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If 6^(th) term in the expansion of ((3)/...

If `6^(th)` term in the expansion of `((3)/(2)+(x)/(3))^(n)` is numerically greatest, when `x=3`, then the sum of possible integral values of `'n'` is (a) `23` (b) `24` (c) `25` (d) `26`

A

`23`

B

`24`

C

`25`

D

`26`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` For `T_(6)` to be numberically greatest term
`5 lt (n+1)/(1+|(3//2)/(3//3)|)lt6`
`5 lt (2)/(5) (n+1) lt 6`
`(25)/(2) lt n+1 lt 15`
`(23)/(2) lt n gt 14`
`:.n=12`, `13`
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