{"id":68041,"date":"2021-09-02T16:33:00","date_gmt":"2021-09-02T11:03:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=68041"},"modified":"2021-09-02T16:48:37","modified_gmt":"2021-09-02T11:18:37","slug":"rd-sharma-solutions-class-11-maths-chapter-23-exercise-23-14","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-23-exercise-23-14\/","title":{"rendered":"RD Sharma Class 11 Solutions Chapter 23 Exercise 23.14 (Updated for 2021-22)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-123442\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Class-11-Solutions-Chapter-23-Exercise-23.14.jpg\" alt=\"RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.14\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Class-11-Solutions-Chapter-23-Exercise-23.14.jpg 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Class-11-Solutions-Chapter-23-Exercise-23.14-768x432.jpg 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.14:\u00a0<\/strong>Before taking the board exam, students can practise solving questions chapter-by-chapter and exercise-by-exercise to boost their confidence. <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-23\/\"><strong>RD Sharma Class 11 Maths Solutions Chapter 23<\/strong><\/a> Exercise 23.14, pdf links are provided here to help students for this chapter.<\/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-69d36f9c51d4c\" 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\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #000000;color:#000000\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input  type=\"checkbox\" id=\"item-69d36f9c51d4c\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-visibility-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-23-exercise-23-14\/#download-rd-sharma-class-11-solutions-chapter-23-exercise-2314-free-pdf\" title=\"Download RD Sharma Class 11 Solutions Chapter 23 Exercise 23.14 Free PDF\">Download RD Sharma Class 11 Solutions Chapter 23 Exercise 23.14 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-11-maths-chapter-23-exercise-23-14\/#access-answers-to-rd-sharma-solutions-class-11-maths-chapter-23-exercise-2314-important-question-with-answers\" title=\"Access answers to RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.14- Important Question with Answers\">Access answers to RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.14- 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-solutions-class-11-maths-chapter-23-exercise-23-14\/#faqs-on-rd-sharma-class-11-solutions-chapter-23-exercise-2314\" title=\"FAQs on RD Sharma Class 11 Solutions Chapter 23 Exercise 23.14\">FAQs on RD Sharma Class 11 Solutions Chapter 23 Exercise 23.14<\/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-solutions-class-11-maths-chapter-23-exercise-23-14\/#where-can-i-download-rd-sharma-class-11-solutions-chapter-23-exercise-2314-free-pdf\" title=\"Where can I download RD Sharma Class 11 Solutions Chapter 23 Exercise 23.14 free PDF?\">Where can I download RD Sharma Class 11 Solutions Chapter 23 Exercise 23.14 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-solutions-class-11-maths-chapter-23-exercise-23-14\/#why-is-kopykitab%e2%80%99s-rd-sharma-solutions-class-11-maths-chapter-23-exercise-2314-the-best-study-material\" title=\"Why is Kopykitab\u2019s RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.14 the best study material?\">Why is Kopykitab\u2019s RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.14 the best study material?<\/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-11-maths-chapter-23-exercise-23-14\/#is-rd-sharma-solutions-for-class-12-maths-chapter-23-exercise-2314-for-free\" title=\"Is RD Sharma Solutions for Class 12 Maths Chapter 23 Exercise 23.14 for free?\">Is RD Sharma Solutions for Class 12 Maths Chapter 23 Exercise 23.14 for free?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-class-11-solutions-chapter-23-exercise-2314-free-pdf\"><\/span>Download RD Sharma Class 11 Solutions Chapter 23 Exercise 23.14 Free PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-11-Maths-Chapter-23-Ex-23.14-1.pdf\">RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.14<\/a><\/p>\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-11-Maths-Chapter-23-Ex-23.14-1.pdf\", \"#example1\");<\/script><\/p>\n<p>This exercise provides an overview of the notion based on the relative positions of two points on a line. Students who are experiencing difficulty in comprehending concepts can use <a href=\"https:\/\/www.kopykitab.com\/blog\/cbse-class-11-maths-rd-sharma-solutions\/\"><strong>RD Sharma Class 11 Solutions<\/strong><\/a>. The solutions were developed by Kopykitab&#8217;s experts based on the students&#8217; grasping ability.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"access-answers-to-rd-sharma-solutions-class-11-maths-chapter-23-exercise-2314-important-question-with-answers\"><\/span>Access answers to RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.14- Important Question with Answers<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>1. Find the values of\u00a0\u03b1\u00a0so that the point P(\u03b1\u00a0<sup>2<\/sup>,\u00a0\u03b1) lies inside or on the triangle formed by the lines x \u2013 5y + 6 = 0, x \u2013 3y + 2 = 0 and x \u2013 2y \u2013 3 = 0.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given:\u00a0<\/p>\n<p>x \u2013 5y + 6 = 0, x \u2013 3y + 2 = 0 and x \u2013 2y \u2013 3 = 0 forming a triangle and point P(\u03b1<sup>2<\/sup>,\u00a0\u03b1) lies inside or on the triangle<\/p>\n<p>Let ABC be the triangle of sides AB, BC and CA whose equations are x\u00a0\u2212\u00a05y + 6 = 0, x\u00a0\u2212\u00a03y + 2 = 0 and x\u00a0\u2212\u00a02y\u00a0\u2212\u00a03 = 0, respectively.<br \/><br \/>On solving the equations, we get A (9, 3), B (4, 2), and C (13, 5) as the coordinates of the vertices.