The minimum force required to move a body up an inclined plane is three times the minimum force required to prevent it from sliding down the plane. If the coefficient of friction between the body and the inclined plane is $\frac{1}{2 \sqrt{3}}$,then the angle of the inclined plane is (in $^{\circ}$)

$A$ sound source is moving towards a stationary observer with $(1/10)$ of the speed of sound. The ratio of apparent to real frequency is .........

The energy of an electron in the $n^{th}$ orbit of a hydrogen atom is expressed as $E_n = \frac{-13.6}{n^2} \text{ eV}$. The shortest and longest wavelengths of the Lyman series are:

Assume that the nuclear binding energy per nucleon $(B/A)$ versus mass number $(A)$ is as shown in the figure. Use this plot to choose the correct choice$(s)$ given below:
$(A)$ Fusion of two nuclei with mass numbers lying in the range of $1 < A < 50$ will release energy.
$(B)$ Fusion of two nuclei with mass numbers lying in the range of $51 < A < 100$ will release energy.
$(C)$ Fission of a nucleus lying in the mass range of $100 < A < 200$ will release energy when broken into two equal fragments.
$(D)$ Fission of a nucleus lying in the mass range of $200 < A < 260$ will release energy when broken into two equal fragments.

The value of $\sum_{n=0}^{\infty}\left(\frac{2 i}{3}\right)^n$ is

The maximum velocity of electrons emitted from a metal surface is $V$ when the frequency of light falling on it is $f$. What is the maximum velocity when the frequency becomes $4f$?