$\frac{d}{dx}{\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^2} = $

The ionization potential of a hydrogen atom is $13.6 \ eV$. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy $12.1 \ eV$. The number of spectral lines emitted by the hydrogen atoms according to Bohr's theory will be

$A$ ray of light is incident on the hypotenuse of a right-angled prism after travelling parallel to the base inside the prism. If $\mu$ is the refractive index of the material of the prism,the maximum value of the base angle for which light is totally reflected from the hypotenuse is

$A$ galvanometer,having a resistance of $50 \Omega$,gives a full-scale deflection for a current of $0.05 \text{ A}$. The length in metres of a resistance wire of cross-sectional area $2.97 \times 10^{-2} \text{ cm}^2$ that can be used to convert the galvanometer into an ammeter which can read a maximum of $5 \text{ A}$ current is: (Specific resistance of the wire $= 5 \times 10^{-7} \Omega\text{-m}$)

What is the total number of orbitals associated with the principal quantum number $n=3$?

An unpolarised light is incident at an interface of two dielectric media having refractive indices of $2$ (incident medium) and $2 \sqrt{3}$ (medium) respectively. To satisfy the condition that reflected and refracted rays are perpendicular to each other, the angle of incidence is . . . . . . .