Question

If the sum of the coefficients of $x^7$ and $x^4$ in the expansion of ${(\frac{x^2}{a}-\frac{b}{x})}^{11}$ is zero, then

• A. ab = -1
• B. ab = 1
• C. a + b = 0
• D. a = b

Answer 1

The correct option is B ab = 1

$Co-efficientof{x}^7={{}^{11}C}_5\frac{(-b{)}^5}{a^6}Co-efficientof{x}^4={{}^{11}C}_6\frac{(-b{)}^6}{a^5}Given{{}^{11}C}_5\frac{(-b{)}^5}{a^6}+{{}^{11}C}_6\frac{(-b{)}^6}{a^5}=0\Rightarrow \frac{1}{a}=b\Rightarrow ab=1$