41 tuning forks are arranged in increasing order of frequency such that each produces 5 beats/second with next tuning fork. If frequency of last tuning fork is double that of frequency of first fork. Then frequency of first and last fork is

In two separate setups for Biprism experiment using same wavelength, fringes of equal width are obtained. If ratio of slit separation is $$2: 3$$ then the ratio of the distance between the slit and screen in the two setups is

A composite slab consists of two materials having coefficient of thermal conductivity $$\mathrm{K}$$ and $$2 \mathrm{~K}$$, thickness $$\mathrm{x}$$ and $$4 \mathrm{x}$$ respectively. The temperature of the two outer surfaces of a composite slab are $$\mathrm{T}_2$$ and $$\mathrm{T}_1\left(\mathrm{~T}_2 > \mathrm{T}_1\right)$$. The rate of heat transfer through the slab in a steady state is $$\left[\frac{\mathrm{A}\left(\mathrm{T}_2-\mathrm{T}_1\right) \mathrm{K}}{\mathrm{x}}\right] \cdot \mathrm{f}$$ where '$$\mathrm{f}$$' is equal to

A black sphere has radius '$$R$$' whose rate of radiation is '$$E$$' at temperature '$$T$$'. If radius is made $$R / 3$$ and temperature '$$3 T$$', the rate of radiation will be