The resistive network shown below is connected to a D.C. source of 16 V. The power consumed by the network is 4 Watt. The value of R is:

The value of numerical aperature of the objective lens of a microscope is 1.25. If light of wavelength 5000 $$\mathop A\limits^o $$ is used, the minimum separation between two points, to be seen as distinct, will be :

In a double slit experiment, when a thin film of thickness t having refractive index $$\mu $$. is introduced in front of one of the slits, the maximum at the centre of the fringe pattern shifts by one fringe width. The value of t is ($$\lambda $$ is the wavelength of the light used) :

A person of mass M is, sitting on a swing of length L and swinging with an angular amplitude $$\theta $$₀. If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his center of mass moves by a distance $$\ell $$($$\ell $$ << L), is close to;