{"id":724,"date":"2023-08-12T09:46:00","date_gmt":"2023-08-12T04:16:00","guid":{"rendered":"https:\/\/iitmadrasstudentscommunity.me\/?p=724"},"modified":"2023-08-15T18:57:48","modified_gmt":"2023-08-15T13:27:48","slug":"maths-week-10-graded-assignments-iit-madras","status":"publish","type":"post","link":"https:\/\/iitmadrasstudentscommunity.me\/maths-week-10-graded-assignments-iit-madras\/","title":{"rendered":"Maths Week 10 Graded Assignments IIT Madras"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"724\" class=\"elementor elementor-724\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-db24a6d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"db24a6d\" 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-072577e\" data-id=\"072577e\" 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-c7aa179 elementor-widget elementor-widget-text-editor\" data-id=\"c7aa179\" 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<section data-id=\"dd3c6c2\" data-element_type=\"section\"><div><div data-id=\"72baf95\" data-element_type=\"column\"><div><div data-id=\"483fb8f\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\"><div><div style=\"--listpad: 20px; --liststyle: disc; --img-m: 24px; margin-bottom: var(--spacing,60px);\"><div data-elementor-type=\"wp-post\" data-elementor-id=\"524\" data-elementor-post-type=\"post\"><section style=\"flex-basis: var(--flex-basis); flex-grow: var(--flex-grow); flex-shrink: var(--flex-shrink); order: var(--order); align-self: var(--align-self); --swiper-theme-color: #000; --swiper-navigation-size: 44px; --swiper-pagination-bullet-size: 6px; --swiper-pagination-bullet-horizontal-gap: 6px; --widgets-spacing: 20px;\" data-id=\"de0c62f\" data-element_type=\"section\"><div style=\"flex-basis: var(--flex-basis); flex-grow: var(--flex-grow); flex-shrink: var(--flex-shrink); order: var(--order); align-self: var(--align-self); --swiper-theme-color: #000; --swiper-navigation-size: 44px; --swiper-pagination-bullet-size: 6px; --swiper-pagination-bullet-horizontal-gap: 6px; --widgets-spacing: 20px; width: 768px;\" data-id=\"4625911\" data-element_type=\"column\"><div style=\"width: 768px;\"><div style=\"--listpad: 15px; --liststyle: disc; --flex-direction: initial; --flex-wrap: initial; --justify-content: initial; --align-items: initial; --align-content: initial; --gap: initial; --flex-basis: initial; --flex-grow: initial; --flex-shrink: initial; --order: initial; --align-self: initial; flex-basis: var(--flex-basis); flex-grow: var(--flex-grow); flex-shrink: var(--flex-shrink); order: var(--order); align-self: var(--align-self); flex-direction: var(--flex-direction); flex-wrap: var(--flex-wrap); justify-content: var(--justify-content); align-items: var(--align-items); align-content: var(--align-content); gap: var(--gap); --swiper-theme-color: #000; --swiper-navigation-size: 44px; --swiper-pagination-bullet-size: 6px; --swiper-pagination-bullet-horizontal-gap: 6px; --widgets-spacing: 20px; width: 748px;\" data-id=\"7ca92d2\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\"><div style=\"transition: background .3s,border .3s,border-radius .3s,box-shadow .3s,transform var(--e-transform-transition-duration,.4s);\"><h5><em style=\"font-family: 'Trebuchet MS', sans-serif;\">Maths week 10 graded assignment Complete\u00a0 Solutions Are 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\u00a0<\/em><\/h5><\/div><\/div><\/div><\/div><\/section><\/div><\/div><p>\u00a0<\/p><\/div><\/div><\/div><\/div><\/div><\/section>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2b3da86 elementor-widget elementor-widget-text-editor\" data-id=\"2b3da86\" 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; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><div id=\"4pXJX5AlMYj1\" 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; background-color: #ffffff; box-shadow: #e1e1e1 1px 1px 1px;\"><div id=\"4pXJX5AlMYj1.0.6384958964760576\" class=\"qt-mc-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><p>1.The maximum number of non-zero entries in an adjacency matrix of a simple graph having\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;\">n<\/span><\/span><\/span><\/span><\/span>\u00a0vertices can be<\/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=\"4pXJX5AlMYj1.0.6384958964760576.0\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"4pXJX5AlMYj1.0.6384958964760576\" type=\"checkbox\" data-index=\"0\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.0.6384958964760576.0\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.0.6384958964760576.0\"><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\" 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;\">n<\/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: 0.864108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.113em;\"><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><\/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=\"4pXJX5AlMYj1.0.6384958964760576.1\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"4pXJX5AlMYj1.0.6384958964760576\" type=\"checkbox\" data-index=\"1\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.0.6384958964760576.1\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.0.6384958964760576.1\"><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\u22121)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\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><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: 1.427em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.314em;\"><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;\">2<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.677em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; 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;\">n<\/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;\">n<\/span><span class=\"mbin\" 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=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/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;\"><p><input id=\"4pXJX5AlMYj1.0.6384958964760576.2\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"4pXJX5AlMYj1.0.6384958964760576\" type=\"checkbox\" data-index=\"2\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.0.6384958964760576.2\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.0.6384958964760576.2\"><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\u22121)4<\/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\" 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: 1.427em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.314em;\"><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;\">4<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.677em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; 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;\">n<\/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;\">n<\/span><span class=\"mbin\" 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=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/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;\"><p><input