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If .^(n)C(r )=84, .^(n)C(r-1)=36 " and" ...

If `.^(n)C_(r )=84, .^(n)C_(r-1)=36 " and" .^(n)C_(r+1)=126`, then find the value of n.

A

`|n-r| = 6`

B

`n + 2r = 15`

C

`|n-3r| = 0`

D

`n+r^(2) = 18`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
`(.^(n)C_(r-1))/(.^(n)C_(r)) = (36)/(84)` and `(.^(n)Cr_(r))/(.^(n)Cr_(r+1) )=(84)/(126)`
`rArr 3n - 10r = -3` and `4n - 10r = 6`
`rArr n = 9` & `r = 3 , :. |n - r| = 6`
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