Question

Find the coeeficient of `x^(-2)` in the exapansion of `(x^(2)+(4)/(x^(5)))^(6)`
A. 240
B. 150
C. 100
D. 180

Answer 1

Correct Answer - A
In the expansion `(ax^(p)+(b)/(x^(q)))^(n)`, the term containing `x^(k)"is"T_(r+1)` where `r=(np-k)/(p+q)`
Here, `r=(12+2)/(5+2)=(14)/(4)=2`
`T_(2+1)=T_(3)=""^(6)C_(2)(x^(2))^(4)((4)/(x^(5)))^(2)=""^(6)C_(2)(16)x^(-2)`
`=(15)(16)x^(-2)`
`:.` The required coefficient =240