<\/p>\n<p><img class=\"wp-image-123591 aligncenter\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/b-5.png\" alt=\"b\" width=\"551\" height=\"257\" \/><\/p>\n<p>It is given that point P (\u03b1<sup>2<\/sup>,\u00a0\u03b1) lies either inside or on the triangle. The three conditions are given below.<\/p>\n<p>(i) A and P must lie on the same side of BC.<\/p>\n<p>(ii) B and P must lie on the same side of AC.<\/p>\n<p>(iii) C and P must lie on the same side of AB.<\/p>\n<p><br \/>If A and P lie on the same side of BC, then<\/p>\n<p>(9 \u2013 9 + 2)(\u03b1<sup>2<\/sup>\u00a0\u2013 3\u03b1\u00a0+ 2)\u00a0\u22650<\/p>\n<p>(\u03b1\u00a0\u2013 2)(\u03b1\u00a0\u2013 1)\u00a0\u2265\u00a00<\/p>\n<p>\u03b1\u00a0\u2208\u00a0(-\u00a0\u221e, 1 ]\u00a0\u222a\u00a0[ 2,\u00a0\u221e) \u2026 (1)<\/p>\n<p><br \/>If B and P lie on the same side of AC, then<\/p>\n<p>(4 \u2013 4 \u2013 3) (\u03b1<sup>2<\/sup>\u00a0\u2013 2\u03b1\u00a0\u2013 3)\u00a0\u2265\u00a00<\/p>\n<p>(\u03b1\u00a0\u2013 3)(\u03b1\u00a0+ 1)\u00a0\u2264\u00a00<\/p>\n<p>\u03b1\u00a0\u2208\u00a0[- 1, 3] \u2026 (2)<\/p>\n<p><br \/>If C and P lie on the same side of AB, then<\/p>\n<p>(13 \u2013 25 + 6)(\u03b1<sup>2<\/sup>\u00a0\u2013 5\u03b1\u00a0+ 6)\u00a0\u22650<\/p>\n<p>(\u03b1\u00a0\u2013 3)(\u03b1\u00a0\u2013 2)\u00a0\u2264\u00a00<\/p>\n<p>\u03b1\u00a0\u2208\u00a0[ 2, 3] \u2026 (3)<\/p>\n<p><br \/>From equations (1), (2), and (3), we get<\/p>\n<p>\u03b1\u2208\u00a0[2, 3]<\/p>\n<p>\u2234 \u03b1\u2208\u00a0[2, 3]<\/p>\n<p><strong>2. Find the values of the parameter a so that the point (a, 2) is an interior point of the triangle formed by the lines x + y \u2013 4 = 0, 3x \u2013 7y \u2013 8 = 0, and 4x \u2013 y \u2013 31 = 0.<\/strong><\/p>\n<p><strong>Solutions:<\/strong><\/p>\n<p><img src=\"https:\/\/farm9.staticflickr.com\/8596\/16145489452_eb0fb5a652_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-Straight-Lines-Ex-23.14-Q-2\" width=\"632\" height=\"570\" \/><\/p>\n<p><strong>3. Determine whether the point (-3, 2) lies inside or outside the triangle whose sides are given by the equations x + y \u2013 4 = 0, 3x \u2013 7y + 8 = 0, 4x \u2013 y \u2013 31 = 0.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img src=\"https:\/\/farm8.staticflickr.com\/7522\/15960485147_f10c903168_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-Straight-Lines-Ex-23.14-Q-3\" width=\"596\" height=\"196\" \/><\/p>\n<p>We have provided complete details of RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.14. If you have any queries related to <a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener\"><strong>CBSE<\/strong><\/a>\u00a0Class 11, feel free to ask us in the comment section below.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"faqs-on-rd-sharma-class-11-solutions-chapter-23-exercise-2314\"><\/span>FAQs on RD Sharma Class 11 Solutions Chapter 23 Exercise 23.14<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-1630580239569\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"where-can-i-download-rd-sharma-class-11-solutions-chapter-23-exercise-2314-free-pdf\"><\/span>Where can I download RD Sharma Class 11 Solutions Chapter 23 Exercise 23.14 free PDF?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can download RD Sharma Solutions for Class 11 Maths Chapter 23 Exercise 23.14 free PDF from the above article.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630580458497\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"why-is-kopykitab%e2%80%99s-rd-sharma-solutions-class-11-maths-chapter-23-exercise-2314-the-best-study-material\"><\/span>Why is Kopykitab\u2019s RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.14 the best study material?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>The RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.14 available on Kopykitab\u2019s website has been created by highly qualified experts to assist students in achieving high scores on the board exam. The solutions are well-organized and logical, giving pupils a clear picture of the most important questions.\u00a0<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630580664633\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"is-rd-sharma-solutions-for-class-12-maths-chapter-23-exercise-2314-for-free\"><\/span>Is RD Sharma Solutions for Class 12 Maths Chapter 23 Exercise 23.14 for free?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes, You can get RD Sharma Solutions Class 12 Maths Chapter 23 Exercise 23.14 for free.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.14:\u00a0Before taking the board exam, students can practise solving questions chapter-by-chapter and exercise-by-exercise to boost their confidence. RD Sharma Class 11 Maths Solutions Chapter 23 Exercise 23.14, pdf links are provided here to help students for this chapter. Download RD Sharma Class 11 Solutions Chapter 23 &#8230; <a title=\"RD Sharma Class 11 Solutions Chapter 23 Exercise 23.14 (Updated for 2021-22)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-23-exercise-23-14\/\" aria-label=\"More on RD Sharma Class 11 Solutions Chapter 23 Exercise 23.14 (Updated for 2021-22)\">Read more<\/a><\/p>\n","protected":false},"author":238,"featured_media":123442,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[73411,2985,73410],"tags":[3428,73334,73564,4388],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68041"}],"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=68041"}],"version-history":[{"count":4,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68041\/revisions"}],"predecessor-version":[{"id":123664,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68041\/revisions\/123664"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/123442"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=68041"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=68041"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=68041"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}