The number of ways of arranging $8$ men and $4$ women around a circular table such that no two women can sit together is

Which of the following has the largest population in a food chain?

If $(2,-1,3)$ is the foot of the perpendicular drawn from the origin to the plane,then the equation of the plane is

Two equal resistances when connected in series to a battery,consume electric power of $60 \ W$. If these resistances are now connected in parallel combination to the same battery,the electric power consumed will be............. $W$

$A$ photoelectric surface is illuminated successively by monochromatic light of wavelengths $\lambda$ and $\frac{\lambda}{2}$. If the maximum kinetic energy of the emitted photoelectrons in the second case is $3$ times that in the first case,the work function of the surface is:

If $X$ is a Poisson variate such that $\alpha = P(X=1) = P(X=2)$,then $P(X=4)$ is equal to