For a binomial variate $X$,if $n=4$ and $P(X=4)=6 P(X=2)$,then the value of $p$ is

$\frac{d}{d x}\left[a \tan ^{-1} x+b \log \left(\frac{x-1}{x+1}\right)\right]=\frac{1}{x^4-1}$
$\Rightarrow a-2 b$ is equal to

An electron accelerated through a potential difference $V$ enters a uniform transverse magnetic field and experiences a force $F$. If the accelerating potential is increased to $2V$,the electron in the same magnetic field will experience a force:

$A$ $x : 1$ molar mixture of $He$ and $CH_4$ is contained in a vessel at $20 \ bar$ pressure. Due to a hole in the vessel,the gas mixture leaks out. If the composition of the mixture effusing out initially is $8 : 1$,then the value of $x$ will be

Which type of chromosome is represented in the given figure?

If $g(x) = \int_0^x \cos^4 t \, dt$,then $g(x + \pi)$ equals