A black body has maximum wavelength ' $\lambda_{\mathrm{m}}$ ' at temperature 2000 K . Its maximum wavelength at 3000 K will be

The moment of inertia of a thin uniform rod of mass ' $M$ ' and length ' $L$ ', about an axis perpendicular to length of the rod and at a distance ' $L / 4$ ' from one end is

The potential difference across the 4 capacitor in the following circuit is

The relation between efficiency $(\eta)$ of Carnot engine and coefficient of performance $\left(\eta_1\right)$ of refrigerator is