{"id":125043,"date":"2023-09-13T18:50:00","date_gmt":"2023-09-13T13:20:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=125043"},"modified":"2023-12-06T11:02:42","modified_gmt":"2023-12-06T05:32:42","slug":"rd-sharma-class-10-solutions-chapter-1-exercise-1-1","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-1-exercise-1-1\/","title":{"rendered":"RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1 (Updated for 2024)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-125044\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-10-Solutions-Chapter-1-Exercise-1.1.jpg\" alt=\"RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-10-Solutions-Chapter-1-Exercise-1.1.jpg 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-10-Solutions-Chapter-1-Exercise-1.1-768x432.jpg 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1:&nbsp;<\/strong>Natural numbers, integers, rational and irrational numbers are all elements of the universal set of real numbers. We will learn about integer divisibility as well as several key features of integers in <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-for-maths\/\"><strong>RD Sharma Solutions Class 10<\/strong><\/a> Exercise 1.1. In this exercise, the main focus is Euclid\u2019s division, Lemma. Students can use the <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-1-real-numbers\/\"><strong>RD Sharma Class 10 Solutions Chapter 1<\/strong><\/a> Exercise 1.1 PDF provided below to solve these questions effectively.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_47_1 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"ez-toc-toggle-icon-1\"><label for=\"item-69d28493480fb\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #000000;color:#000000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" 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href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-1-exercise-1-1\/#download-rd-sharma-class-10-solutions-chapter-1-exercise-11-free-pdf\" title=\"Download RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1 Free PDF\">Download RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1 Free PDF<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-1-exercise-1-1\/#access-answers-to-rd-sharma-class-10-solutions-chapter-1-exercise-11-important-question-with-answers\" title=\"Access answers to RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1- Important Question with Answers\">Access answers to RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1- Important Question with Answers<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-1-exercise-1-1\/#faqs-on-rd-sharma-class-10-solutions-chapter-1-exercise-11\" title=\"FAQs on RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1\">FAQs on RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-1-exercise-1-1\/#where-can-i-download-rd-sharma-class-10-solutions-chapter-1-exercise-11-free-pdf\" title=\"Where can I download RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1 free PDF?\">Where can I download RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1 free PDF?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-1-exercise-1-1\/#is-it-required-to-remember-all-of-the-questions-in-rd-sharma-class-10-solutions-chapter-1-exercise-11\" title=\"Is it required to remember all of the questions in RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1?\">Is it required to remember all of the questions in RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-1-exercise-1-1\/#what-are-the-benefits-of-using-rd-sharma-class-10-solutions-chapter-1-exercise-11\" title=\"What are the benefits of using RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1?