Two particles of masses $m_1$ and $m_2$ are separated by a distance $d$. The shift in the centre of mass when the two particles are interchanged is:

The difference between the fundamental frequencies of an open pipe and a closed pipe of the same length is $100 \ Hz$. The difference between the frequencies of the second harmonic of the open pipe and the third harmonic of the closed pipe is: (in $Hz$)

The circuit shown in the following figure contains two diodes $D_1$ and $D_2$, each with a forward resistance of $50 \, \Omega$ and infinite backward resistance. If the battery voltage is $6 \, V$, find the current through the $100 \, \Omega$ resistor (in amperes).

$A$ light string fixed at one end to a clamp on the ground passes over a fixed pulley and hangs on the other side. It makes an angle of $30^{\circ}$ with the ground. $A$ monkey of mass $5 \, kg$ climbs up the rope. The clamp can tolerate a vertical force of $40 \, N$ only. The maximum acceleration in the upward direction with which the monkey can climb safely is ............ $m/s^2$ (neglect friction and take $g = 10 \, m/s^2$).

If $f(x)$ satisfies the relation $f\left( \frac{5x - 3y}{2} \right) = \frac{5f(x) - 3f(y)}{2}$ for all $x, y \in R$ and $f(0)=1, f'(0)=2$,then the period of $\sin(f(x))$ is:

In an elastic collision of two particles,which of the following quantities is conserved?