If $A=\left(\begin{array}{cc}1 & 2 \\ 2 & -1\end{array}\right)$, then which ONE of the following is $A^8$ ?

The value of $x$ such that $x>1$, satisfying the equation $\int_1^x t \ln t d t=\frac{1}{4}$ is

Let $L, M$, and $N$ be non-singular matrices of order 3 satisfying the equations $L^2=L^{-1}, M=L^8$ and $N=L^2$. Which ONE of the following is the value of the determinant of $(M-N)$ ?

Let $P(x)$ be an arbitrary predicate over the domain of natural numbers. Which ONE of the following statements is TRUE?