\">What are the benefits of using RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-class-10-solutions-chapter-1-exercise-11-free-pdf\"><\/span>Download RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1 Free PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div id=\"example1\" style=\"text-align: justify;\">&nbsp;<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 800px;}<br \/>\n.pdfobject { border: 1px solid #666; }<br \/>\n<\/style><\/p>\n<p style=\"text-align: justify;\"><script src=\"https:\/\/www.kopykitab.com\/_utility\/js\/pdfobject.min.js\"><\/script><br><script>PDFObject.embed(\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-SHARMA-Solutions-Class-10-Maths-Chapter-1-Ex-1.1.pdf\", \"#example1\");<\/script><\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-SHARMA-Solutions-Class-10-Maths-Chapter-1-Ex-1.1.pdf\">RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1 PDF<\/a><\/p>\n<h3><span class=\"ez-toc-section\" id=\"access-answers-to-rd-sharma-class-10-solutions-chapter-1-exercise-11-important-question-with-answers\"><\/span>Access answers to RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1- Important Question with Answers<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Question 1.<\/strong><br>If a and b are two odd positive integers such that a &gt; b, then prove that one of the two numbers a+b2 and a\u2212b2 are odd and the other is even.<br><strong>Solution:<\/strong><br>a and b are two odd numbers such that a &gt; b<br>Let a = 2n + 1, then b = 2n + 3<br><img src=\"https:\/\/farm2.staticflickr.com\/1731\/42375451792_ddcf761890_o.png\" alt=\"RD Sharma Class 10 Chapter 1 Real Numbers Ex 1.1\" width=\"322\" height=\"182\"><\/p>\n<p><strong>Question 2.<\/strong><br>Prove that the product of two consecutive positive integers is divisible by 2.<br><strong>Solution:<\/strong><br>Let n and n + 1 be two consecutive positive integer<br>We know that n is of the form n = 2q and n + 1 = 2q + 1<br>n (n + 1) = 2q (2q + 1) = 2 (2q<sup>2<\/sup>&nbsp;+ q)<br>Which is divisible by 2<br>If n = 2q + 1, then<br>n (n + 1) = (2q + 1) (2q + 2)<br>= (2q + 1) x 2(q + 1)<br>= 2(2q + 1)(q + 1)<br>Which is also divisible by 2<br>Hence the product of two consecutive positive integers is divisible by 2.<\/p>\n<p><strong>Question 3.<\/strong><br>Prove that the product of three consecutive positive integers is divisible by 6.<br><strong>Solution<\/strong>:<br>Let n be the positive any integer Then<br>n(n + 1) (n + 2) = (n<sup>2<\/sup>&nbsp;+ n) (n + 2)<br><img src=\"https:\/\/farm2.staticflickr.com\/1738\/41702423124_537d0aa769_o.png\" alt=\"RD Sharma Class 10 Solutions Real Numbers\" height=\"604\"><br>Which is also divisible by 6<br>Hence the product of three consecutive positive integers is divisible by 6.<\/p>\n<p><strong>Question 4.<\/strong><br>For any positive integer n, prove that n<sup>3<\/sup>&nbsp;\u2013 n is divisible by 6.<br><strong>Solution:<\/strong><br><img src=\"https:\/\/farm2.staticflickr.com\/1732\/41702423474_3d4f9b0380_o.png\" alt=\"Real Numbers Class 10 RD Sharma\" width=\"327\" height=\"242\"><br><img src=\"https:\/\/farm2.staticflickr.com\/1753\/41702423314_b56bb51038_o.png\" alt=\"RD Sharma Class 10 Solutions Chapter 1 Real Numbers Ex 1.1\" width=\"270\" height=\"145\"><br>Which is divisible by 6<br>Hence we can similarly, prove that n<sup>2<\/sup>&nbsp;\u2013 n is divisible by 6 for any positive integer n.<br>Hence proved.<\/p>\n<p><strong>Question 5.<\/strong><br>Prove that if a positive integer is of the form 6q + 5, then it is of the form 3q + 2 for some integer q, but not conversely.<br><strong>Solution<\/strong>:<br>Let n = 6q + 5, where q is a positive integer<br>We know that any positive integer is of the form 3k or 3k + 1 or 3k + 2, 1<br>q = 3k or 3k + 1 or 3k + 2<br>If q = 3k, then n = 6q + 5<br><img src=\"https:\/\/farm2.staticflickr.com\/1733\/41702423614_283dbb432d_o.png\" alt=\"RD Sharma Class 10 Pdf Chapter 1 Real Numbers Ex 1.1\" width=\"330\" height=\"329\"><\/p>\n<p><strong>Question 6.