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Given positive integers r gt1, n gt2 and...

Given positive integers `r gt1,` `n gt2` and that the coefficient of `(3r d)t h` and `(r+2)t h` terms in the binomial expansion of `(1+x)^(2n)` are equal. Then

A

`n = 2r`

B

`n = 2r + 1`

C

`n = 3r`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
In the expansion `(1+x)^2n,t_(3r)=.^2nC_(3r-1)(x)^(3r+1)`.
and `t_(r+2)= .^2nC_r+1(x)^(r-1)`
Since, binomial coefficients of `t_3r and t_(r+2)` are equal.
`therefore .^2nC_(3r-1)=.^2nC_r+1`
`rArr 3r-1= 1 or 2n=(3r-1)+(r+1)`
` rArr 2r=2 or 2n =4r`
`rArr r=1 or n=2r`
But `r gt 1`
`therefore` We take , `n=2r`.
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