The modulus and amplitude of $\frac{1 + 2i}{1 - (1 - i)^2}$ are

If $x y \neq 0, x+y \neq 0$ and $x^m y^n=(x+y)^{m+n}$, where $m, n \notin N$, then $\frac{d y}{d x}$ is equal to

The length of the perpendicular from the point $P(2, -1, 4)$ to the straight line $\frac{x+3}{10} = \frac{y-2}{-7} = \frac{z}{1}$ is:

Product $(A)$ is

$A$ horizontal pipe of non-uniform cross-section allows water to flow through it with a velocity $1 \ m/s$ when pressure is $50 \ kPa$ at a point. If the velocity of flow has to be $2 \ m/s$ at some other point,the pressure at that point should be (in $kPa$)

If $A+C=2B$,then $\frac{\cos C-\cos A}{\sin A-\sin C}$ is equal to