<\/strong><br>Prove that the square of any positive integer of the form 5q + 1 is of the same form.<br><strong>Solution:<\/strong><br>Let a be any positive integer<br>Then a = 5m + 1<br>a<sup>2<\/sup>&nbsp;= (5m + 1 )<sup>2<\/sup>&nbsp;= 25m<sup>2<\/sup>&nbsp;+ 10m + 1<br>= 5 (5m<sup>2<\/sup>&nbsp;+ 2m) + 1<br>= 5q + 1 where q = 5m<sup>2<\/sup>&nbsp;+ 2m<br>Which is of the same form as given<br>Hence proved.<\/p>\n<p><strong>Question 7.<\/strong><br>Prove that the square of any positive, integer is of the form 3m or, 3m + 1 but not of form 3m + 2.<br><strong>Solution:<\/strong><br>Let a be any positive integer<br>Let it be in the form of 3m or 3m + 1<br>Let a = 3q, then<br><img src=\"https:\/\/farm1.staticflickr.com\/878\/41523055585_d80346e915_o.png\" alt=\"RD Sharma Solutions Class 10 Chapter 1 Real Numbers Ex 1.1\" width=\"260\" height=\"317\"><br>Hence proved.<\/p>\n<p><strong>Question 8.<\/strong><br>Prove that the square of any positive integer is of the form 4q or 4q + 1 for some integer q.<br><strong>Solution:<\/strong><br>Let a be the positive integer and<br>Let a = 4m<br><img src=\"https:\/\/farm1.staticflickr.com\/897\/41523055635_8478db5937_o.png\" alt=\"RD Sharma Solutions Class 10 Chapter 1 Real Numbers Ex 1.1\" width=\"247\" height=\"175\"><br>Hence proved.<\/p>\n<p><strong>Question 9.<\/strong><br>Prove that the square of any positive integer is of the form 5q, 5q + 1, 5q + 4 for some integer q.<br><strong>Solution:<\/strong><br>Let a be the positive integer, and<br>Let a = 5m, then<br><img src=\"https:\/\/farm2.staticflickr.com\/1739\/41523055985_12a9c394a3_o.png\" alt=\"Learncbse.In Class 10 Chapter 1 Real Numbers Ex 1.1\" width=\"321\" height=\"572\"><\/p>\n<p><strong>Question 10.<\/strong><br>Show that the square of an odd positive integer is of the form 8q + 1, for some integer q.<br><strong>Solution:<\/strong><br>Let n be any positive odd integer<br>Let n = 4p + 1, then<br>(4p + 1)<sup>2<\/sup>&nbsp;= 16p<sup>2<\/sup>&nbsp;+ 8p + 1<br>n<sup>2<\/sup>&nbsp;= 8p (2p + 1) + 1<br>= 8q + 1 where q = p(2p + 1)<br>Hence proved.<\/p>\n<p><strong>Question 11.<\/strong><br>Show that any positive odd integer is of the form 6q + 1 or 6q + 3 or 6q + 5, where q is some integer.<br><strong>Solution:<\/strong><br>Let n be any positive odd integer and<br>let n = 6q + r<br>=&gt; 6q + r, b = 6, and 0 \u2264 r &lt; 6<br>or r = 0, 1, 2, 3, 4, 5<br>If n = 6q = 2 x 3q<br>But it is not odd<br>When n = 6q + 1 which is odd<br>When n = 6q + 2 which is not odd = 2 (3q+ 1)<br>When n = 6q + 3 which is odd<br>When n = 6q + 4 = 2 (3q + 2) which is not odd<br>When n = 6q + 5, which is odd<br>Hence 6q + 1 or 6q + 3 or 6q + 5 are odd numbers.<\/p>\n<p><strong>Question 12.<\/strong><br>Show that the square of any positive integer cannot be of form 6m + 2 or 6m + 5 for any integer m. [NCERT Exemplar]<br><strong>Solution:<\/strong><br>Let a be an arbitrary positive integer, then by Euclid\u2019s division algorithm, corresponding to the positive integers a and 6, there exist non-negative integers q and r such that<br><img src=\"https:\/\/farm1.staticflickr.com\/873\/40617635460_d820435565_o.png\" alt=\"Class 10 RD Sharma Solutions Chapter 1 Real Numbers Ex 1.1\" width=\"349\" height=\"398\"><br><img src=\"https:\/\/farm1.staticflickr.com\/893\/41523056175_b145c80071_o.png\" alt=\"RD Sharma Class 10 Pdf Free Download Full Book Chapter 1 Real Numbers Ex 1.1\"><br>Hence, the square of any positive integer cannot be of form 6m + 2 or 6m + 5 for any integer m.<\/p>\n<p><strong>Question 13.