Question

In the expansion of $(1 + x)^{11}$, the fifth term is 24 times the third term. Then the value of $x^2$ is

• A. 4
• B. 9
• C. 16
• D. 24

Answer 1

Answer: (A)

$T_{5} = 24\,T_{3}$
$\therefore \,{}^{11}c_{4}x^{4} = 24\cdot^{11}c_{2}x^{2}$
$\Rightarrow \frac{11\times10\times 9\times 8}{1\times 2\times 3\times 4}x^{4}$
$= 24 \frac{11\times 10}{1\times 2}x^{2}$
$\Rightarrow \frac{9\times 8}{3\times 4}x^{2} = 24$
$\Rightarrow x^{2} = \frac{24\times 3\times 4}{9\times 8} = 4$