Question

Assertion (A) : The coefficient of $x^7$ in $(\frac{x^2}{2}-\frac{2}{x}{)}^9$ is zero

Reason (R) : $r$ in $t_{r+1}$ that contains coefficient of $x^7$ is not positive integer

• 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 A Both A and R are true and R is the correct explanation of A

$(\frac{x^2}{2}-2x^{-1}{)}^9$
$T_{r+1}=(-1{)}^r{}^9{C}_r{x}^{18-3r}{2}^{2r-9}$
For the coefficient of $x^7$,
$18-3r=7$
$3r=11$
$r=\frac{11}{3}$
Since, the value of $r$ for the coefficient of $x^7$ is not a positive integer. Hence, the coefficient of $x^7$ is zero.