Question

if $\frac{1}{9!}+\frac{1}{10!}=\frac{x}{11!}$ , then the value of $x$ is :

• A. $11$
• B. $121$
• C. $10$
• D. $100$

Answer 1

The correct option is B $121$

We have,
$\frac{1}{9!}+\frac{1}{10!}=\frac{x}{11!}$
$\Rightarrow \frac{1}{9!}+\frac{1}{10\times 9!}=\frac{x}{11\times 10\times 9!}$
$\Rightarrow \frac{1}{9!}[1+\frac{1}{10}]=\left(\frac{x}{11\times 10}\right)\times \frac{1}{9!}$
$\Rightarrow 1+\frac{1}{10}=\frac{x}{11\times 10}$
$\Rightarrow \frac{11}{10}=\frac{x}{11\times 10}$
$\Rightarrow x=11\times 11=121$