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)

$T_5=24T_3$
$\therefore {}^{11}{c}_4{x}^4=24{\cdot }^{11}{c}_2{x}^2$
$\Rightarrow \frac{11\times 10\times 9\times 8}{1\times 2\times 3\times 4}{x}^4$
$=24\frac{11\times 10}{1\times 2}{x}^2$
$\Rightarrow \frac{9\times 8}{3\times 4}{x}^2=24$
$\Rightarrow x^2=\frac{24\times 3\times 4}{9\times 8}=4$