$\int_0^{\pi / 2} \frac{d x}{1+\tan ^3 x}$ is equal to :

For $|x| < 1$,the constant term in the expansion of $\frac{1}{(x-1)^2(x-2)}$ is

Let $f: R \rightarrow R$ be defined by $f(x) = \begin{cases} x+2, & x \leq -1 \\ x^2, & -1 < x < 1 \\ 2-x, & x \geq 1 \end{cases}$. Then the value of $f(-1.75) + f(0.5) + f(1.5)$ is

The line $x=\frac{\pi}{4}$ divides the area of the region bounded by $y=\sin x$,$y=\cos x$ and the $x$-axis $(0 \leq x \leq \frac{\pi}{2})$ into two regions of areas $A_1$ and $A_2$. Then $A_1 : A_2$ equals (in $: 1$)

If the amplitude of $z - 2 - 3i$ is $\pi / 4$,then the locus of $z = x + iy$ is

If a $p-n$ junction is forward biased,then which of the following figures gives the correct direction of current inside the semiconductor?