{"id":69064,"date":"2021-08-28T13:28:00","date_gmt":"2021-08-28T07:58:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=69064"},"modified":"2021-08-28T14:48:25","modified_gmt":"2021-08-28T09:18:25","slug":"rd-sharma-solutions-class-12-maths-chapter-15-exercise-15-1","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-15-exercise-15-1\/","title":{"rendered":"RD Sharma Class 12 Solutions Chapter 15 Exercise 15.1 (Updated for 2021-22)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-120932\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-15-Exercise-15.1.jpg\" alt=\"RD Sharma Solutions Class 12 Maths Chapter 15 Exercise 15.1\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-15-Exercise-15.1.jpg 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-15-Exercise-15.1-768x432.jpg 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>RD Sharma Solutions Class 12 Maths Chapter 15 Exercise 15.1\u00a0<\/strong>is mentioned in this article. The key topics covered in exercise 15.1 are Rolle&#8217;s theorem, the geometrical theorem of Rolle&#8217;s theorem of given functions, and illustrative examples. Our experts have created exercise-wise <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-12-solutions\/\"><strong>RD Sharma Class 12 Solutions<\/strong><\/a> with explanations for each step to make problem-solving easier for students. It allows them to assess their understanding of the concepts covered in this chapter. Students can utilise <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-15-mean-value-theorems\/\"><strong>RD Sharma Solutions for Class 12 Maths Chapter 15<\/strong><\/a> Mean Value Theorems Exercise 15.1 as reference materials to analyse Maths.<\/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-69ff8ed99cade\" 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\" 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href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-15-exercise-15-1\/#download-rd-sharma-solutions-class-12-maths-chapter-15-exercise-151-free-pdf\" title=\"Download RD Sharma Solutions Class 12 Maths Chapter 15 Exercise 15.1 Free PDF\">Download RD Sharma Solutions Class 12 Maths Chapter 15 Exercise 15.1 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-solutions-class-12-maths-chapter-15-exercise-15-1\/#access-answers-to-maths-rd-sharma-solutions-for-class-12-chapter-15-%e2%80%93-mean-value-theorems-exercise-151-important-questions-with-solution\" title=\"Access answers to Maths RD Sharma Solutions For Class 12 Chapter 15 \u2013 Mean Value Theorems Exercise 15.1 Important Questions With Solution\">Access answers to Maths RD Sharma Solutions For Class 12 Chapter 15 \u2013 Mean Value Theorems Exercise 15.1 Important Questions With Solution<\/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-solutions-class-12-maths-chapter-15-exercise-15-1\/#rd-sharma-class-12-solutions-chapter-15-exercise-151-important-concepts\" title=\"RD Sharma Class 12 Solutions Chapter 15 Exercise 15.1 | Important Concepts\">RD Sharma Class 12 Solutions Chapter 15 Exercise 15.1 | Important Concepts<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-15-exercise-15-1\/#faqs-on-rd-sharma-solutions-class-12-maths-chapter-15-exercise-151\" title=\"FAQs on RD Sharma Solutions Class 12 Maths Chapter 15 Exercise 15.1\">FAQs on RD Sharma Solutions Class 12 Maths Chapter 15 Exercise 15.1<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-15-exercise-15-1\/#how-many-questions-are-there-in-rd-sharma-solutions-class-12-maths-chapter-15-exercise-151\" title=\"How many questions are there in RD Sharma Solutions Class 12 Maths Chapter 15 Exercise 15.1?\">How many questions are there in RD Sharma Solutions Class 12 Maths Chapter 15 Exercise 15.1?<\/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-solutions-class-12-maths-chapter-15-exercise-15-1\/#where-can-i-get-rd-sharma-class-12-maths-solutions-chapter-15-exercise-151-free-pdf\" title=\"Where can I get RD Sharma Class 12 Maths Solutions Chapter 15 Exercise 15.1 Free PDF?\">Where can I get RD Sharma Class 12 Maths Solutions Chapter 15 Exercise 15.1 Free PDF?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-15-exercise-15-1\/#is-it-required-to-practice-all-of-the-questions-in-exercise-151-chapter-15-of-rd-sharma-solutions-for-class-12-maths\" title=\"Is it required to practice all of the questions in Exercise 15.1 Chapter 15 of RD Sharma Solutions for Class 12 Maths?