A rectangular black body of temperature $127^{\circ} \mathrm{C}$ has surface area $4 \mathrm{~cm} \times 2 \mathrm{~cm}$ and rate of radiation is E . If its temperature is increased by $400^{\circ} \mathrm{C}$ and surface area is reduced to half of the initial value then the rate of radiation is

The reactance of a capacitor is $\mathrm{X}_{\mathrm{C}}$. If the frequency and the capacitance are doubled, then the new reactance will be

Two discs of moment of inertia ' $\mathrm{I}_1$ ' and ' $\mathrm{I}_2$ ' and angular speeds ' $\omega_1$ ' and ' $\omega_2$ ' are rotating along the collinear axes passing through their centre of mass and perpendicular to their plane. If the two discs are made to rotate together along the same axis. The rotational kinetic energy of the system will be