List of top Questions asked in MET- 2015

Two wires of same lengths are shaped into a square and a circle. If they carry same current, then the ratio of their magnetic moments is

The time constant of L-R circuit is

In wave mechanics, the angular momentum of an electron is given by

A rectangular glass slab ABCD of refractive index \(n_1\) is immersed in water of refractive index \(n_2\) \((n_1>n_2)\). A ray of light is incident at the surface AB of the slab as shown. The maximum value of the angle of incidence \(\alpha_{\max}\) such that the ray comes out only from the another surface CD is given by

Under what conditions current passing through the resistance \(R\) can be increased by short circuiting the battery of emf \(E_2\)? The internal resistances of the two batteries are \(r_1\) and \(r_2\) respectively.

In a nuclear reactor, \(^{235}\text{U}\) undergoes fission liberating 200 MeV of energy. The reactor has a 10% efficiency and produces 1000 MW power. If the reactor is to function for 10 yr, then find the total mass of uranium required.

A sinusoidal wave travelling in the positive direction on stretched string has amplitude 20 cm, wavelength 1 m and wave velocity 5 m/s. At \(x = 0\) and \(t = 0\), it is given that \(y = 0\) and \(\dfrac{dy}{dt}<0\). Find the wave function \(y(x,t)\).

A capacitor of capacitance \(10\mu\text{F}\) is charged to potential 50 V with a battery. The battery is now disconnected and an additional charge \(200\mu\text{C}\) is given to the positive plate of the capacitor. The potential difference across the capacitor will be

The following configuration of gate is equivalent to

The two blocks of masses \(m_1\) and \(m_2\) are kept on a smooth horizontal table as shown. Block of mass \(m_1\) but not \(m_2\) is fastened to the spring. If now both the blocks are pushed to the left, so that the spring is compressed at a distance \(d\). The amplitude of oscillation of block of mass \(m_1\) after the system is released, is

Two coils have mutual inductance 0.005 H. The current changes in the first coil according to equation \(I = I_0 \sin \omega t\), where \(I_0 = 10\text{ A}\) and \(\omega = 100\pi\text{ rad/s}\). The maximum value of emf in the second coil is

A coil in the shape of an equilateral triangle of side \(l\) is suspended between the pole pieces of a permanent magnet such that \(\mathbf{B}\) is in the plane of the coil. If due to current \(i\) in the triangle, a torque \(\tau\) acts on it. The side \(l\) of the triangle is

A ball is projected from the point O with velocity 20 m/s at an angle of 60° with horizontal. At highest point of its trajectory, it strikes a smooth plane of inclination 30° at point A. The collision is perfectly inelastic. The maximum height from the ground attained by the ball is

A juggler keeps on moving four balls in air throwing the balls after regular intervals. When one ball leaves his hand (speed = \(20\text{ ms}^{-1}\)), the position of other balls (height in metre) will be (take \(g = 10\text{ ms}^{-2}\))

A coil having \(n\) turns and resistance \(R\Omega\) is connected with a galvanometer of resistance \(4R\Omega\). This combination is moved in time \(t\) second from a magnetic field \(w_1\) weber to \(w_2\) weber. The induced current in the circuit is

Two moles of helium are mixed with \(n\) moles of hydrogen. The root mean square (rms) speed of gas molecules in the mixture is \(\sqrt{2}\) times the speed of sound in the mixture. Then, the value of \(n\) is

We have a galvanometer of resistance \(25\Omega\). It is shunted by \(2.5\Omega\) wire. The part of the total current that flows through the galvanometer is given as

The energy of a hydrogen atom in its ground state is \(-13.6\text{ eV}\). The energy of the level corresponding to the quantum number \(n = 5\) is

A thin film of soap solution (\(\mu_s = 1.4\)) lies on the top of a glass plate (\(\mu_g = 1.5\)). When incident light is almost normal to the plate, two adjacent reflection maxima are observed at two wavelengths 420 nm and 630 nm. The minimum thickness of the soap solution is

Two point charges \(2q\) and \(8q\) are placed at a distance \(r\) apart. Where should a third charge \(-q\) be placed between them, so that the electrical potential energy of the system is minimum?

If levels 1 and 2 are separated by an energy \(E_2 - E_1\), such that the corresponding transition frequency falls in the middle of the visible range, calculate the ratio of the populations of two levels in thermal equilibrium at room temperature.