CUET Mathematics Mock Test - 4

What is $\int e^x\left(\sqrt{x}+\frac{1}{2\sqrt{x}}\right)dx$ equal to?

The area enclosed between the curves $y^2=x$ and $y=|x|$ is:

Let $f$ be a differentiable function such that $f(1)=2$ and $f^{\prime }(x)=f(x)$ for all $x\in \mathbb{R}$. If $h(x)=f(f(x))$, then $h^{\prime }(1)$ is equal to:

The plane $2x-3y+6z-11=0$ makes an angle ${\sin }^{-1}(\alpha )$ with the X-axis. The value of $\alpha$ is equal to:

The magnitude of the projection of the vector $2\hat{i}+3\hat{j}+\hat{k}$ on the vector perpendicular to the plane containing the vectors $\hat{i}+\hat{j}+\hat{k}$ and $\hat{i}+2\hat{j}+3\hat{k}$ is: