Calculate the surface temperature of the planet,if the energy radiated by unit area in unit time is $5.67 \times 10^4 \, W$. (Assume the planet is a black body).

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

If the equation of the locus of a point equidistant from the points $(a_1, b_1)$ and $(a_2, b_2)$ is $(a_1 - a_2)x + (b_1 - b_2)y + c = 0$,then the value of $c$ is

$A$ conducting rod $PQ$ of length $5\,m$ oriented as shown in the figure is moving with a velocity $\vec{v} = (2\,m/s)\hat{i}$ without any rotation in a uniform magnetic field $\vec{B} = (3\hat{j} + 4\hat{k})\,T$. The induced $EMF$ in the rod is........$V$.

Two bodies have their moments of inertia $I$ and $2I$ respectively about their axis of rotation. If their kinetic energies of rotation are equal,their angular momenta will be in the ratio

An atomic power nuclear reactor can deliver $300\, MW$. The energy released due to fission of each nucleus of uranium atom $^{235}U$ is $170\, MeV$. The number of uranium atoms fissioned per hour will be