id=\"4pXJX5AlMYj1.0.6384958964760576.3\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"4pXJX5AlMYj1.0.6384958964760576\" type=\"checkbox\" data-index=\"3\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.0.6384958964760576.3\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.0.6384958964760576.3\"><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\u22121)<\/span><strong><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; color: #0000ff;\" 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; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">n<\/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;\">n<\/span><span class=\"mbin\" 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=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/strong><\/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; background-color: #ffffff; 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=\"4pXJX5AlMYj1.1.5755643176681472\" 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;\">1 point<\/em><\/div><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p>2.We have a graph\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;\">G<\/span><\/span><\/span><\/span><\/span>\u00a0with 6 vertices. We write down the degrees of all vertices in\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;\">G<\/span><\/span><\/span><\/span><\/span>\u00a0in descending order. Which of the following is a possible listing of the degrees?<\/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=\"4pXJX5AlMYj1.1.5755643176681472.0\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"4pXJX5AlMYj1.1.5755643176681472\" type=\"checkbox\" data-index=\"0\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.1.5755643176681472.0\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.1.5755643176681472.0\"><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;\">6,5,4,3,2,1<\/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\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">6<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">4<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/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><\/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=\"4pXJX5AlMYj1.1.5755643176681472.1\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"4pXJX5AlMYj1.1.5755643176681472\" type=\"checkbox\" data-index=\"1\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.1.5755643176681472.1\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.1.5755643176681472.1\"><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;\">5,5,2,2,1,1<\/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\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/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=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/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=\"4pXJX5AlMYj1.1.5755643176681472.2\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"4pXJX5AlMYj1.1.5755643176681472\" type=\"checkbox\" data-index=\"2\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.1.5755643176681472.2\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.1.5755643176681472.2\"><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;\">5,3,3,2,2,1<\/span><strong><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; color: #0000ff;\" 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;\">5<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/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><\/span><\/strong><\/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=\"4pXJX5AlMYj1.1.5755643176681472.3\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"4pXJX5AlMYj1.1.5755643176681472\" type=\"checkbox\" data-index=\"3\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.1.5755643176681472.3\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.1.5755643176681472.3\"><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;\">2,1,1,1,1,1<\/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\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/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=\"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=\"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=\"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=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/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; background-color: #ffffff; 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=\"4pXJX5AlMYj1.2.6705231815507968\" 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;\">1 point<\/em><\/div><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\">3.We are trying to find the correct path in a maze. We start at the entrance. At some points, we have to choose a direction to explore. If we reach a dead end, we come back to the most recent intersection where we still have an unexplored direction to investigate. What is a good data structure to keep track of the intersections we have visited?<\/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=\"4pXJX5AlMYj1.2.6705231815507968.0\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"4pXJX5AlMYj1.2.6705231815507968\" type=\"checkbox\" data-index=\"0\" \/><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.2.6705231815507968.0\">List<\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"4pXJX5AlMYj1.2.6705231815507968.1\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"4pXJX5AlMYj1.2.6705231815507968\" type=\"checkbox\" data-index=\"1\" \/><span style=\"color: #0000ff;\"><strong><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.2.6705231815507968.1\">Stack<\/label><\/strong><\/span><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"4pXJX5AlMYj1.2.6705231815507968.2\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"4pXJX5AlMYj1.2.6705231815507968\" type=\"checkbox\" data-index=\"2\" \/><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.2.6705231815507968.2\">Queue<\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"4pXJX5AlMYj1.2.6705231815507968.3\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"4pXJX5AlMYj1.2.6705231815507968\" type=\"checkbox\" data-index=\"3\" \/><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.2.6705231815507968.3\">Array<\/label><\/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; background-color: #ffffff; 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=\"4pXJX5AlMYj1.3.6175479811801088\" 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;\">1 point<\/em><\/div><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p>4.Suppose we obtain the following BFS tree rooted at node 1 for an undirected graph with vertices\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;\">(1,2,3,4,5,&#8230;..14).<\/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;\">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;\">2<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">4<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">&#8230;..14<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mord\" 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 auto; padding: 0px; vertical-align: middle; display: block;\" title=\"\" src=\"https:\/\/backend.seek.onlinedegree.iitm.ac.in\/21t1_ma1001\/assets\/img\/GA5.png\" alt=\"\" \/><br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/>Which of the following cannot be an edge in the original graph?