><\/label><\/span><\/strong><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><p><input id=\"1JE3n9dorwhE.0.6725429545140224.3\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"1JE3n9dorwhE.0.6725429545140224\" type=\"checkbox\" data-index=\"3\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"1JE3n9dorwhE.0.6725429545140224.3\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"1JE3n9dorwhE.0.6725429545140224.3\">i)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a0b)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a01), ii)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a0c)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a03), iii)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a0a)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a02).<\/label><\/label><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"1JE3n9dorwhE.1.4589111335714816\" class=\"qt-mc-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">100 point<\/em><\/div><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p>2. A cylinder of radius\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><\/span><\/span><\/span><\/span>\u00a0and height\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">2\u210e<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">h<\/span><\/span><\/span><\/span><\/span>\u00a0is to be inscribed in a sphere of radius\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.00773em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">R<\/span><\/span><\/span><\/span><\/span>\u00a0centered at O as shown in Figure M2W3G1<br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<img decoding=\"async\" class=\"yui-img\" style=\"margin: 0px; padding: 0px; vertical-align: middle;\" title=\"\" src=\"https:\/\/backend.seek.onlinedegree.iitm.ac.in\/21t3_ma1003\/assets\/img\/T3W3GA-2.jpg\" alt=\"\" \/><br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/>The volume of such a cylinder is given by\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=2\ufffd\ufffd2\u210e<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.22222em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">V<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">\u03c0<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">h<\/span><\/span><\/span><\/span><\/span>\u00a0and the surface area of the outer curved surface is given by\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=4\ufffd\ufffd\u210e<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.05764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">S<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">4<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">\u03c0<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">h<\/span><\/span><\/span><\/span><\/span>. Choose the set of correct options.<\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"qt-choices\" style=\"margin: 16px 0px 0px; padding: 0px;\"><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><p><input id=\"1JE3n9dorwhE.1.4589111335714816.0\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"1JE3n9dorwhE.1.4589111335714816\" type=\"checkbox\" data-index=\"0\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"1JE3n9dorwhE.1.4589111335714816.0\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"1JE3n9dorwhE.1.4589111335714816.0\">The cylinder has maximum volume amongst all cylinders which can be inscribed when\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u210e=\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">h<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.00773em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">R<\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><p><input id=\"1JE3n9dorwhE.1.4589111335714816.1\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"1JE3n9dorwhE.1.4589111335714816\" type=\"checkbox\" data-index=\"1\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"1JE3n9dorwhE.1.4589111335714816.1\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"1JE3n9dorwhE.1.4589111335714816.1\">The cylinder has maximum volume amongst all cylinders which can be inscribed when\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u210e=3\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">h<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord sqrt\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.90722em;\"><span class=\"svg-align\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px 0px 0px 0.833em; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.00773em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">R<\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><p><input id=\"1JE3n9dorwhE.1.4589111335714816.2\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"1JE3n9dorwhE.1.4589111335714816\" type=\"checkbox\" data-index=\"2\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><strong><span style=\"color: #0000ff;\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"1JE3n9dorwhE.1.4589111335714816.2\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"1JE3n9dorwhE.1.4589111335714816.2\">The cylinder has maximum volume amongst all cylinders which can be inscribed when\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u210e=\ufffd3<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">h<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.872331em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55101em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord sqrt mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.912845em;\"><span class=\"svg-align\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; text-align: left; display: block; height: 0px; position: relative; top: -3em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px 0px 0px 0.833em; border-color: currentcolor; display: inline-block;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.394em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px 0.00773em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">R<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><\/span><\/strong><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><p><input id=\"1JE3n9dorwhE.1.4589111335714816.3\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"1JE3n9dorwhE.1.4589111335714816\" type=\"checkbox\" data-index=\"3\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"1JE3n9dorwhE.1.4589111335714816.3\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"1JE3n9dorwhE.1.4589111335714816.3\">The cylinder has maximum surface area of its curved surface, amongst all cylinders which can be inscribed, when\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u210e=2\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">h<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.00773em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">R<\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><p><input id=\"1JE3n9dorwhE.1.4589111335714816.4\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"1JE3n9dorwhE.1.4589111335714816\" type=\"checkbox\" data-index=\"4\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><span style=\"color: #0000ff;\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"1JE3n9dorwhE.1.4589111335714816.4\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"1JE3n9dorwhE.1.4589111335714816.4\">The cylinder has maximum surface area of its curved surface, amongst all cylinders