{"id":6933,"date":"2021-10-22T01:43:15","date_gmt":"2021-10-21T20:13:15","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6933"},"modified":"2021-10-25T01:31:16","modified_gmt":"2021-10-24T20:01:16","slug":"let-t_n-be-the-number-of-all-possible-triangles-formed-by-joining-vertices-of-an-n-sided-regular-polygon-if-t_n1-t_n-10-then-the-value-of-n-is","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/let-t_n-be-the-number-of-all-possible-triangles-formed-by-joining-vertices-of-an-n-sided-regular-polygon-if-t_n1-t_n-10-then-the-value-of-n-is\/","title":{"rendered":"Let \\(T_n\\) be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If \\(T_{n+1}\\) – \\(T_n\\) = 10, then the value of n is"},"content":{"rendered":"

Solution :<\/h2>\n

Given, \\(T_n\\) = \\(^nC_3\\)<\/p>\n

\\(T_{n+1}\\) = \\(^{n+1}C_3\\)<\/p>\n

\\(\\therefore\\) \\(T_{n+1}\\) – \\(T_n\\) = \\(^{n+1}C_3\\)\u00a0 – \\(^{n}C_3\\)\u00a0 = 10\u00a0 [given]<\/p>\n

\\(\\therefore\\) \\(^nC_2\\) + \\(^nC_3\\) – \\(^nC_3\\) = 10<\/p>\n

\\(\\implies\\) \\(^nC_2\\) = 10<\/p>\n

\\(\\therefore\\) n = 5<\/p>\n

\n

Similar Questions<\/h3>\n

How many different words can be formed by jumbling the letters in the word \u2018MISSISSIPPI\u2019 in which no two S are adjacent ?<\/a><\/p>\n

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then, the number of such arrangements is<\/a><\/p>\n

There are 10 points in a plane, out of these 6 are collinear. If N is the number of triangles formed by joining these points, then<\/a><\/p>\n

In how many ways can 5 different mangoes, 4 different oranges & 3 different apples be distributed among 3 children such that each gets atleast one mango?<\/a><\/p>\n

From a group of 10 persons consisting of 5 lawyers, 3 doctors and 2 engineers, four persons are selected at random. The probability that selection contains one of each category is<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Given, \\(T_n\\) = \\(^nC_3\\) \\(T_{n+1}\\) = \\(^{n+1}C_3\\) \\(\\therefore\\) \\(T_{n+1}\\) – \\(T_n\\) = \\(^{n+1}C_3\\)\u00a0 – \\(^{n}C_3\\)\u00a0 = 10\u00a0 [given] \\(\\therefore\\) \\(^nC_2\\) + \\(^nC_3\\) – \\(^nC_3\\) = 10 \\(\\implies\\) \\(^nC_2\\) = 10 \\(\\therefore\\) n = 5 Similar Questions How many different words can be formed by jumbling the letters in the word \u2018MISSISSIPPI\u2019 in which …<\/p>\n

Let \\(T_n\\) be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If \\(T_{n+1}\\) – \\(T_n\\) = 10, then the value of n is<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,47],"tags":[],"yoast_head":"\nLet \\(T_n\\) be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. 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