Question

Let $a=\underset{x\to 1}{\mathrm{Lim}}\frac{x}{\ln x}-\frac{1}{x\ln x};b=\underset{x\to 0}{\mathrm{Lim}}\frac{x^3-16x}{4x+x^2};c=\underset{x\to 0}{\mathrm{Lim}}\frac{\ln (1+\sin x)}{x}$ and $d=\underset{x\to -1}{\mathrm{Lim}}\frac{(x+1{)}^3}{3(\sin (x+1)-(x+1))}$, then the matrix $\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$ is

• A. Idempotent
• B. Involutary
• C. Non singular
• D. Nilpotent

Answer 1

Answer: (D)

Correct answer is (d) Nilpotent