The mean of four observations is $3$. If the sum of the squares of these observations is $48$,then their standard deviation is

Three positive charges of equal value $q$ are placed at the vertices of an equilateral triangle. The resulting lines of force should be sketched as in

$A$ rod of length $L$ is held vertically on a smooth horizontal surface. The top end of the rod is given a gentle push. At a certain instant of time,when the rod makes an angle $\theta$ with the horizontal,the velocity of the $COM$ of the rod is $v_0$. The velocity of the end of the rod in contact with the surface at that instant is:

Two simple harmonic motions are represented by $y_{1} = 5[\sin 2 \pi t + \sqrt{3} \cos 2 \pi t]$ and $y_{2} = 5 \sin (2 \pi t + \frac{\pi}{4})$. The ratio of their amplitudes is

Which of the following methods uses a rotary shaker?

In the given $LCR$ circuit,the voltage across the terminals of the resistance and the current in the circuit will be: