Ball $P$ of mass $m$ moving with velocity $\text{'}v\text{'}$ collides with another ball $Q$ of mass $2 \mathrm{m},$ at rest. If $v_P$ and $v_Q$ are the final velocities of $P$ and $Q$ respectively, after collision, then
(Assume the coefficient of restitution is $1/3$)

A small ball is thrown at an angle \(45^{\circ}\) to the horizontal with an initial velocity of \(2 \sqrt{2} \mathrm{~m} / \mathrm{s}\). The magnitude of mean velocity averaged over the first \(2 \mathrm{~s}\) is [talse, acceleration due to gravity, \(g=10 \mathrm{~m} / \mathrm{s}^2\) ]

In Young's double slit interference experiment the wavelength of light used is \(6000 Å\). If the path difference between waves reaching a point \(P\) on the screen is 1.5 microns, then at that point \(P\).

Water is pumped steadily out of a flooded basement, at the speed of $10 \mathrm{m} {\mathrm{s}}^{-1}$ through a hose (tube) of radius, $1 \mathrm{cm},$ passing through a window, $3 \mathrm{m}$ above the water level. The power of the pump is (Assume $g=10 \mathrm{m} {\mathrm{s}}^{-2}$, density of water $=1000 \mathrm{kg} {\mathrm{m}}^{-3}$)

A laser beam is operating at \(100 \mathrm{~mW}\). The amount of energy stored by \(90 \mathrm{~cm}\) length of this laser beam will be

Assertion (A) Electromagnetic force is enormously strong as compared to gravitational force. Yet, gravity dominates in the large-scale phenomena (e.g. formation of galaxies). Reason \((R)\) Existence of positive and negative charges make matter mostly electrically neutral. Which of the following is true?

The maximum length of water column that can stay without falling in a vertically held capillary tube of diameter 1 mm and open at both the ends is
(Acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\) and surface tension of water \(=0.07 \mathrm{Nm}^{-1}\) )

A very long wire carrying a current \(4 \sqrt{2} \mathrm{~A}\) is bent at a right angles. The magnitude of magnetic field ( \(|\mathbf{B}|)\) at a point \(P\) lying on a line perpendicular to the bent wire at a distance, \(d=20 \mathrm{~cm}\) from the point of the bending will be (Let \(\mu_0=4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}\) )

Two identical bar magnets of magnetic moment \(M\) each, are placed along \(X\) and \(Y\)-axes, respectively at a distance \(d\) from the origin (as shown in the figure). The origin lies on perpendicular bisector of magnet placed on \(X\)-axis and on the magnetic axis of magnet placed on \(Y\)-axis. If the magnitude of total magnetic field at the origin is \(B=\alpha\left[\frac{\mu_0}{4 \pi} \frac{M}{d^3}\right]\), then the value of constant \(\alpha\) will be \(\langle d>>l\), where \(l\) is the length of the bar magnets and direction of \(\mathrm{N}\) to \(\mathrm{S}\) in magnets is opposite with respect to each other)

In atomic scale the weakest force in nature is

The ratio of the kinetic energies of the electrons in the third and fourth excited states of hydrogen atom is

The tyre of a motor car contains air at \(15^{\circ} \mathrm{C}\). If the temperature increases to \(35^{\circ} \mathrm{C}\), the approximate percentage increase in pressure is (ignore to expansion of tyre)

A coil has 1000 turns and \(500 \mathrm{~cm}^2\) as its area. The plane of the coil is placed at right angles to a magnetic induction field of \(2 \times 10^{-5} \mathrm{~Wb} / \mathrm{m}^2\). The coil is rotated through \(180^{\circ}\) in \(0.2 \mathrm{~s}\). The average emf induced in the coil, in \(\mathrm{mV}\), is