In how many ways can $3$ letters be posted in $4$ letter-boxes,if all the letters are not posted in the same letter-box?

Find the derivative of the function $(x+\sec x)(x-\tan x)$.

If the tangent at point $(1, 2)$ on the curve $y = ax^2 + bx + \frac{1}{2}$ is parallel to the normal at $(-2, 2)$ on the curve $y = x^2 + 6x + 10$,then:

$\int \frac{x^{49} \tan ^{-1}\left(x^{50}\right)}{1+x^{100}} d x = k\left(\tan ^{-1}\left(x^{50}\right)\right)^2 + c$,then $k$ is equal to

If $\sin 6 \theta = 32 \cos^5 \theta \sin \theta - 32 \cos^3 \theta \sin \theta + 3x$,then $x$ is equal to:

Two capacitors $C_1 = 2 \, \mu F$ and $C_2 = 4 \, \mu F$ are connected in a circuit as shown in the figure. The potential difference $(V_A - V_B)$ is.....$V$.