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		<title>IIT Madras Online Degree</title>
		<link>/iit-madras-online-degree/</link>
					<comments>/iit-madras-online-degree/#respond</comments>
		
		<dc:creator><![CDATA[KHUSHI]]></dc:creator>
		<pubDate>Sun, 27 Aug 2023 03:48:28 +0000</pubDate>
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					<description><![CDATA[Joining IIT Madras Online Degree Program: A Comprehensive Guide   IIT Madras offers a transformative opportunity through its online degree programs, designed for both current Class 12 students and graduates, without any age restrictions. This guide presents a step-by-step process to join the program via the official website. Here&#8217;s why you should consider this incredible&#8230;&#160;<a href="/iit-madras-online-degree/" class="" rel="bookmark">Read More &#187;<span class="screen-reader-text">IIT Madras Online Degree</span></a>]]></description>
										<content:encoded><![CDATA[		<div data-elementor-type="wp-post" data-elementor-id="1522" class="elementor elementor-1522" data-elementor-post-type="post">
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								<div class="elementor-element elementor-element-05e6a8f elementor-widget elementor-widget-text-editor" data-id="05e6a8f" data-element_type="widget" data-widget_type="text-editor.default">
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.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>				<p><strong>Joining IIT Madras Online Degree Program: A Comprehensive Guide</strong></p><p> </p><p>IIT Madras offers a transformative opportunity through its online degree programs, designed for both current Class 12 students and graduates, without any age restrictions. This guide presents a step-by-step process to join the program via the official website. Here&#8217;s why you should consider this incredible opportunity:</p><p> </p><p><strong>1. Eligibility and Multiple Reattempts:</strong></p><p>Whether you&#8217;re a Class 12 student or a graduate, there&#8217;s no age limit to join IIT Madras&#8217; online degree program. The entry barrier is set at a minimum of 40% marks in each of the four subjects: Mathematics, Computer Technology (CT), Statistics, and English. In IIT Madras Own Qualifier Exam .Furthermore, the program allows for multiple reattempts, ensuring you have ample opportunities to succeed. <strong>Through JEE You Can Take Direct Entry</strong></p><p> </p><p><strong>2. Affordable Fees:</strong></p><p>The first year of the program comes at an exceptionally low cost – just 4000 per course. This affordability opens doors for aspiring learners from all walks of life to access a prestigious education from one of India&#8217;s top institutions.</p><p> </p><p><strong>3. Why Choose IIT Madras Online Degree :</strong></p><p>IIT Madras boasts the highest NIRF ranking, standing as a testament to its academic excellence and commitment to providing top-notch education. By enrolling in this online degree program, you align yourself with a prestigious institution known for producing top talents across various fields.</p><p> </p><p><strong>4. Quality Facilities and Instruction:</strong></p><p>Studying at IIT Madras means you&#8217;ll have access to world-class facilities and resources. All lectures are conducted in English, ensuring that language is not a barrier to your learning. The faculty consists of renowned experts who are passionate about imparting knowledge and guiding your academic journey.</p><p> </p><p><strong>5. Campus Visit and Paradox Event:</strong></p><p>Once a year, you have the exciting opportunity to visit the IIT Madras campus during the &#8220;Paradox&#8221; event – the largest student community gathering that spans 4-5 days. This event draws students from all over India, offering a vibrant platform to engage in various sports, functions, and innovative events like Hack-O-Pitch. It&#8217;s a chance to immerse yourself in the rich cultural and academic environment of IIT Madras.</p><p> </p><h3><strong>Step-by-Step Guide to Joining:</strong></h3><p> </p><p><strong>Step 1: Visit the Official Website:</strong></p><p>Start by accessing the official IIT Madras website. Navigate to the dedicated section for online degree programs.</p><p> </p><p><strong>Step 2: Explore Programs Like DS Or ES and Choose Your Path:</strong></p><p>Browse through the array of online degree programs offered. Each program has specific requirements and courses tailored to various disciplines. Choose the one that aligns with your academic and career aspirations.</p><p> </p><p><strong>Step 3: Verify Eligibility:</strong></p><p>Ensure you meet the eligibility criteria – Passed Or At Class 12</p><p> </p><p><strong>Step 4: Online Registration:</strong></p><p>Click on the provided registration link. Fill in accurate personal and educational information. Make sure to provide a valid email address for future communications.</p><p> </p><p><strong>Step 5: Document Submission:</strong></p><p>Upload clear, scanned copies of essential documents such as educational certificates, identity proof, and photographs.</p><p> </p><p><strong>Step 6: Fee Payment Basically This Step Occurs Before Documents Sumission :</strong></p><p>Pay the registration fee, which is kept affordable at 4000 per course for the first year. Payment options will be available online , And or Qualifiers Or Joining Fees 3000 For A Month .</p><p> </p><p><strong>Step 7: Select Your Courses:</strong></p><p>After confirming registration and fee payment, log in to your account. Choose the courses you wish to enroll in for the upcoming semester. Read course descriptions and prerequisites carefully.</p><p> </p><p><strong>Step 8: Access Learning Materials:</strong></p><p>Upon enrolling in courses, gain access to the online learning platform. Here, find lecture videos, assignments, resources, and announcements.</p><p> </p><p><strong>Step 9: Engage and Learn:</strong></p><p>Actively participate in courses, engage with course content, complete assignments, and interact with peers through online discussions.</p><p> </p><p><strong>Step 10: Reattempt for Success:</strong></p><p>If needed, utilize the option of multiple reattempts to improve your performance and understanding.</p><p> </p><p><strong>Conclusion:</strong></p><p><em>Enrolling in IIT Madras&#8217; online degree program is an opportunity that opens doors to a world of academic excellence, enriched learning, and valuable experiences. With the step-by-step guide provided here, you&#8217;re equipped to embark on a journey that combines flexibility, affordability, and top-notch education from India&#8217;s finest institution. Don&#8217;t miss out on the chance to be part of IIT Madras&#8217; legacy and to experience the campus&#8217;s vibrancy through the annual Paradox event. Your future awaits – take the first step today!</em></p>						</div>
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		<title>BS In Electronic System WhatsApp Group Link</title>
		<link>/bs-in-electronic-system-whatsapp-group-link/</link>
					<comments>/bs-in-electronic-system-whatsapp-group-link/#respond</comments>
		
		<dc:creator><![CDATA[KHUSHI]]></dc:creator>
		<pubDate>Sat, 26 Aug 2023 15:00:24 +0000</pubDate>
				<category><![CDATA[Uncategorized]]></category>
		<guid isPermaLink="false">/?p=1439</guid>

					<description><![CDATA[Join Subject-Wise  Bs In Electronic System IIT Madras : A Comprehensive Guide to Applying for IIT Madras ES Degree Online Introduction: The Electronic System  (ES) at IIT Madras opens doors to a world of knowledge and career advancement .Check Below Link To ensure you stay well-informed and connected throughout your application process, this guide introduces subject-wise&#8230;&#160;<a href="/bs-in-electronic-system-whatsapp-group-link/" class="" rel="bookmark">Read More &#187;<span class="screen-reader-text">BS In Electronic System WhatsApp Group Link</span></a>]]></description>
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							<p><strong>Join Subject-Wise  Bs In Electronic System IIT Madras </strong><strong style="background-color: var(--nv-site-bg); color: var(--nv-text-color); font-size: var(--bodyfontsize); letter-spacing: var(--bodyletterspacing); text-transform: var(--bodytexttransform);">: A Comprehensive Guide to Applying for IIT Madras ES Degree Online</strong></p><p><strong>Introduction:</strong></p><p>The Electronic System  (ES) at IIT Madras opens doors to a world of knowledge and career advancement .<strong>Check Below Link</strong> To ensure you stay well-informed and connected throughout your application process, this guide introduces subject-wise WhatsApp groups. These groups serve as platforms for sharing insights, clarifying doubts, and receiving support from like-minded individuals.</p><p>Joining the WhatsApp Groups Engaging with these groups is a straightforward process:</p><ol><li><p><strong>Visit the IIT Madras Students Community Page</strong>: Access the official IITM Students Community webpage to find the links to the subject-wise WhatsApp groups.</p></li><li><p><strong>Select a Group</strong>: Click on the link that corresponds to your academic background and interests.</p></li><li><p><strong>Join the Group</strong>: Upon clicking the link, you&#8217;ll be redirected to WhatsApp. Click &#8220;Join Group&#8221; to become a member.</p></li><li><p><strong>Introduce Yourself</strong>: Once in the group, introduce yourself briefly. Share a snapshot of your educational background and your motivation for pursuing the Online Electronic System Degree.</p></li></ol><p><strong>Step 4:</strong> Active Engagement and Contribution Actively participate in the group discussions. Pose questions, share your insights, and benefit from the collective wisdom of your fellow applicants. Remember, these groups provide a unique networking opportunity and a chance to gain diverse perspectives.</p><p><strong>Step 5:</strong> Application Process Insights While these WhatsApp groups are an invaluable resource for peer interaction, remember to cross-reference crucial application details from official IIT Madras sources, emails, and the application portal for the most accurate information.</p><p><strong>Step 6:</strong> Cultivating a Positive Environment Ensure that your contributions to the WhatsApp groups are constructive and respectful. Avoid excessive promotion or sharing unrelated content.</p><p><strong>Step 7</strong>: Doubt Resolution and Networking Leverage the WhatsApp groups to clarify doubts related to the application process or the Online Electronic System Degree program. Fellow group members and even program representatives might offer valuable insights.</p><p><em>Conclusion: Subject-wise WhatsApp groups established by the IITM Students Community are a fantastic way to connect with like-minded peers while pursuing the Online Electronic System Degree from IIT Madras. Active participation will broaden your knowledge, provide valuable insights, and offer the support you need throughout the application journey. Remember, these groups complement official communications and information from IIT Madras and should not replace official sources. Best of luck as you embark on your academic pursuit!</em></p>						</div>
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		<title>How To Apply For Bs In Electronic System IIT Madras</title>
		<link>/how-to-apply-for-bs-in-electronic-system-iit-madras/</link>
					<comments>/how-to-apply-for-bs-in-electronic-system-iit-madras/#respond</comments>
		
		<dc:creator><![CDATA[KHUSHI]]></dc:creator>
		<pubDate>Sat, 26 Aug 2023 14:33:13 +0000</pubDate>
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		<guid isPermaLink="false">/?p=1405</guid>

					<description><![CDATA[Hii In This Blog Full Steps Are Given How To Apply For Electronic System At IIT Madras 2023 From Registration Form. If Having Problem To Understand Below Full Video Is Also Given  Title: A Step-by-Step Guide to Applying for IIT Madras Executive Master&#8217;s in ES Degree Online Introduction:Pursuing higher education is a significant milestone in&#8230;&#160;<a href="/how-to-apply-for-bs-in-electronic-system-iit-madras/" class="" rel="bookmark">Read More &#187;<span class="screen-reader-text">How To Apply For Bs In Electronic System IIT Madras</span></a>]]></description>
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							<p>Hii In This Blog Full Steps Are Given <strong>How To Apply For Electronic System At IIT Madras 2023</strong> From Registration Form. If Having Problem To Understand Below Full Video Is Also Given </p><p><strong>Title: A Step-by-Step Guide to Applying for IIT Madras Executive Master&#8217;s in ES Degree Online</strong></p><p><strong>Introduction:</strong><br />Pursuing higher education is a significant milestone in one&#8217;s career journey. If you&#8217;re aiming to advance your expertise in Environmental Sustainability (ES), the Executive Master&#8217;s program at IIT Madras is an excellent choice. This blog post serves as a comprehensive guide to help you navigate through the application process for the IIT Madras ES Degree online.</p><p><strong>Step 1: Research and Program Evaluation</strong><br />Begin by thoroughly Online Degree the Executive Master&#8217;s in ES program offered by IIT Madras. Understand the curriculum, course structure, faculty, and the unique features that make this program stand out.</p><p><strong>Step 2: Eligibility Check</strong><br />Ensure that you meet the eligibility criteria for the program. Passed Class 12 Or At Class 12 </p><p><strong>Step 3: Online Application Portal</strong><br />Visit the official IIT Madras website and locate the online application portal for the ES Degree program. Create an account or log in if you already have one.</p><p><strong>Step 4: Fill Out Personal Information</strong><br />Provide your personal details such as name, date of birth, contact information, and address. Make sure all the information is accurate and up to date.</p><p><strong>Step 5: Academic and Professional Details</strong><br />Enter details about your educational background, including degrees obtained, institutions attended, and relevant certifications. Include information about your professional experience, highlighting roles related to environmental sustainability.</p><p><strong>Step 6: Statement of Purpose (SOP)</strong><br />Write a compelling Statement of Purpose that outlines your reasons for pursuing the ES Degree at IIT Madras. Explain your career goals, how this program aligns with your aspirations, and what you hope to contribute to the field.</p><p><strong>Step 7: Letters of Recommendation</strong><br />Provide contact details of individuals who can write letters of recommendation for you. These should be professionals who can attest to your academic abilities, work ethics, and potential for success in the program.</p><p><strong>Step 8: Upload Documents</strong><br />Upload scanned copies of your academic transcripts, certificates, passport-sized photograph, and any other documents requested by the application portal.</p><p><strong>Step 9: Application Fee [Basically This Step Occurs Before Documents Submitting] </strong><br />Pay the application fee 6000 as specified in the guidelines. Keep the payment confirmation receipt for future reference And Its Free For JEE Students .</p><p><strong>Step 10: Review and Submit</strong><br />Before submitting, carefully review all the information you&#8217;ve entered and the documents you&#8217;ve uploaded. Ensure accuracy and completeness.</p><p><strong>Step 11: Submission Confirmation</strong><br />After successfully submitting your application, you should receive a confirmation email. This email may contain further instructions or information about the selection process.</p><p><strong>Step 12: Selection Process</strong><br />The IIT Madras admissions committee will review all applications and shortlist candidates for further rounds, which might include interviews or additional assessments.</p><p><strong>Conclusion:</strong><br />Check Out Full Screenshot With Detailed Video Below If Having Doubt Anymore  !</p><p><a href="https://study.iitm.ac.in/es/" target="_blank" rel="noopener">https://study.iitm.ac.in/es/</a></p><p>  <img decoding="async" fetchpriority="high" src="https://gradedassignments.github.io/videos/ES/1.jpg" width="995" height="516" /></p><p><img decoding="async" src="https://gradedassignments.github.io/videos/ES/2.jpg" width="1009" height="513" /></p><p><img decoding="async" src="https://gradedassignments.github.io/videos/ES/3.jpg" width="1014" height="524" /></p><p><img decoding="async" loading="lazy" src="https://gradedassignments.github.io/videos/ES/4.jpg" width="1015" height="512" /></p><p><img decoding="async" loading="lazy" src="https://gradedassignments.github.io/videos/ES/6.jpg" width="1018" height="505" /></p><p><img decoding="async" loading="lazy" src="https://gradedassignments.github.io/videos/ES/7.jpg" width="1020" height="508" /></p><p><img decoding="async" loading="lazy" src="https://gradedassignments.github.io/videos/ES/8.jpg" width="1025" height="495" /></p>						</div>
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		<title>Maths Week 10 Graded Assignments IIT Madras</title>
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		<dc:creator><![CDATA[KHUSHI]]></dc:creator>
		<pubDate>Sat, 12 Aug 2023 04:16:00 +0000</pubDate>
				<category><![CDATA[Foundation Graded Assignments]]></category>
		<category><![CDATA[Uncategorized]]></category>
		<category><![CDATA[Assignments IIT Madras]]></category>
		<category><![CDATA[Graded Assignments Week 10]]></category>
		<category><![CDATA[IIT Madras Graded Assignments]]></category>
		<category><![CDATA[Week 10 Graded Assignments]]></category>
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					<description><![CDATA[Maths week 10 graded assignment Complete  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    1.The maximum number of non-zero entries in an adjacency matrix of a simple graph having �n vertices can be     �2n2&#8230;&#160;<a href="/maths-week-10-graded-assignments-iit-madras/" class="" rel="bookmark">Read More &#187;<span class="screen-reader-text">Maths Week 10 Graded Assignments IIT Madras</span></a>]]></description>
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							<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  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 </em></h5></div></div></div></div></section></div></div><p> </p></div></div></div></div></div></section>						</div>
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							<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 <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;">�</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> vertices can be</p><div style="margin: 0px; padding: 0px;"> </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;"> </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;">�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="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;"> </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;"> </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;">�(�−1)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;">−</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;"> </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;"> </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;">�(�−1)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;">−</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;"> </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;"> </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;">�(�−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;"><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;">−</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;"> </div></div></div><div class="qt-feedback qt-hidden" style="margin: 0px; padding: 0px;" role="alert"> </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;"> </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;"> </div><p>2.We have a graph <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;">�</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> with 6 vertices. We write down the degrees of all vertices in <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;">�</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> in descending order. Which of the following is a possible listing of the degrees?</p><div style="margin: 0px; padding: 0px;"> </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;"> </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;"> </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;"> </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;"> </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;"> </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;"> </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;"> </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;"> </div></div></div><div class="qt-feedback qt-hidden" style="margin: 0px; padding: 0px;" role="alert"> </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;"> </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"> </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;"> </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;"> </div><p>4.Suppose we obtain the following BFS tree rooted at node 1 for an undirected graph with vertices <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;"> </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;"> </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;"> </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;"> </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;"> </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;"> </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;"> </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;"> </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;"> </div></div></div><div class="qt-feedback qt-hidden" style="margin: 0px; padding: 0px;" role="alert"> </div></div></div><div class="qt-feedback qt-hidden" style="margin: 0px; padding: 0px;" role="alert"> </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;"> </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;"> </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;"> </div><p>Which of the following graphs satisfies the below properties:<br style="margin: 0px; padding: 0px;" />   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;">∣��(�)∣</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><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;">∣</span></span></span></span></span> = <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 <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;">��(�)</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> is the minimum vertex cover of a graph <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;">�.</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;" />   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;">∣��(�)∣</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><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;">∣</span></span></span></span></span> = <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 <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;">��(�)</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> is the perfect matching of a graph <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;">�.</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;" />   3. The graph is a 3-colouring.</p><div style="margin: 0px; padding: 0px;"> </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"> </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;"> </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;"> </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 <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;">�</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> in any graph, in terms of number of edges, where vertex <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;">�</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> is the starting vertex.</label></label></span></p><div style="margin: 0px; padding: 0px;"> </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;"> </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 <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;">�.</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;"> </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;"> </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 <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;">�</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> to every other vertex in the graph, in terms of number of edges.</label></label></p><div style="margin: 0px; padding: 0px;"> </div></div></div><div class="qt-feedback qt-hidden" style="margin: 0px; padding: 0px;" role="alert"> </div></div></div><div class="qt-feedback qt-hidden" style="margin: 0px; padding: 0px;" role="alert"> </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;"> </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;"> </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;"> </div><p>If A = <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;">⎣</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;">⎡</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;">⎦</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;">⎤</span></span></span></span></span></span></span></span></span></span></span></span></span> represents adjacency matrix of a graph <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;">�,</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> then the cardinality of the maximum independent set of the graph <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;">�</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> is</p><div style="margin: 0px; padding: 0px;"> </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"> </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;"> </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;"> </div><p>A company manufactures <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> chemicals <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,&#8230;.�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;"><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> Certain 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;"> </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"> </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;"> </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;"> </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, ‘<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>’ denotes color <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 ‘<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>’ denotes color <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>						</div>
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		<dc:creator><![CDATA[KHUSHI]]></dc:creator>
		<pubDate>Tue, 08 Aug 2023 13:29:32 +0000</pubDate>
				<category><![CDATA[Notes]]></category>
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					<description><![CDATA[The Foundational Level comprises courses in Mathematics, Statistics, Basics of Programming and Python, and English. These courses have been chosen to ensure that the learner who passes these successfully is well prepared to proceed to the Diploma Level courses. MATHEMATICS I This course introduces functions (straight lines, polynomials, exponentials and logarithms) and discrete mathematics (basics,&#8230;&#160;<a href="/qualifiers-notes-iit-madras/" class="" rel="bookmark">Read More &#187;<span class="screen-reader-text">Qualifiers Notes</span></a>]]></description>
										<content:encoded><![CDATA[		<div data-elementor-type="wp-post" data-elementor-id="319" class="elementor elementor-319" data-elementor-post-type="post">
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							<p>The Foundational Level comprises courses in Mathematics, Statistics, Basics of Programming and Python, and English. These courses have been chosen to ensure that the learner who passes these successfully is well prepared to proceed to the Diploma Level courses.</p>						</div>
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			<h2 class="elementor-heading-title elementor-size-default">MATHEMATICS I</h2>		</div>
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							<p>This course introduces functions (straight lines, polynomials, exponentials and logarithms) and discrete mathematics (basics, graphs) with many examples. The students will be exposed to the idea of using abstract mathematical structures to represent concrete real life situations.</p>						</div>
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			<h2 class="elementor-heading-title elementor-size-default">STATISTICS I</h2>		</div>
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							<p>The students will be introduced to large datasets. Using this data, the students will be introduced to various insights one can glean from the data. Basic concepts of probability also will be introduced during the course leading to a discussion on Random variables.</p>						</div>
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								<div class="elementor-element elementor-element-b4eee2f elementor-button-success elementor-align-justify elementor-widget elementor-widget-button" data-id="b4eee2f" data-element_type="widget" data-widget_type="button.default">
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					<div class="elementor-button-wrapper">
			<a class="elementor-button elementor-button-link elementor-size-sm" href="https://drive.google.com/drive/folders/1CJksev6YYSduDrZxNk997DMxzwQphz1I" target="_blank" rel="noopener">
						<span class="elementor-button-content-wrapper">
						<span class="elementor-button-text">Stats I: Week 1 - 12 (Gagneet Kaur)</span>
		</span>
					</a>
		</div>
				</div>
				</div>
				<div class="elementor-element elementor-element-eb15821 elementor-button-danger elementor-align-justify elementor-widget elementor-widget-button" data-id="eb15821" data-element_type="widget" data-widget_type="button.default">
				<div class="elementor-widget-container">
					<div class="elementor-button-wrapper">
			<a class="elementor-button elementor-button-link elementor-size-sm" href="https://drive.google.com/file/d/1WvHq5pTt4lD5zwj7N_BByfDqFtxI6b4t/view" target="_blank" rel="noopener">
						<span class="elementor-button-content-wrapper">
						<span class="elementor-button-text">Stats I: Week 1 - 10 (P.V. Shabarish)</span>
		</span>
					</a>
		</div>
				</div>