which can be inscribed, when\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u210e=\ufffd2<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">h<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.872331em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55101em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord sqrt mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.912845em;\"><span class=\"svg-align\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; text-align: left; display: block; height: 0px; position: relative; top: -3em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px 0px 0px 0.833em; border-color: currentcolor; display: inline-block;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.394em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px 0.00773em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">R<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><\/span><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><p><input id=\"1JE3n9dorwhE.1.4589111335714816.5\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"1JE3n9dorwhE.1.4589111335714816\" type=\"checkbox\" data-index=\"5\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"1JE3n9dorwhE.1.4589111335714816.5\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"1JE3n9dorwhE.1.4589111335714816.5\">The cylinder has maximum surface area of its curved surface, amongst all cylinders which can be inscribed, when\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u210e=2<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">h<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord sqrt\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.90722em;\"><span class=\"svg-align\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px 0px 0px 0.833em; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"1JE3n9dorwhE.2.5340182660251648\" class=\"qt-mc-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1000 point<\/em><\/div><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p>3. Which of the curves in the following figures enclose a negative area on the\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">X<\/span><\/span><\/span><\/span><\/span>\u00a0axis in the interval\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">[0,1]<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">[<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">]<\/span><\/span><\/span><\/span><\/span>?<br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/><img decoding=\"async\" class=\"yui-img\" style=\"margin: 0px; padding: 0px; vertical-align: middle;\" title=\"\" src=\"https:\/\/backend.seek.onlinedegree.iitm.ac.in\/21t3_ma1003\/assets\/img\/T3W3GA-3.jpg\" alt=\"\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"qt-choices\" style=\"margin: 16px 0px 0px; padding: 0px;\"><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"1JE3n9dorwhE.2.5340182660251648.0\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"1JE3n9dorwhE.2.5340182660251648\" type=\"checkbox\" data-index=\"0\" \/><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"1JE3n9dorwhE.2.5340182660251648.0\">Curve 1<\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"1JE3n9dorwhE.2.5340182660251648.1\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"1JE3n9dorwhE.2.5340182660251648\" type=\"checkbox\" data-index=\"1\" \/><span style=\"color: #0000ff;\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"1JE3n9dorwhE.2.5340182660251648.1\">Curve 2<\/label><\/span><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"1JE3n9dorwhE.2.5340182660251648.2\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"1JE3n9dorwhE.2.5340182660251648\" type=\"checkbox\" data-index=\"2\" \/><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"1JE3n9dorwhE.2.5340182660251648.2\">Curve 3<\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"1JE3n9dorwhE.2.5340182660251648.3\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"1JE3n9dorwhE.2.5340182660251648\" type=\"checkbox\" data-index=\"3\" \/><span style=\"color: #0000ff;\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"1JE3n9dorwhE.2.5340182660251648.3\">Curve 4<\/label><\/span><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><div style=\"margin: 0px; padding: 0px;\"><div id=\"uYy82i2rA1vt\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\"><p>Suppose\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd1(\ufffd)=\ufffd3<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.10764em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0and\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd2(\ufffd)=\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.10764em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><\/span><\/span><\/span><\/span>\u00a0denote the profits of Company A and Company B, respectively, throughout 1 year (the beginning of the year is denoted by\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=0<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><\/span><\/span>\u00a0and the ending denoted by\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=1<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span>). The predicted profits of Company A and Company B in the same year are given by the functions\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd1(\ufffd)=\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">g<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.03588em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord sqrt\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.80028em;\"><span class=\"svg-align\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px 0px 0px 0.833em; border-color: currentcolor; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0and\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd2(\ufffd)=\ufffd\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">g<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.03588em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">e<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.664392em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, respectively. The curves represented by the functions\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd1<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.10764em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0and\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd1<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">g<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.03588em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0are shown in Figure M2W3G2, and the curves represented by the functions\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd2<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.10764em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0and\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd2<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">g<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.03588em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0are shown in Figure M2W3G3.