AIEEE 2011 PYQ Mock Test

Let $A$ and $B$ be two symmetric matrices of order $3$.Statement-1 : $ABA$ and $A{B}^{2}A$ are symmetric matrices.Statement-2 : $AB$ is a symmetric matrix if matrix multiplication of $A$ and $B$ is commutative.

If $\omega \ne 1$ is a cube root of unity, and $(1+{\omega }^2{)}^7=A+B\omega$. Then $(A,B)$ equals:

The values of $p$ and $q$ for which the function
$$f(x)=\{\begin{array}{ll}\frac{\sin (p+1)x+\sin x}{x},& x<0\\ q,& x=0\\ \frac{\sqrt{x+x^2}-\sqrt{x}}{x^{3/2}},& x>0\end{array}$$
is continuous for all $x$ in $\mathbb{R}$, are:

The area of the region enclosed by the curves $y=x$, $x=e$, $y=1/x$ and the positive $x$ -axis is:

For $x\in (0,5\pi /2)$, define $f(x)={\int }_0^{x}t\sin tdt$. Then $f$ has: