A monochromatic beam of light is incident at 60$$^\circ$$ on one face of an equilateral prism of refractive index n and emerges from the opposite face making an angle $$\theta$$(n) with the normal (see figure). For n = $$\sqrt 3 $$ the value of $$\theta$$ is 60$$^\circ$$ and $${{d\theta } \over {dn}} = m$$. The value of m is

In the following circuit, the current through the resistor R(=2$$\Omega$$) is I amperes. The value of I is :

An electron in an excited state of Li²⁺ ion has angular momentum $${{3h} \over {2\pi }}$$. The de Broglie wavelength of the electron in this state is p$$\pi$$a₀ (where a₀ is the Bohr radius). The value of p is

A large spherical mass M is fixed at one position and two identical masses m are kept on a line passing through the centre of M (see figure). The point masses are connected by a rigid massless rod of length l and this assembly is free to move along the line connecting them.


All three masses interact only through their mutual gravitational interaction. When the point mass nearer to M is at a distance r = 3l from M the tension in the rod is zero for m = $$k\left( {{M \over {288}}} \right)$$. The value of k is