<\/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=\"4pXJX5AlMYj1.3.6175479811801088.0\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"4pXJX5AlMYj1.3.6175479811801088\" type=\"checkbox\" data-index=\"0\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.3.6175479811801088.0\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.3.6175479811801088.0\"><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;\">(8,11)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; color: #0000ff;\" 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;\">8<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">11<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/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=\"4pXJX5AlMYj1.3.6175479811801088.1\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"4pXJX5AlMYj1.3.6175479811801088\" type=\"checkbox\" data-index=\"1\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.3.6175479811801088.1\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.3.6175479811801088.1\"><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;\">(3,10)<\/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=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">10<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/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=\"4pXJX5AlMYj1.3.6175479811801088.2\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"4pXJX5AlMYj1.3.6175479811801088\" type=\"checkbox\" data-index=\"2\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.3.6175479811801088.2\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.3.6175479811801088.2\"><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;\">(4,5)<\/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;\">4<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/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=\"4pXJX5AlMYj1.3.6175479811801088.3\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"4pXJX5AlMYj1.3.6175479811801088\" type=\"checkbox\" data-index=\"3\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.3.6175479811801088.3\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"4pXJX5AlMYj1.3.6175479811801088.3\"><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;\">(6,9)<\/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;\">6<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">9<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/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=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><p><br style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\" \/><span style=\"margin: 0px; padding: 0px; font-weight: bolder; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><br style=\"margin: 0px; padding: 0px;\" \/>2 MUTIPLE SELECT QUESTIONS:<br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/><\/span><\/p><div style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><div id=\"y6dKInwdK32q\" 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; background-color: #ffffff; 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=\"y6dKInwdK32q.0.5353876366557184\" 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;\">1 point<\/em><\/div><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p>Which of the following graphs satisfies the below properties:<br style=\"margin: 0px; padding: 0px;\" \/>\u00a0 \u00a01.\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;\">\u2223\ufffd\ufffd(\ufffd)\u2223<\/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;\">\u2223<\/span><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=\"mord mathnormal\" style=\"margin: 0px 0.07153em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">C<\/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;\">G<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2223<\/span><\/span><\/span><\/span><\/span>\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;\">3<\/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;\">3<\/span><\/span><\/span><\/span><\/span>, where\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(\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 0.22222em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">V<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.07153em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">C<\/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;\">G<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0is the minimum vertex cover of a graph\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;\">G<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">.<\/span><\/span><\/span><\/span><\/span><br style=\"margin: 0px; padding: 0px;\" \/>\u00a0 \u00a02.\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;\">\u2223\ufffd\ufffd(\ufffd)\u2223<\/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;\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.10903em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">PM<\/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;\">G<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2223<\/span><\/span><\/span><\/span><\/span>\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;\">3<\/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;\">3<\/span><\/span><\/span><\/span><\/span>, where\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(\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 0.10903em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">PM<\/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;\">G<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0is the perfect matching of a graph\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;\">G<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">.<\/span><\/span><\/span><\/span><\/span><br style=\"margin: 0px; padding: 0px;\" \/>\u00a0 \u00a03. The graph is a 3-colouring.<\/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=\"y6dKInwdK32q.0.5353876366557184.0\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"y6dKInwdK32q.0.5353876366557184\" type=\"checkbox\" data-index=\"0\" \/><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"y6dKInwdK32q.0.5353876366557184.0\"><img decoding=\"async\" class=\"yui-img\" style=\"margin: 0px auto; padding: 0px; vertical-align: middle; display: block;\" title=\"\" src=\"https:\/\/backend.seek.onlinedegree.iitm.ac.in\/21t1_ma1001\/assets\/img\/6.1.png\" alt=\"\" \/><\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"y6dKInwdK32q.0.5353876366557184.1\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"y6dKInwdK32q.0.5353876366557184\" type=\"checkbox\" data-index=\"1\" \/><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"y6dKInwdK32q.0.5353876366557184.1\"><img decoding=\"async\" class=\"yui-img\" style=\"margin: 0px auto; padding: 0px; vertical-align: middle; display: block;\" title=\"\" src=\"https:\/\/backend.seek.onlinedegree.iitm.ac.in\/21t1_ma1001\/assets\/img\/6.2.png\" alt=\"\" \/><\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"y6dKInwdK32q.0.5353876366557184.2\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"y6dKInwdK32q.0.5353876366557184\" type=\"checkbox\" data-index=\"2\" \/><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"y6dKInwdK32q.0.5353876366557184.2\"><img decoding=\"async\" class=\"yui-img\" style=\"margin: 0px auto; padding: 0px; vertical-align: middle; display: block;\" title=\"\" src=\"https:\/\/backend.seek.onlinedegree.iitm.ac.in\/21t1_ma1001\/assets\/img\/6.3.png\" alt=\"\" \/><strong><span style=\"color: #0000ff;\">CORRECT Answers c And D<\/span><\/strong><\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"y6dKInwdK32q.0.5353876366557184.3\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"y6dKInwdK32q.0.5353876366557184\" type=\"checkbox\" data-index=\"3\" \/><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"y6dKInwdK32q.0.5353876366557184.3\"><img decoding=\"async\" class=\"yui-img\" style=\"margin: 0px auto; padding: 0px; vertical-align: middle; display: block;\" title=\"\" src=\"https:\/\/backend.seek.onlinedegree.iitm.ac.in\/21t1_ma1001\/assets\/img\/6.4.png\" alt=\"\" \/><\/label><\/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; background-color: #ffffff; 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=\"y6dKInwdK32q.1.4633782418145280\" 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;\">1 point<\/em><\/div><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\">7.Which of the following statements is(are) true?<\/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=\"y6dKInwdK32q.1.4633782418145280.0\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"y6dKInwdK32q.1.4633782418145280\" type=\"checkbox\" data-index=\"0\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><span style=\"color: #0000ff;\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"y6dKInwdK32q.1.4633782418145280.0\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"y6dKInwdK32q.1.4633782418145280.0\">BFS can be used to identify the vertex which is at the farthest distance from\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 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">v<\/span><\/span><\/span><\/span><\/span>\u00a0in any graph, in terms of number of edges, where vertex\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 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">v<\/span><\/span><\/span><\/span><\/span>\u00a0is the starting vertex.<\/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=\"y6dKInwdK32q.1.4633782418145280.1\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"y6dKInwdK32q.1.4633782418145280\" type=\"checkbox\" data-index=\"1\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><span style=\"color: #0000ff;\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"y6dKInwdK32q.1.4633782418145280.1\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"y6dKInwdK32q.1.4633782418145280.1\">BFS and DFS identifies all the vertices reachable from the starting vertex\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 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">v<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">.<\/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;\"><input id=\"y6dKInwdK32q.1.4633782418145280.2\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"y6dKInwdK32q.1.4633782418145280\" type=\"checkbox\" data-index=\"2\" \/><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"y6dKInwdK32q.1.4633782418145280.2\">BFS cannot be used to check for cycles in the graph while DFS can be used to check for cycles in the graph.<\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><p><input id=\"y6dKInwdK32q.1.4633782418145280.3\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"y6dKInwdK32q.1.4633782418145280\" type=\"checkbox\" data-index=\"3\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"y6dKInwdK32q.1.4633782418145280.3\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"y6dKInwdK32q.1.4633782418145280.3\">DFS can be used to identify the shortest distance from starting vertex\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 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">v<\/span><\/span><\/span><\/span><\/span>\u00a0to every other vertex in the graph, in terms of number of edges.<\/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=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><p><br style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\" \/><span style=\"margin: 0px; padding: 0px; font-weight: bolder; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><br style=\"margin: 0px; padding: 0px;\" \/>3 NUMERICAL ANSWER TYPE:<br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/><\/span><\/p><div style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><div id=\"6upSbJkIcr5M\" 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; background-color: #ffffff; 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=\"6upSbJkIcr5M.0.6309872400334848\" 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>If A =\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;\">[0101000101101001000001100111000100001010000001000]<\/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=\"minner\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"delimsizing mult\" 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: 4.45006em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.51104em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a3<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -10.1111em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a1<\/span><\/span><\/span><\/span><\/span><\/span><\/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-c\" 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; text-align: center;\"><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: 4.45em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -6.61em;\"><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><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -5.41em;\"><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;\">1<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -4.21em;\"><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><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.01em;\"><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;\">1<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -1.81em;\"><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><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -0.61em;\"><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><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: 0.59em;\"><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><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-c\" 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; text-align: center;\"><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: 