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If the 4th term in the expansion of `(a x+1//x)^n` is 5/2, then a. `a=1/2` b. `n=8` c. `a=2/3` d. `n=6`

A

`a = 1/2`

B

`n = 8`

C

`a = 2/3`

D

`n = 6`

Text Solution

Verified by Experts

The correct Answer is:
A, D
It is given the fourth term in the expansion of `(ax+(1)/(x))^(n)` is `5/2`, therefore,
`.^(n)C_(3) (ax)^(n-3) (1/x)^(3) = 5/2 rArr .^(n)C_(3) a^(n-3)x^(n-6) = 5/2" "(1)`
`rArr n = 6` [`:'` R.H.S. is independent of x]
Putting`n = 6`in (1), we get `.^(6)C_(3) a^(3) = 5/2` or `a^(3) = 1/8` or `a = 1/2`
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