<\/strong><br>Show that the cube of a positive integer is of the form 6q + r, where q is an integer and r = 0, 1, 2, 3, 4, 5. [NCERT Exemplar]<br><strong>Solution:<\/strong><br>Let a be an arbitrary positive integer. Then, by Euclid\u2019s division algorithm, corresponding to the positive integers \u2018a\u2019 and 6, there exist non-negative integers q and r such that<br><img src=\"https:\/\/farm2.staticflickr.com\/1727\/40617636080_b8e7ae9cb5_o.png\" alt=\"RD Sharma Class 10 Solution Chapter 1 Real Numbers Ex 1.1\" width=\"350\" height=\"290\"><br><img src=\"https:\/\/farm1.staticflickr.com\/881\/40617635760_cd84558780_o.png\" alt=\"RD Sharma Class 10 Pdf Ebook Chapter 1 Real Numbers Ex 1.1\" width=\"351\" height=\"396\"><br><img src=\"https:\/\/farm2.staticflickr.com\/1755\/41523056615_0b367cce45_o.png\" alt=\"RD Sharma Maths Class 10 Solutions Pdf Free Download Chapter 1 Real Numbers Ex 1.1\" width=\"349\" height=\"340\"><br>Hence, the cube of a positive integer of the form 6q + r, q is an integer and r = 0, 1, 2, 3, 4, 5 is also of the forms 6m, 6m + 1, 6m + 3, 6m + 3, 6m + 4 and 6m + 5 i.e., 6m + r.<\/p>\n<p><strong>Question 14.<\/strong><br>Show that one and only one out of n, n + 4, n + 8, n + 12, and n + 16 is divisible by 5, where n is any positive integer. [NCERT Exemplar]<br><strong>Solution:<\/strong><br>Given numbers are n, (n + 4), (n + 8), (n + 12), and (n + 16), where n is any positive integer.<br>Then, let n = 5q, 5q + 1, 5q + 2, 5q + 3, 5q + 4 for q \u2208N [By Euclid\u2019s algorithm]<br>Then, in each case, we put the different values of n in the given numbers. We definitely get one and only one of the given numbers is divisible by 5.<br>Hence, one and only one out of n, n + 4, n + 8, n + 12, and n + 16 is divisible by 5.<br>Alternate Method<br>On dividing n by 5, let q be the quotient and r be the remainder.<br>Then n = 5q + r, where 0 \u2264 r &lt; 5. n = 5q + r, where r = 0, 1, 2, 3, 4<br>=&gt; n = 5q or 5q + 1 or 5q + 2 or 5q + 3 or 5q + 4<br>Case I: If n = 5q, then n is only divisible by 5. .<br>Case II: If n = 5q + 1, then n + 4 = 5q + 1 + 4 = 5q + 5 = 5(q + 1), which is only divisible by 5.<br>So, in this case, (n + 4) is divisible by 5.<br>Case III : If n = 5q + 3, then n + 2 = 5q + 3 + 12 = 5q + 15 = 5(q + 3), which is divisible by 5.<br>So, in this case (n + 12) is only divisible by 5.<br>Case IV : If n = 5q + 4, then n + 16 = 5q + 4 + 16 = 5q + 20 = 5(q + 4), which is divisible by 5.<br>So, in this case, (n + 16) is only divisible by 5.<br>Hence, one and only one out of n, n + 4, n + 8, n + 12, and n + 16 is divisible by 5, where n is any positive integer.<\/p>\n<p><strong>Question 15.<\/strong><br>Show that the square of an odd positive integer can be of the form 6q + 1 or 6q + 3 for some integer. [NCERT Exemplar]<br><strong>Solution:<\/strong><br>We know that any positive integer can be of the form 6m, 6m + 1, 6m + 2, 6m + 3, 6m + 4 or 6m + 5, for some integer m.<br>Thus, an odd positive integer can be of the form 6m + 1, 6m + 3, or 6m + 5 Thus we have:<br><img src=\"https:\/\/farm2.staticflickr.com\/1747\/40617636160_b1d640ff5c_o.png\" alt=\"RD Sharma Class 10 Book Pdf Free Download Chapter 1 Real Numbers Ex 1.1\" width=\"324\" height=\"137\"><br>Thus, the square of an odd positive integer can be of the form 6q + 1 or 6q + 3.<\/p>\n<p><strong>Question 16.<\/strong><br>A positive integer is of the form 3q + 1, q being a natural number. Can you write its square in any form other than 3m + 1, 3m, or 3m + 2 for some integer m? Justify your answer.<br><strong>Solution:<\/strong><br>No, by Euclid\u2019s Lemma, b = aq + r, 0 \u2264 r &lt; a<br>Here, b is any positive integer<br><img src=\"https:\/\/farm2.staticflickr.com\/1727\/40617636320_a2eca5c5ce_o.png\" alt=\"Class 10 RD Sharma Chapter 1 Real Numbers Ex 1.1\" width=\"325\" height=\"319\"><\/p>\n<p><strong>Question 17.<\/strong><br>Show that the square of any positive integer cannot be of form 3m + 2, where m is a natural number.<br><strong>Solution:<\/strong><br>By Euclid\u2019s lemma, b = aq + r, 0 \u2264 r \u2264 a<br>Here, b is any positive integer,<br>a = 3, b = 3q + r for 0 \u2264 r \u2264 2<br>So, any positive integer is of the form 3k, 3k + 1, or 3k + 2<br><img src=\"https:\/\/farm2.staticflickr.com\/1758\/40617636390_00f0dfec6e_o.png\" alt=\"RD Sharma Class 10 Textbook Pdf Chapter 1 Real Numbers Ex 1.1\" width=\"327\" height=\"214\"><br>Which is in the form of 3m + 1. Hence, a square of any positive number cannot be of form 3m + 2.