Question

Assertion (A) : The coefficient of $x^{-2}$ in the expansion of $(x^2+\frac{1}{x}{)}^5$ is equal to ${}^5{C}_4$
Reason (R) : The value of r for the above expansion is 3.

• A. Both A and R are true and R is the correct explanation of A
• B. Both A and R are true and R is not the correct explanation of A
• C. A is true, but R is false
• D. A is false, but R is true

Answer 1

The correct option is C A is true, but R is false

For $(x^2-x^{-1}{)}^5$,
$T_{r+1}={}^5{C}_r{x}^{10-3r}$ ...(i)
For the coefficient of $x^{-2}$
$10-3r=-2$
$3r=12$
$r=4$
Substituting in equation (i)
$T_5={}^5{C}_4$