A magnetic compass needle oscillates 30 times per minute at a place where the dip is 45^o, and 40 times per minute where the dip is 30^o. If B₁ and B₂ are respectively the total magnetic field due to the earth at the two places, then the ratio $${{{B_1}} \over {{B_2}}}$$ is best given by :

Which of the following combinations has the dimension of electrical resistance ($$ \in $$₀ is the permittivity of vacuum and $$\mu $$₀ is the permeability of vacuum)?

The transfer characteristic curve of a transistor, having input and output resistance 100 $$\Omega $$ and 100 k$$\Omega $$ respectively is shown in the figure. The voltage and power gain, are respectively:

When M₁ gram of ice at –10^oC (specific heat = 0.5 cal g^{–1 o}C^–1 ) is added to M₂ gram of water at 50C, finally no ice is left and the water is at 0°C. The value of latent heat of ice, in cal g^–1 is :