\u00a0<img decoding=\"async\" class=\"yui-img\" style=\"margin: 0px; padding: 0px; vertical-align: middle; width: 450px; height: 300px;\" src=\"https:\/\/backend.seek.onlinedegree.iitm.ac.in\/22t2_ma1001\/assets\/img\/paw9.png?seed=50233&amp;url=assets\/img\/paw9.png\" \/><br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">Suppose the area of the region bounded by the two curves (the original curve and the predicted curve) in the interval\u00a0\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">[0,1]<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">[<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">]<\/span><\/span><\/span><\/span><\/span>is defined to be the error in prediction.<\/div><div style=\"margin: 0px; padding: 0px;\">\u00a0Using the information above, answer the following questions.<\/div><\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"uYy82i2rA1vt.0.6201109156724736\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p>4. What will the absolute difference between the minimum values of\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd2<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.10764em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0and\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd2<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">g<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.03588em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0in the interval\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">[0,1]<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">[<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">]<\/span><\/span><\/span><\/span><\/span>\u00a0be?<\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header faculty-answer\">Accepted Answers:<\/h3><div class=\"faculty-answer\">(Type: Numeric) 1<\/div><div class=\"faculty-answer\">(Type: Numeric) -1<\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">167 point<\/em><\/div><\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"uYy82i2rA1vt.1.5564565576220672\" class=\"qt-mc-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1866 point<\/em><\/div><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\">5. Choose the correct options from the following.<\/div><div class=\"qt-choices\" style=\"margin: 16px 0px 0px; padding: 0px;\"><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><p><span style=\"color: #0000ff;\"><input id=\"uYy82i2rA1vt.1.5564565576220672.0\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"uYy82i2rA1vt.1.5564565576220672\" type=\"checkbox\" data-index=\"0\" \/><\/span><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><span style=\"color: #0000ff;\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"uYy82i2rA1vt.1.5564565576220672.0\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"uYy82i2rA1vt.1.5564565576220672.0\">The error in prediction for company A is\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">512<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.845108em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.655em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">12<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.394em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><\/span><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><p><input id=\"uYy82i2rA1vt.1.5564565576220672.1\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"uYy82i2rA1vt.1.5564565576220672\" type=\"checkbox\" data-index=\"1\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"uYy82i2rA1vt.1.5564565576220672.1\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"uYy82i2rA1vt.1.5564565576220672.1\">The error in prediction for company A is\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">1112<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.845108em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.655em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">12<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.394em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">11<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"uYy82i2rA1vt.1.5564565576220672.2\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"uYy82i2rA1vt.1.5564565576220672\" type=\"checkbox\" data-index=\"2\" \/><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"uYy82i2rA1vt.1.5564565576220672.2\">The error in prediction for company A is more than that for company B.<\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"uYy82i2rA1vt.1.5564565576220672.3\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"uYy82i2rA1vt.1.5564565576220672\" type=\"checkbox\" data-index=\"3\" \/><span style=\"color: #0000ff;\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"uYy82i2rA1vt.1.5564565576220672.3\">The error in prediction for company B is more than that for company A.<\/label><\/span><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"uYy82i2rA1vt.1.5564565576220672.4\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"uYy82i2rA1vt.1.5564565576220672\" type=\"checkbox\" data-index=\"4\" \/><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"uYy82i2rA1vt.1.5564565576220672.4\">The error in prediction for Company A and Company B, cannot be compared using the given information.<\/label><\/div><div><h3 class=\"feedback-header faculty-answer\">Accepted Answers:<\/h3><div class=\"faculty-answer\"><div><div><div>\u00a0<\/div><label for=\"uYy82i2rA1vt.1.5564565576220672.0\"><label for=\"uYy82i2rA1vt.1.5564565576220672.0\">The error in prediction for company A is\u00a0<span class=\"inline-equation\"><span class=\"katex\"><span class=\"katex-mathml\">512<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">12<\/span><\/span><\/span><span class=\"\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">5<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><div>\u00a0<\/div><\/div><div><label for=\"uYy82i2rA1vt.1.5564565576220672.3\">The error in prediction for company B is more than that for company A.<\/label><\/div><\/div><\/div><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><div style=\"margin: 0px; padding: 0px;\"><div id=\"3eYsCS0vtrDl\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\">\u00a0<\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"3eYsCS0vtrDl.0.6206747744141312\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p>6. Let\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)=\ufffd3\u22123\ufffd+11<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">11<\/span><\/span><\/span><\/span><\/span>. What is the local minimum value of\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><\/span><\/span><\/span><\/span>\u00a0attained at a critical point?<\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header faculty-answer\">Accepted Answers:<\/h3><div class=\"faculty-answer\">(Type: Numeric) 9<\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1999 point<\/em><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><div style=\"margin: 0px; padding: 0px;\"><div id=\"OjS2otVlLAyC\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\">\u00a0<\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"OjS2otVlLAyC.0.6629804916867072\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p>7. Let\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)=38\ufffd2+406<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">38<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.845108em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.655em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">6<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.394em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">40<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">0\u2264\ufffd\u22646<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2264<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2264<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">6<\/span><\/span><\/span><\/span><\/span>. The estimated area obtained by dividing the interval into 3 sub-intervals of equal length and the left end points of the sub-intervals for height of the rectangles is (in square units)<\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header faculty-answer\">Accepted Answers:<\/h3><div class=\"faculty-answer\"><span style=\"color: #0000ff;\">(Type: Numeric) 1560<\/span><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">199 point<\/em><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><div style=\"margin: 0px; padding: 0px;\"><div id=\"CcQcHvo5EGBH\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\">\u00a0<\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"CcQcHvo5EGBH.0.6492319448563712\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p>Let<br style=\"margin: 0px; padding: 0px;\" \/><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)={\u22122\ufffd+90\u2264\ufffd\u226410\ufffd210&lt;\ufffd\u226420<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"minner\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen delimcenter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; top: 0em;\"><span class=\"delimsizing size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">{<\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mtable\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"col-align-l\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.69em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.69em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">9<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.25em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-l\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.69em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.69em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2264<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2264<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">10<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.25em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">10<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">&lt;<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2264<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">20<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/>8. What is the global minimum of\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><\/span><\/span><\/span><\/span>\u00a0on\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">[0,20]<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">[<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">20<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">]<\/span><\/span><\/span><\/span><\/span><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header faculty-answer\">Accepted Answers:<\/h3><div class=\"faculty-answer\"><span style=\"color: #0000ff;\">(Type: Numeric) -11<\/span><\/div><div class=\"faculty-answer\"><span style=\"color: #0000ff;\">(Type: Numeric) 10<\/span><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><div style=\"margin: 0px; padding: 0px;\"><div id=\"d0DEhCLWG8lM\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\">\u00a0<\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"d0DEhCLWG8lM.0.4661414895550464\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p>9. If\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd\u2212\ufffd=10<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">y<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">10<\/span><\/span><\/span><\/span><\/span>, find the least value of\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">2\ufffd\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">y<\/span><\/span><\/span><\/span><\/span>.<\/p><\/div><div style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header faculty-answer\">Accepted Answers:<\/h3><div class=\"faculty-answer\"><span style=\"color: #0000ff;\">(Type: Numeric) -50<\/span><\/div><\/div><div>\u00a0<\/div><\/div><\/div><\/div><\/div>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-89b1ba4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"89b1ba4\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-e62f612\" data-id=\"e62f612\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-0e0d71b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0e0d71b\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-f159b79\" data-id=\"f159b79\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-569207d elementor-button-success elementor-align-center elementor-widget elementor-widget-button\" data-id=\"569207d\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-lg\" href=\"https:\/\/drive.google.com\/drive\/folders\/15whlEXcbyshK1UjEZ3Uvdqt4tUa8YTXe?usp=sharing\" id=\"1\" target=\"_blank\" rel=\"noopener\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-icon elementor-align-icon-left\">\n\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-file-pdf\"><\/i>\t\t\t<\/span>\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Access Here <\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5070f86 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5070f86\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-bdbaa9b\" data-id=\"bdbaa9b\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-66 elementor-top-column elementor-element elementor-element-17d47bf\" data-id=\"17d47bf\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Maths week 9 graded assignment Complete\u00a0 Questions Discussed In This Blog We Hope This Might Help You All In Matching Answers . Or For Some Others Reasons Not Able To Complete Graded Assignments &#8211; Best Of Luck \u00a0Check Below For Answers Link 1. Match the functions in Column A with the corresponding (signed) area between&hellip;&nbsp;<a href=\"https:\/\/iitmadrasstudentscommunity.me\/maths-week-9-graded-assignments-iit-madras\/\" class=\"\" rel=\"bookmark\">Read More &raquo;<span class=\"screen-reader-text\">Maths Week 9 Graded Assignments IIT Madras<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":746,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"page-templates\/template-pagebuilder-full-width.php","meta":{"neve_meta_sidebar":"","neve_meta_container":"","neve_meta_enable_content_width":"","neve_meta_content_width":0,"neve_meta_title_alignment":"","neve_meta_author_avatar":"","neve_post_elements_order":"","neve_meta_disable_header":"","neve_meta_disable_footer":"","neve_meta_disable_title":"","neve_meta_reading_time":"","_themeisle_gutenberg_block_has_review":false,"_ti_tpc_template_sync":false,"_ti_tpc_template_id":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/pages\/666"}],"collection":[{"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/comments?post=666"}],"version-history":[{"count":17,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/pages\/666\/revisions"}],"predecessor-version":[{"id":942,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/pages\/666\/revisions\/942"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/media\/746"}],"wp:attachment":[{"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/media?parent=666"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}