If $\tanh ^{-1} x = a \log \left(\frac{1+x}{1-x}\right)$,$|x| < 1$,then $a$ is equal to

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

The figure shows wave fronts in still water,moving in the direction of the arrow towards the interface $PQ$ between a shallow region and a deep (denser) region. Which of the lines shown may represent one of the wave fronts in the deep region?

The area (in sq. units) of the region described by $\{(x,y): y^2 \le 2x \text{ and } y \ge 4x - 1\}$ is

Which of the following inhibits leaf abscission?

In the circuit given below,$V(t)$ is the sinusoidal voltage source. The voltage drop $V_{AB}(t)$ across the resistance $R$ is: