SATHEE: Permutations and Combinations 2 Question 11

Permutations and Combinations 2 Question 11

11. 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

(2013 Main)

(a) 7

(b) 5

(c) 10

(d) 8

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Answer:

Correct Answer: 11. (b)

Solution:

Given, $T_{n} =^{n} C_{3} \Rightarrow T_{n + 1} =^{n + 1} C_{3}$

$\begin{array}{lrlr} ∴ & T_{n + 1} - T_{n} & =^{n + 1} C_{3} -^{n} C_{3} = 10 & [given] \\ \Rightarrow & ^{n} C_{2} +^{n} C_{3} -^{n} C_{3} & = 10 & [∵^{n} C_{r} +^{n} C_{r + 1} =^{n + 1} C_{r + 1}] \\ \Rightarrow & ^{n} C_{2} & = 10 \\ \Rightarrow & n & n \end{array}$

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Permutations and Combinations 2 Question 11

11. Let Tn be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If Tn+1−Tn=10, then the value of n is

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11. 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