JEE Mains · Maths · STD 11 - 6. permutation and combination
Let \(p_n\) denote the total number of triangles formed by joining the vertices of an \(n\)-side regular polygon. If \(p_{n+1} - p_n = 66\), then the sum of all distinct prime divisors of \(n\) is:
- A \(7\)
- B \(8\)
- C \(5\)
- D \(6\)
Answer & Solution
Correct Answer
(C) \(5\)
Step-by-step Solution
Detailed explanation
The number of triangles formed by joining the vertices of an \(n\)-sided regular polygon is given by \(p_n = ^{n}C_{3}\). Given that \(p_{n+1} - p_n = 66\). \(^{n+1}C_{3} - ^{n}C_{3} = 66\) Using the property \(^{n+1}C_{r} - ^{n}C_{r} = ^{n}C_{r-1}\), we get: \(^{n}C_{2} = 66\)…
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