				</div>
					</div>
		</div>
				<div class="elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-c5a256d" data-id="c5a256d" data-element_type="column">
			<div class="elementor-widget-wrap elementor-element-populated">
								<div class="elementor-element elementor-element-7c7af38 elementor-button-warning elementor-align-justify elementor-widget elementor-widget-button" data-id="7c7af38" data-element_type="widget" data-widget_type="button.default">
				<div class="elementor-widget-container">
					<div class="elementor-button-wrapper">
			<a class="elementor-button elementor-button-link elementor-size-sm" href="https://drive.google.com/file/d/1XnZOjJPpBNUn3lk-7ynCgT-AIjTL9AK_/view" target="_blank" rel="noopener">
						<span class="elementor-button-content-wrapper">
						<span class="elementor-button-text">Stats I: Week 1 - 12 (Palash)</span>
		</span>
					</a>
		</div>
				</div>
				</div>
				<div class="elementor-element elementor-element-9dfb9a4 elementor-button-info elementor-align-justify elementor-widget elementor-widget-button" data-id="9dfb9a4" data-element_type="widget" data-widget_type="button.default">
				<div class="elementor-widget-container">
					<div class="elementor-button-wrapper">
			<a class="elementor-button elementor-button-link elementor-size-sm" href="https://drive.google.com/file/d/1qFplfEds6Ij9hon8vMhe6WErmoApS1mO/view" target="_blank" rel="noopener">
						<span class="elementor-button-content-wrapper">
						<span class="elementor-button-text">Stats I: Week 1 - 9 (Anonymous)</span>
		</span>
					</a>
		</div>
				</div>
				</div>
					</div>
		</div>
							</div>
		</section>
					</div>
		</div>
							</div>
		</section>
				<section class="elementor-section elementor-top-section elementor-element elementor-element-86104dd elementor-section-boxed elementor-section-height-default elementor-section-height-default" data-id="86104dd" data-element_type="section">
						<div class="elementor-container elementor-column-gap-default">
					<div class="elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-b374506" data-id="b374506" data-element_type="column">
			<div class="elementor-widget-wrap elementor-element-populated">
								<div class="elementor-element elementor-element-defb1a1 elementor-widget elementor-widget-spacer" data-id="defb1a1" data-element_type="widget" data-widget_type="spacer.default">
				<div class="elementor-widget-container">
					<div class="elementor-spacer">
			<div class="elementor-spacer-inner"></div>
		</div>
				</div>
				</div>
				<div class="elementor-element elementor-element-5dd1e2d elementor-widget elementor-widget-heading" data-id="5dd1e2d" data-element_type="widget" data-widget_type="heading.default">
				<div class="elementor-widget-container">
			<h2 class="elementor-heading-title elementor-size-default">ENGLISH I</h2>		</div>
				</div>
				<div class="elementor-element elementor-element-5885a96 elementor-widget elementor-widget-text-editor" data-id="5885a96" data-element_type="widget" data-widget_type="text-editor.default">
				<div class="elementor-widget-container">
							<p>This course aims at achieving fluency and confidence in spoken and written English. This course will use insights from theories of learning and dominant methods of teaching language</p>						</div>
				</div>
				<section class="elementor-section elementor-inner-section elementor-element elementor-element-87fef50 elementor-section-boxed elementor-section-height-default elementor-section-height-default" data-id="87fef50" data-element_type="section">
						<div class="elementor-container elementor-column-gap-default">
					<div class="elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-97b9409" data-id="97b9409" data-element_type="column">
			<div class="elementor-widget-wrap elementor-element-populated">
								<div class="elementor-element elementor-element-3c49fe5 elementor-button-info elementor-align-justify elementor-widget elementor-widget-button" data-id="3c49fe5" data-element_type="widget" data-widget_type="button.default">
				<div class="elementor-widget-container">
					<div class="elementor-button-wrapper">
			<a class="elementor-button elementor-button-link elementor-size-sm" href="https://drive.google.com/drive/folders/1YJhK2hSn-gK128HgQd2OZnOb_IsP8ziD" target="_blank" rel="noopener">
						<span class="elementor-button-content-wrapper">
						<span class="elementor-button-text">English I: Week 1 - 9 (Gagneet Kaur)</span>
		</span>
					</a>
		</div>
				</div>
				</div>
					</div>
		</div>
				<div class="elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-82b04dc" data-id="82b04dc" data-element_type="column">
			<div class="elementor-widget-wrap elementor-element-populated">
								<div class="elementor-element elementor-element-0ca143a elementor-button-success elementor-align-justify elementor-widget elementor-widget-button" data-id="0ca143a" data-element_type="widget" data-widget_type="button.default">
				<div class="elementor-widget-container">
					<div class="elementor-button-wrapper">
			<a class="elementor-button elementor-button-link elementor-size-sm" href="https://drive.google.com/file/d/18w-ECQbOfreuBfuV4cwudyQBDWuXBt6z/view" target="_blank" rel="noopener">
						<span class="elementor-button-content-wrapper">
						<span class="elementor-button-text">English I: Week 1 - 9 (Aditya Dwivedi)</span>
		</span>
					</a>
		</div>
				</div>
				</div>
					</div>
		</div>
							</div>
		</section>
					</div>
		</div>
							</div>
		</section>
				<section class="elementor-section elementor-top-section elementor-element elementor-element-fee8870 elementor-section-boxed elementor-section-height-default elementor-section-height-default" data-id="fee8870" data-element_type="section" id="3">
						<div class="elementor-container elementor-column-gap-default">
					<div class="elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-9a430f7" data-id="9a430f7" data-element_type="column">
			<div class="elementor-widget-wrap elementor-element-populated">
								<div class="elementor-element elementor-element-8730aee elementor-widget elementor-widget-spacer" data-id="8730aee" data-element_type="widget" data-widget_type="spacer.default">
				<div class="elementor-widget-container">
					<div class="elementor-spacer">
			<div class="elementor-spacer-inner"></div>
		</div>
				</div>
				</div>
				<div class="elementor-element elementor-element-44fc604 elementor-widget elementor-widget-heading" data-id="44fc604" data-element_type="widget" data-widget_type="heading.default">
				<div class="elementor-widget-container">
			<h2 class="elementor-heading-title elementor-size-default">COMPUTATIONAL THINKING</h2>		</div>
				</div>
				<div class="elementor-element elementor-element-4fd8cd2 elementor-widget elementor-widget-text-editor" data-id="4fd8cd2" data-element_type="widget" data-widget_type="text-editor.default">
				<div class="elementor-widget-container">
							<p>The students will be introduced to a number of programming concepts using illustrative examples which will be solved almost entirely manually. The manual execution of each solution allows for close inspection of the concepts being discussed.</p>						</div>
				</div>
				<section class="elementor-section elementor-inner-section elementor-element elementor-element-5d131ea elementor-section-boxed elementor-section-height-default elementor-section-height-default" data-id="5d131ea" data-element_type="section">
						<div class="elementor-container elementor-column-gap-default">
					<div class="elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-8b0b7d3" data-id="8b0b7d3" data-element_type="column">
			<div class="elementor-widget-wrap elementor-element-populated">
								<div class="elementor-element elementor-element-b8b25ad elementor-button-info elementor-align-justify elementor-widget elementor-widget-button" data-id="b8b25ad" data-element_type="widget" data-widget_type="button.default">
				<div class="elementor-widget-container">
					<div class="elementor-button-wrapper">
			<a class="elementor-button elementor-button-link elementor-size-sm" href="https://drive.google.com/file/d/1RP9PPtHSdmF2BCcl5H7p0pkxiQ1_8olb/view" target="_blank" rel="noopener">
						<span class="elementor-button-content-wrapper">
						<span class="elementor-button-text">CT: Week 1 - 10 (Gagneet Kaur)</span>
		</span>
					</a>
		</div>
				</div>
				</div>
					</div>
		</div>
				<div class="elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-d06dd34" data-id="d06dd34" data-element_type="column">
			<div class="elementor-widget-wrap elementor-element-populated">
								<div class="elementor-element elementor-element-b4d96d5 elementor-button-success elementor-align-justify elementor-widget elementor-widget-button" data-id="b4d96d5" data-element_type="widget" data-widget_type="button.default">
				<div class="elementor-widget-container">
					<div class="elementor-button-wrapper">
			<a class="elementor-button elementor-button-link elementor-size-sm" href="https://drive.google.com/file/d/1ONSILLrGO2lWVUTt__q3gLkGe-Cf8QJf/view" target="_blank" rel="noopener">
						<span class="elementor-button-content-wrapper">
						<span class="elementor-button-text">CT: Week 1 - 12 (Visist Thallam)</span>
		</span>
					</a>
		</div>
				</div>
				</div>
					</div>
		</div>
							</div>
		</section>
					</div>
		</div>
							</div>
		</section>
							</div>
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		<dc:creator><![CDATA[KHUSHI]]></dc:creator>
		<pubDate>Mon, 07 Aug 2023 12:33:42 +0000</pubDate>
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					<description><![CDATA[ok 👌]]></description>
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		<dc:creator><![CDATA[KHUSHI]]></dc:creator>
		<pubDate>Mon, 07 Aug 2023 12:19:11 +0000</pubDate>
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					<description><![CDATA[Welcome to WordPress. This is your first post. Edit or delete it, then start writing!]]></description>
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<p>Welcome to WordPress. This is your first post. Edit or delete it, then start writing!</p>
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