Two stars are 10 light years away from the earth. They are seen through a telescope of objective diameter 30 cm. The wavelength of light is 600 nm. To see the stars just resolved by the telescope, the minimum distance between them should be (1 light year = 9.46 $$ \times $$ 10¹⁵ m) of the order of :

A neutron moving with a speed ‘v’ makes a head on collision with a stationary hydrogen atom in ground state. The minimum kinetic energy of the neutron for which inelastic collision will take place is :

A modulated signal C_m(t) has the form C_m(t) = 30 sin 300 $$\pi $$t + 10 (cos 200 $$\pi $$t −cos 400 $$\pi $$t). The carrier frequency c, the modulating frequency (message frequency) f_{$$\omega $$}, and the modulation index $$\mu $$ are respectively given by :

A particle of mass m is acted upon by a force F given by the empirical law F =$${R \over {{t^2}}}\,v\left( t \right).$$ If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot :