Question

If $\left[x\right]$ denotes the integral part of $x$ and $m=\left[\frac{|x|}{1+x^2}\right],n=$ integral value of $\frac{1}{2-\sin 3x}$ then

• A. $(n+1{)}^{m+1}=16$
• B. $(n+1{)}^{m+1}=9$
• C. $(n+1{)}^{m+1}=4$
• D. $(n+1{)}^{m+1}=2$

Answer 1

Answer: (A)

$(n+1{)}^{m+1}=16$

Given that

$m=\left[\frac{\left|x\right|}{1+x^2}\right]$

$n=\int \frac{1}{2\sin 3x}dx$

$={\left(n+1\right)}^{m+1}$

$=16$

Hence, the option $\left(A\right)$ is correct answer.