\">Is it required to practice all of the questions in Exercise 15.1 Chapter 15 of RD Sharma Solutions for Class 12 Maths?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-solutions-class-12-maths-chapter-15-exercise-151-free-pdf\"><\/span>Download RD Sharma Solutions Class 12 Maths Chapter 15 Exercise 15.1 Free PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div id=\"example1\" style=\"text-align: justify;\">\u00a0<\/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\/01\/RD-Sharma-Solutions-Class-12-Maths-Chapter-15-Ex-15.1-1.pdf\", \"#example1\");<\/script><\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Maths-Chapter-15-Ex-15.1-1.pdf\">RD Sharma Solutions Class 12 Maths Chapter 15 Exercise 15.1<\/a><\/p>\n<h3><span class=\"ez-toc-section\" id=\"access-answers-to-maths-rd-sharma-solutions-for-class-12-chapter-15-%e2%80%93-mean-value-theorems-exercise-151-important-questions-with-solution\"><\/span>Access answers to Maths RD Sharma Solutions For Class 12 Chapter 15 \u2013 Mean Value Theorems Exercise 15.1 Important Questions With Solution<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>1. Discuss the applicability of Rolle\u2019s Theorem for the following functions on the indicated intervals:<\/strong><\/p>\n<p><img class=\"alignnone size-full wp-image-120960\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/1-1.gif\" alt=\"1\" width=\"279\" height=\"23\" \/><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img src=\"https:\/\/farm8.staticflickr.com\/7512\/16053811819_ee20d01dd7_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Online Mean Value Theorems Ex 15.1 Q1-i\" width=\"407\" height=\"259\" \/><\/p>\n<p><strong>(ii) f (x) = [x] for -1 \u2264 x \u2264 1, where [x] denotes the greatest integer not exceeding x<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img src=\"https:\/\/farm9.staticflickr.com\/8561\/16239940085_21d35e593a_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Online Mean Value Theorems Ex 15.1 Q1-ii\" width=\"395\" height=\"309\" \/><\/p>\n<p><img class=\"alignnone size-full wp-image-120961\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/2-3.gif\" alt=\"2\" width=\"276\" height=\"40\" \/><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img src=\"https:\/\/farm8.staticflickr.com\/7493\/16052414098_ae9a9f52e9_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Online Mean Value Theorems Ex 15.1 Q1-iii\" width=\"468\" height=\"491\" \/><\/p>\n<p><strong>(iv) f (x) = 2x<sup>2<\/sup>\u00a0\u2013 5x + 3 on [1, 3]<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given function is f (x) = 2x<sup>2<\/sup>\u00a0\u2013 5x + 3 on [1, 3]<\/p>\n<p>Since given function f is a polynomial. So, it is continuous and differentiable everywhere.<\/p>\n<p>Now, we find the values of function at the extreme values.<\/p>\n<p>\u21d2\u00a0f (1) = 2(1)<sup>2<\/sup>\u20135(1) + 3<\/p>\n<p>\u21d2\u00a0f (1) = 2 \u2013 5 + 3<\/p>\n<p>\u21d2\u00a0f (1) = 0\u2026\u2026 (1)<\/p>\n<p>\u21d2\u00a0f (3) = 2(3)<sup>2<\/sup>\u20135(3) + 3<\/p>\n<p>\u21d2\u00a0f (3) = 2(9)\u201315 + 3<\/p>\n<p>\u21d2\u00a0f (3) = 18 \u2013 12<\/p>\n<p>\u21d2\u00a0f (3) = 6\u2026\u2026 (2)<\/p>\n<p>From (1) and (2), we can say that, f (1) \u2260 f (3)<\/p>\n<p>\u2234\u00a0Rolle\u2019s Theorem is not applicable for the function f in interval [1, 3].<\/p>\n<p><strong>(v) f (x) = x<sup>2\/3<\/sup>\u00a0on [-1, 1]<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img src=\"https:\/\/farm9.staticflickr.com\/8573\/16214041166_ed1009c71e_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Online Mean Value Theorems Ex 15.1 Q1-v\" width=\"370\" height=\"267\" \/><\/p>\n<p><img class=\"alignnone size-full wp-image-120962\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/3-3.gif\" alt=\"3\" width=\"275\" height=\"45\" \/><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img src=\"https:\/\/farm8.staticflickr.com\/7524\/16052548580_b217032f9b_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q1-vi\" width=\"390\" height=\"388\" \/><\/p>\n<p><strong>2. Verify the Rolle\u2019s Theorem for each of the following functions on the indicated intervals:<\/strong><\/p>\n<p><strong>(i) f (x) = x<sup>2<\/sup>\u00a0\u2013 8x + 12 on [2, 6]<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img src=\"https:\/\/farm9.staticflickr.com\/8603\/16053813429_1ec7f2e99f_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q5-i\" width=\"392\" height=\"441\" \/><\/p>\n<p><strong>(ii) f(x) = x<sup>2<\/sup>\u00a0\u2013 4x + 3 on [1, 3]<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img src=\"https:\/\/farm8.staticflickr.com\/7538\/15620071613_7c6cd406d0_o.jpg\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q5-ii\" width=\"626\" height=\"393\" \/><\/p>\n<p><strong>(iii) f (x) = (x \u2013 1) (x \u2013 2)<sup>2<\/sup>\u00a0on [1, 2]<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img src=\"https:\/\/farm8.staticflickr.com\/7496\/15620071583_1c5e5b7c8b_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q5-iii\" width=\"416\" height=\"511\" \/><\/p>\n<p><strong>Mean Value Theorems Ex 15.1 Q2(iv)<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7521\/16238082801_7fe16e7b37_o.jpg\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q5-iv\" width=\"430\" height=\"550\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q2(v)<\/strong><br \/><img src=\"https:\/\/farm9.staticflickr.com\/8650\/16239109192_a9515921e7_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q5-v\" width=\"477\" height=\"572\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q2(vi)<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7471\/15617519934_3ea5eee879_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Online Mean Value Theorems Ex 15.1 Q2\" width=\"449\" height=\"609\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q2(vii)<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7487\/16239109372_f8045ab7cf_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Online Mean Value Theorems Ex 15.1 Q3\" width=\"416\" height=\"496\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q2(viii)<\/strong><br \/><img src=\"https:\/\/farm9.staticflickr.com\/8591\/16052548460_bfd3881710_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q4\" width=\"453\" height=\"613\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q3(i)<\/strong><br \/><img src=\"https:\/\/farm9.staticflickr.com\/8613\/16239109182_8f046a39ca_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q6-i\" width=\"494\" height=\"671\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q3(ii)<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7465\/16238082701_67c6c085eb_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q6-ii\" width=\"485\" height=\"564\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q3(iii)<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7549\/15617519724_6582d7c756_o.jpg\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q6-iii\" width=\"498\" height=\"568\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q3(iv)<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7550\/16052415548_0eea2e88ee_o.jpg\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q6-iv\" width=\"526\" height=\"578\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q3(v)<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7550\/16052548080_9ee5d2755e_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q6-v\" width=\"527\" height=\"644\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q3(vi)<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7556\/16238082561_208d83dba4_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q6-vi\" width=\"508\" height=\"502\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q3(vii)<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7472\/16052548040_2dc1519616_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q6-vii\" width=\"667\" height=\"698\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q3(viii)<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7550\/15620071243_038db9bd6c_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Online Mean Value Theorems Ex 15.1 Q6-viii\" width=\"494\" height=\"534\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q3(ix)<\/strong><br \/><img src=\"https:\/\/farm9.staticflickr.com\/8573\/15617519654_d6e88ffab3_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Online Mean Value Theorems Ex 15.1 Q6-ix\" width=\"501\" height=\"512\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q3(x)<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7552\/16239109012_fdb318cdc5_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q6-x\" width=\"519\" height=\"516\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q3(xi)<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7535\/15620071193_f6867062ff_o.jpg\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q6-xi\" width=\"552\" height=\"594\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q3(xii)<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7535\/15620071143_21676711a6_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Online Mean Value Theorems Ex 15.1 Q6-xii\" width=\"517\" height=\"618\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q3(xiii)<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7488\/15617519424_602aac543a_o.jpg\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q6-xiii\" width=\"568\" height=\"1086\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q3(xiv)<\/strong><br \/><img src=\"https:\/\/farm9.staticflickr.com\/8630\/16239941265_bd97eb2b3c_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q6-xiv\" width=\"683\" height=\"538\" \/><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7581\/16052415268_3e4ac25da8_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q6-xv\" width=\"410\" height=\"426\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q3(xv)<\/strong><br \/><img src=\"https:\/\/farm9.staticflickr.com\/8573\/16052415278_59180cc093_o.jpg\" alt=\"Free Online RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q6-xvi\" width=\"628\" height=\"518\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q3(xvi)<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7555\/15620071003_2110ed4bb2_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q6-xvii\" width=\"511\" height=\"472\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q3(xvii)<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7505\/16053812949_8df2c44d14_o.png\" alt=\"Free Online RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q6-xviii\" width=\"520\" height=\"667\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q3(xvii)<\/strong><br \/><img src=\"https:\/\/c1.staticflickr.com\/1\/630\/32681376392_1f938f627b_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Online Mean Value Theorems Ex 15.1 Q3(xviii)\" width=\"568\" height=\"521\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q3(xviii)<\/strong><br \/><img src=\"https:\/\/c1.staticflickr.com\/1\/630\/32681376392_1f938f627b_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Online Mean Value Theorems Ex 15.1 Q3(xviii)\" width=\"568\" height=\"521\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q7<\/strong><br \/><img src=\"https:\/\/farm9.staticflickr.com\/8564\/16052415128_8fa96e1744_o.jpg\" alt=\"Free Online RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q7\" width=\"403\" height=\"241\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q8(i)<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7465\/16239108702_185ce7ab9c_o.jpg\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q8-i\" width=\"460\" height=\"431\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q8(ii)<\/strong><br \/><img src=\"https:\/\/farm9.staticflickr.com\/8654\/15620070883_7ba30fee87_o.jpg\" alt=\"Free Online RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q8-ii\" width=\"541\" height=\"409\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q8(iii)<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7529\/16052415018_09df8a598e_o.jpg\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q8-iii\" width=\"531\" height=\"323\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q9<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7462\/16239940885_1d00b6608b_o.gif\" alt=\"Free Online RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q9\" width=\"524\" height=\"530\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q10<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7491\/16214040446_73e476825f_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q10-i\" width=\"676\" height=\"579\" \/><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7509\/16052414928_4df37f6174_o.png\" alt=\"Free Online RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q10-ii\" width=\"636\" height=\"493\" \/><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7470\/15617518974_75d5e5f0ba_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q10-iii\" width=\"619\" height=\"521\" \/><br \/><img src=\"https:\/\/farm9.staticflickr.com\/8574\/15617518904_8997665537_o.gif\" alt=\"Free Online RD Sharma Class 12 Solutions Chapter 15 Mean Value Theorems Ex 15.1 Q10-iv\" width=\"584\" height=\"227\" \/><br \/><strong>Mean Value Theorems Ex 15.1 Q11<\/strong><br \/><img src=\"https:\/\/c1.staticflickr.com\/3\/2505\/32681376472_08d482efe7_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 15 Online Mean Value Theorems Ex 15.1 Q11\" width=\"457\" height=\"435\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"rd-sharma-class-12-solutions-chapter-15-exercise-151-important-concepts\"><\/span>RD Sharma Class 12 Solutions Chapter 15 Exercise 15.1 | Important Concepts<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The following are some of the most essential topics\u00a0of this exercise.