4.45em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -6.61em;\"><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;\">1<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -5.41em;\"><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><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -4.21em;\"><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;\">1<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.01em;\"><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;\">1<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -1.81em;\"><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><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -0.61em;\"><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;\">1<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: 0.59em;\"><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><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-c\" 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; text-align: center;\"><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: 4.45em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -6.61em;\"><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><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -5.41em;\"><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;\">1<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -4.21em;\"><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><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.01em;\"><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><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -1.81em;\"><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><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -0.61em;\"><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><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: 0.59em;\"><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><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-c\" 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; text-align: center;\"><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: 4.45em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -6.61em;\"><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;\">1<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -5.41em;\"><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;\">1<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -4.21em;\"><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><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.01em;\"><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><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -1.81em;\"><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;\">1<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -0.61em;\"><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;\">1<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: 0.59em;\"><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;\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-c\" 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; text-align: center;\"><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: 4.45em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -6.61em;\"><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><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -5.41em;\"><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><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -4.21em;\"><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><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.01em;\"><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;\">1<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -1.81em;\"><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><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -0.61em;\"><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><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: 0.59em;\"><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><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-c\" 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; text-align: center;\"><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: 4.45em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -6.61em;\"><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><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -5.41em;\"><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;\">1<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -4.21em;\"><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><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.01em;\"><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;\">1<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -1.81em;\"><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><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -0.61em;\"><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><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: 0.59em;\"><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><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-c\" 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; text-align: center;\"><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: 4.45em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -6.61em;\"><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><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -5.41em;\"><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><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -4.21em;\"><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><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.01em;\"><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;\">1<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -1.81em;\"><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><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -0.61em;\"><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><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: 0.59em;\"><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><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"delimsizing mult\" 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: 4.45006em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.51104em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a6<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -10.1111em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0represents adjacency matrix of a graph\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;\">G<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><\/span><\/span><\/span><\/span>\u00a0then the cardinality of the maximum independent set of the graph\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;\">G<\/span><\/span><\/span><\/span><\/span>\u00a0is<\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\">Answers = <span style=\"color: #0000ff;\">5<\/span><\/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=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; background-color: #ffffff; 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=\"6upSbJkIcr5M.1.6491979013685248\" 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>A company manufactures\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;\">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\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">10<\/span><\/span><\/span><\/span><\/span>\u00a0chemicals\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,\ufffd2,\ufffd3,&#8230;.