The energy emitted per second by a black body at $27^{\circ}C$ is $10 \ J$. If the temperature of the black body is increased to $327^{\circ}C$,the energy emitted per second will be ......... $J$.

An iron rod is placed parallel to a magnetic field of intensity $2000 \ A \ m^{-1}$. The magnetic flux through the rod is $6 \times 10^{-4} \ Wb$ and its cross-sectional area is $3 \ cm^2$. The magnetic permeability of the rod in $Wb \ A^{-1} \ m^{-1}$ is:

$A$ very small hole in an electric furnace is used for heating metals. The hole nearly acts as a black body. The area of the hole is $200 ~mm^2$. To keep a metal at $727^{\circ} C$,the heat energy flowing through this hole per second,in joules,is $\left(\sigma = 5.67 \times 10^{-8} ~W m^{-2} K^{-4}\right)$.

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

In an $ac$ circuit,the instantaneous values of e.m.f. and current are $e = 200 \sin(314t) \text{ V}$ and $i = \sin(314t + \frac{\pi}{3}) \text{ A}$. The average power consumed in watt is

$\int(x+1)^2 e^x d x$ is equal to