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If x^4 occurs in the rth term in the exp...

If `x^4` occurs in the rth term in the expansion of `(x^4+1/(x^3))^(15),` then find the value of `rdot`

A

4

B

8

C

9

D

10

Text Solution

Verified by Experts

The correct Answer is:
C
In the expansion of `(x^(4)+(1)/(x^(3)))^(15)`, let `T_(r)` is the `n_(th)` term
`T_(r)=""^(15)C_(r-1)(x^(4))^(15-r+1)((1)/(x^(3)))^(r-1)`
`=15_(C_(r-1))x^(64-4r-3r+3)=15_(C_(r-1))x^(67-7r)`
`x^(4)` occurs in this term
`rArr" "4=67-7r`
`rArr" "7r=63`
`rArr" "r=9.`
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