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In the expansion of (x^3-1/(x^2))^n ,n i...

In the expansion of `(x^3-1/(x^2))^n ,n in N` , if the sum of the coefficients of `x^5a n dx^(10)` is zero , then `n` is a. 25 b. 20 c. 15 d. none of these

A

`25`

B

`20`

C

`15`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `((1)/(x^(2))-x^(3))^(n)`
`T_(r+1)=(n!)/(r!(n-r)!)(-1)^(n-r)x^(5r-2n)`
If `5r-2n=5`, then `5r=2n+5`
`r=(2n)/(5)+1`
If `5r-2n=10`, then `5r=2n+10`
`r=(2n)/(5)+2`
Let `n=5k`
According to question
`(5k!)/((2k+1)!(3k-1)!)-(5k!)/((2k+2)!(3k-2)!)=0`
`(1)/(3k-1)-(1)/(2k+2)=0`
`k=3`, `n=15`
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