If the mean and variance of eight numbers 3, 7, 9, 12, 13, 20, x and y be 10 and 25 respectively, then x.y is equal to _______.

If the function ƒ defined on $$\left( { - {1 \over 3},{1 \over 3}} \right)$$ by

f(x) = $$\left\{ {\matrix{ {{1 \over x}{{\log }_e}\left( {{{1 + 3x} \over {1 - 2x}}} \right),} & {when\,x \ne 0} \cr {k,} & {when\,x = 0} \cr } } \right.$$

is continuous, then k is equal to_______.

An electron (of mass m) and a photon have the same energy E in the range of a few eV. The ratio of the de-Broglie wavelength associated with the electron and the wavelength of the photon is (c = speed of light in vaccuum)

The activity of a radioactive sample falls from 700 s^–1 to 500 s^–1 in 30 minutes. Its half life is close to: