If ${}^n{P_4} : {}^n{P_5} = 1 : 2$,then $n = $

The most general value of $\theta$ which satisfies both the equations $\tan \theta = -1$ and $\cos \theta = \frac{1}{\sqrt{2}}$ is

$A$ conducting sphere of radius $R$ carrying a charge $q$ is joined to a conducting sphere of radius $2R$ carrying a charge $-2q$. The charge flowing between them will be

The velocity $v$ reached by a car of mass $m$ at a certain distance from the starting point,driven with constant power $P$,is such that:

$A$ car travels from point $A$ to point $B$ with a speed of $40 \ km/h$ and returns from $B$ to $A$ with a speed of $60 \ km/h$. What is the average speed of the car for the entire journey (in $km/h$)?

If $\frac{3x+2}{(x+1)(2x^2+3)} = \frac{A}{x+1} + \frac{Bx+C}{2x^2+3}$, then $A+C-B$ is equal to :