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If .^(n)C(4),.^(n)C(5), .^(n)C(6) are in...

If `.^(n)C_(4),.^(n)C_(5), .^(n)C_(6)` are in A.P., then find the value of n.

A

14

B

11

C

9

D

12

Text Solution

Verified by Experts

The correct Answer is:
A
as `.^(n)C_(4), .^(n)C_(5), .^(n)C_(6)` are in A.P.
`rArr 2. (n!)/((n-5)!5!) = (n!)/((n-4)!4!) + (n!)/((n-6)|6!) rArr (2)/((n-5)xx5) = (1)/((n-4)(n-5)) + (1)/(6.5)`
`rArr (2)/((n-5) xx5) - (1)/((n-4)(n-5)) = (1)/(65) rArr 6(2n-13) = n^(2) - 9n + 20`
`rArr n^(2) - 21n + 98 = 0 rArr (n - 14)(n - 7) = 0 rArr n = 7` or = 14
`rArr n = 14`
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