\ufffd10.<\/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; 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 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 0em; 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=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/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 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 0em; 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=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/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 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 0em; 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;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">&#8230;.<\/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 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 0em; 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;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">10<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">.<\/span><\/span><\/span><\/span><\/span>\u00a0Certain pairs of these chemicals are incompatible and would cause explosions if brought into contact with each other. Below graph shows the incompatibility of the chemicals, each vertex represents the chemical and each edge between a pair of chemicals represents that those two chemicals are incompatible. As a precautionary measure the company wishes to partition its warehouse into compartments, and store incompatible chemicals in different compartments. What is the least number of compartments into which the warehouse should be partitioned?<br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/><img decoding=\"async\" style=\"margin: 0px auto; padding: 0px; vertical-align: middle; display: block; width: 505.675px;\" title=\"Graph\" src=\"https:\/\/backend.seek.onlinedegree.iitm.ac.in\/21t1_ma1001\/assets\/img\/9.png\" alt=\"\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\">Answer =<strong><span style=\"color: #0000ff;\"> 3<\/span><\/strong><\/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=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; background-color: #ffffff; 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=\"6upSbJkIcr5M.2.6476694458204160\" 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>10. An incomplete undirected graph is given below and the numbering on each vertex denotes the colouring of the graph(&#8216;<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;\">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\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span>&#8216; denotes color 1, \u2018<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<\/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><\/span><\/span><\/span>\u2019 denotes color\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<\/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><\/span><\/span><\/span>, and \u2018<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;\">3<\/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;\">3<\/span><\/span><\/span><\/span><\/span>\u2019 denotes color\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;\">3<\/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;\">3<\/span><\/span><\/span><\/span><\/span>). Find the number of maximum edges that can be added to the given graph such that the colouring is retained and the graph is planar.<br style=\"margin: 0px; padding: 0px;\" \/>NOTE: Planar graph is a graph that can be drawn on the plane in such a way that its edges intersect only at their endpoints.<br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/><img decoding=\"async\" style=\"margin: 0px auto; padding: 0px; vertical-align: middle; display: block;\" title=\"Graph\" src=\"https:\/\/backend.seek.onlinedegree.iitm.ac.in\/21t1_ma1001\/assets\/img\/10.png\" alt=\"\" \/><\/p><\/div><div>Answer &#8211;<strong><span style=\"color: #0000ff;\">6<\/span><\/strong><\/div><\/div><\/div><\/div><\/div>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-b92fd3f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b92fd3f\" 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-50 elementor-inner-column elementor-element elementor-element-10e646b\" data-id=\"10e646b\" 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-d32db6b elementor-button-success elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"d32db6b\" 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-sm\" href=\"https:\/\/drive.google.com\/drive\/folders\/1rWIcg0qVaEUPoR5YSXr19EftGhLJPWfZ?usp=drive_link\" 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-text\">Complete PDF Solutions <\/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<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-84dcefa\" data-id=\"84dcefa\" 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-a068614 elementor-button-info elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"a068614\" 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-sm\" href=\"https:\/\/www.youtube.com\/watch?v=k_RpRO0rRgU&#038;ab_channel=IITMadrasStudentsCommunity\" 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-text\">Complete Video Solutions<\/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\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-1dd7fba elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1dd7fba\" 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-d8ab325\" data-id=\"d8ab325\" 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\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 10 graded assignment Complete\u00a0 Solutions Are 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\u00a0 \u00a0 1.The maximum number of non-zero entries in an adjacency matrix of a simple graph having\u00a0\ufffdn\u00a0vertices can be \u00a0 \u00a0 \ufffd2n2&hellip;&nbsp;<a href=\"https:\/\/iitmadrasstudentscommunity.me\/maths-week-10-graded-assignments-iit-madras\/\" class=\"\" rel=\"bookmark\">Read More &raquo;<span class=\"screen-reader-text\">Maths Week 10 Graded Assignments IIT Madras<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":779,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","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":""},"categories":[10,1],"tags":[56,78,69,21],"_links":{"self":[{"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/posts\/724"}],"collection":[{"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/types\/post"}],"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=724"}],"version-history":[{"count":17,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/posts\/724\/revisions"}],"predecessor-version":[{"id":1191,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/posts\/724\/revisions\/1191"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/media\/779"}],"wp:attachment":[{"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/media?parent=724"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/categories?post=724"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/tags?post=724"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}