Consider the expansion of `(sqrt(x)-(2)/(x^(2)))^(16)`

Options

A. There is a term independent of x
B. Coefficinet of `x^(3)=480`
C. There is no term independent of x
D. Coefficient of `x^(3)=240`

Answer

B, C

Explanation

`(sqrt(x)-(2)/(x^(2)))^(16)`
`T_(r+1)=` .^(16)C_(r)(-(2)/(x^(2)))^(r)(sqrt(x))^(16-r)`
`T_(r+1)=` .^(16)C_(r)(-2)^(r)(x)^((16-5r)/(2))`
(i). `(16-5r)/(2)=0`
(2). For Coeff of `x^(3).16-5r=6`
`r=2`
`impliesr=(16)/(5)`
`T_(3)= .^(16)C_(2)(-2)^(2)=480`