An inclined plane makes an angle $30^{\circ}$ with horizontal. A solid sphere rolls down from the top of the inclined plane from rest without slipping has a linear acceleration along the plane equal to (where $g$ is acceleration due to gravity) (given $\sin 30^{\circ}=0.5$)

An ink mark is made on a piece of paper. A glass slab of thickness ' $t$ ' is placed on it. The ink mark appears to be raised up through a distance ' $x$ ' when viewed at nearly normal incidence. If the refractive index of material of glass slab is ' $\mu$ ' then thickness of glass slab ' $t$ ' is given by

The ratio of energies of photons produced due to transition of electron of hydrogen atom from its (a) second to first energy level and (b) highest energy level to second level is

The magnetic flux near the axis and inside the air core solenoid of length 80 cm carrying current ' I ' is $1.57 \times 10^{-6} \mathrm{~Wb}$. Its magnetic moment will be [cross-sectional area of a solenoid is very small as compared to its length, $\mu_0=4 \pi \times 10^{-7}$ SI unit $](\pi=3.14)$