Let $f(x) = \frac{2\sin^2 x - 1}{\cos x} + \frac{\cos x(2\sin x + 1)}{1 + \sin x}$. Then find $\int e^x (f(x) + f'(x)) dx$ (where $c$ is the constant of integration).

Let $n_e$ be the number density of electrons and $v_d$ be the drift velocity in a semiconductor. When the temperature is increased:

$A$ ball is dropped from a height of $20 \ m$ above the surface of water in a lake. The refractive index of water is $4/3$. $A$ fish inside the lake, in the line of fall of the ball, is looking at the ball. At an instant, when the ball is $12.8 \ m$ above the water surface, the fish sees the speed of the ball as ........ $m/s$ $[g = 10 \ m/s^2.]$

Which one of the following is not a second messenger in hormone action?

$\int_{-1}^1 (a x^3 + b x) d x = 0$ for

The image of the line $x+y-2=0$ in the $y$-axis is