The excess pressure inside the first soap bubble is three times that inside the second soap bubble. The ratio of the volume of the first soap bubble to the volume of the second soap bubble is

Two soap bubbles, A and B, have radii in the ratio $3 : 2$. The excess pressure inside the bubble A to that of B is in the ratio

A black body emits radiation of maximum intensity of wavelength '$\lambda$' at temperature 'T' K. Its corresponding wavelength at temperature $(2.5T)$ K will be

In a composite slab there are two materials having coefficients of thermal conductivity K and 2K, thickness x and 4x repectively. The temperature of the two outer surfaces of a composite slab are $T_2$ and $T_1$ $(T_2 > T_1)$. $T_2$ is on side K and $T_1$ is on side 2K. The rate of heat transfer through the slab in a steady state is $\left[\dfrac{A(T_2 - T_1)K}{x}\right] \cdot f$, where f is equal to