Question

If $(n+2)!=2550\times n!$then the value of $n$ is equal to

• A. $48$
• B. $49$
• C. $50$
• D. $51$
• E. $52$

Answer 1

The correct option is B

$49$

Explanation for correct option

Given that $(n+2)!=2550\times n!$

$$\begin{gathered} \Rightarrow \frac{(n+2)!}{\left(n\right)!}=2550 \\ \Rightarrow \left(n+1\right)\left(n+2\right)=2550 \\ \Rightarrow n^2+3n+2=2550 \\ \Rightarrow n^2+3n-2548=0 \\ \Rightarrow n^2-49n+52n-2548=0 \\ \Rightarrow n\left(n-49\right)+52\left(n-49\right)=0 \\ \Rightarrow \left(n-49\right)\left(n+52\right)=0 \\ \therefore n=49,-52 \end{gathered}$$

Hence option(B) i.e. $49$ is correct