In a Young's double slit experiment, the path difference, at a certain point on the screen, between two interfering waves is $${1 \over 8}$$ th of wavelength. The ratio of the intensity at this point to that at the centre of a bright fringe is close to :

Two equal resistances when connected in series to a battery, consume electric power of 60 W. If these resistances are now connected in parallel combination to the same battery, the electric power consumed will be :

The force of interaction between two atoms is given by F = $$\alpha $$$$\beta $$exp $$\left( { - {{{x^2}} \over {\alpha kt}}} \right)$$; where x is the distance, k is the Boltzmann constant and T is temperature and $$\alpha $$ and $$\beta $$ are two constants. The dimension of $$\beta $$ is :

There are two long co-axial solenoids of same length $$l$$. The inner and outer coils have radii r₁ and r₂ and number of turns per unit length n₁ and n₂, respectively. The ratio of mutual inductance to the self - inductance of the inner-coil is :