<\/p>\n<ul>\n<li>Rolle\u2019s theorem<\/li>\n<li>Geometrical interpretation of Rolle\u2019s theorem<\/li>\n<li>Algebraic interpretation of Rolle\u2019s theorem<\/li>\n<li>Checking the applicability of Rolle\u2019s theorem<\/li>\n<li>Verification of Rolle\u2019s theorem for a given function defined on a given interval<\/li>\n<li>Miscellaneous applications of Rolle\u2019s theorem<\/li>\n<\/ul>\n<p>RD Sharma Solutions for Class 12 Maths Chapter 15 Exercise 15.1 are immensely helpful while doing your homework and also while preparing for <a href=\"http:\/\/cbse.nic.in\/\" target=\"_blank\" rel=\"noopener\">CBSE<\/a>\u00a0finals.\u00a0If you have any queries, feel free to ask us in the comment section below.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"faqs-on-rd-sharma-solutions-class-12-maths-chapter-15-exercise-151\"><\/span>FAQs on RD Sharma Solutions Class 12 Maths Chapter 15 Exercise 15.1<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-1630141765429\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"how-many-questions-are-there-in-rd-sharma-solutions-class-12-maths-chapter-15-exercise-151\"><\/span>How many questions are there in RD Sharma Solutions Class 12 Maths Chapter 15 Exercise 15.1?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>There are a total of 10 questions in RD Sharma Solutions Class 12 Maths Chapter 15 Exercise 15.1.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630141935960\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"where-can-i-get-rd-sharma-class-12-maths-solutions-chapter-15-exercise-151-free-pdf\"><\/span>Where can I get RD Sharma Class 12 Maths Solutions Chapter 15 Exercise 15.1 Free PDF?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can get RD Sharma Solutions Class 12 Maths Chapter 15 Exercise 15.1 Free PDF from the above article.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630141971718\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"is-it-required-to-practice-all-of-the-questions-in-exercise-151-chapter-15-of-rd-sharma-solutions-for-class-12-maths\"><\/span>Is it required to practice all of the questions in Exercise 15.1 Chapter 15 of RD Sharma Solutions for Class 12 Maths?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes, it is important to attend all of the questions offered in RD Sharma Solutions for Class 12 Maths Chapter 15 Exercise 15.1 in order to answer all types of questions that may appear in examinations.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RD Sharma Solutions Class 12 Maths Chapter 15 Exercise 15.1\u00a0is mentioned in this article. The key topics covered in exercise 15.1 are Rolle&#8217;s theorem, the geometrical theorem of Rolle&#8217;s theorem of given functions, and illustrative examples. Our experts have created exercise-wise RD Sharma Class 12 Solutions with explanations for each step to make problem-solving easier &#8230; <a title=\"RD Sharma Class 12 Solutions Chapter 15 Exercise 15.1 (Updated for 2021-22)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-15-exercise-15-1\/\" aria-label=\"More on RD Sharma Class 12 Solutions Chapter 15 Exercise 15.1 (Updated for 2021-22)\">Read more<\/a><\/p>\n","protected":false},"author":238,"featured_media":120932,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[73411,2985,73410],"tags":[3429,73223,73664,4388],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/69064"}],"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=69064"}],"version-history":[{"count":5,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/69064\/revisions"}],"predecessor-version":[{"id":120980,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/69064\/revisions\/120980"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/120932"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=69064"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=69064"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=69064"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}