<\/p>\n<p>We have provided complete details of RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1. If you have any queries related to <a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener\"><strong>CBSE<\/strong><\/a> Class 10, feel free to ask us in the comment section below.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"faqs-on-rd-sharma-class-10-solutions-chapter-1-exercise-11\"><\/span>FAQs on RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n<div id=\"rank-math-faq\" class=\"rank-math-block\">\n<div class=\"rank-math-list \">\n<div id=\"faq-question-1631019464926\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"where-can-i-download-rd-sharma-class-10-solutions-chapter-1-exercise-11-free-pdf\"><\/span>Where can I download RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1 free PDF?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can download RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1 free PDF from the above article.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1631019630770\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"is-it-required-to-remember-all-of-the-questions-in-rd-sharma-class-10-solutions-chapter-1-exercise-11\"><\/span>Is it required to remember all of the questions in RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes, all of the questions in RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1 must be learned. These questions may appear on both board exams and class tests. Students will be prepared for their board exams if they learn these questions.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1631019756363\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"what-are-the-benefits-of-using-rd-sharma-class-10-solutions-chapter-1-exercise-11\"><\/span>What are the benefits of using RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>1. Correct answers according to the latest CBSE guidelines and syllabus.<br \/>2. The RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1 is written in simple language to assist students in their board examination, &amp; competitive examination preparation.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1:&nbsp;Natural numbers, integers, rational and irrational numbers are all elements of the universal set of real numbers. We will learn about integer divisibility as well as several key features of integers in RD Sharma Solutions Class 10 Exercise 1.1. In this exercise, the main focus is Euclid\u2019s &#8230; <a title=\"RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1 (Updated for 2024)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-1-exercise-1-1\/\" aria-label=\"More on RD Sharma Class 10 Solutions Chapter 1 Exercise 1.1 (Updated for 2024)\">Read more<\/a><\/p>\n","protected":false},"author":238,"featured_media":125044,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[73411,2985,73410],"tags":[3243,9206,73520,4388],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/125043"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/238"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=125043"}],"version-history":[{"count":5,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/125043\/revisions"}],"predecessor-version":[{"id":517699,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/125043\/revisions\/517699"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/125044"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=125043"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=125043"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=125043"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}