List of top Questions asked in MHT CET

A series LCR circuit is subjected to an AC signal of $ 200 \, \text{V}, 50 \, \text{Hz} $. If the voltage across the inductor ($ L = 10 \, \text{mH} $) is $ 31.4 \, \text{V} $, then the current in this circuit is:

The mass of proton, neutron, and helium nucleus are respectively $ 1.0073 \, \text{u}, 1.0087 \, \text{u}, \, 4.0015 \, \text{u} $. The binding energy of the helium nucleus is:

A particle performs simple harmonic motion with amplitude $ A $. Its speed is tripled at the instant that it is at a distance $ \frac{2A}{3} $ from the equilibrium position. The new amplitude of the motion is:

The difference between threshold wavelengths for two metal surfaces $ A $ and $ B $ having work functions $ \phi_A = 9 \, \text{eV} $ and $ \phi_B = 4.5 \, \text{eV} $ is: \[ \text{(Given: } h c = 1242 \, \text{eV nm)} \]

In an a.c. circuit, voltage and current are given by: \[ V = 100 \sin(100t) \, \text{V} \quad \text{and} \quad I = 100 \sin\left(100t + \frac{\pi}{3}\right) \, \text{mA}. \] The average power dissipated in one cycle is:

A mixture of one mole of monoatomic gas and one mole of diatomic gas (rigid) are kept at room temperature ($ 27^\circ \text{C} $). The ratio of specific heat of gases at constant volume respectively is:

For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through $ O $ (the center of mass) and $ O' $ (corner point) is:

In a coil, the current changes from $ -2 \, \text{A} $ to $ +2 \, \text{A} $ in $ 0.2 \, \text{s} $ and induces an emf of $ 0.1 \, \text{V} $. The self-inductance of the coil is:

Eight equal drops of water are falling through air with a steady speed of $ 10 \, \text{cm/s} $. If the drops coalesce, the new velocity is:

A particle is executing Simple Harmonic Motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be:

In an unbiased $ p$-$ n $ junction, electrons diffuse from $ n$-region to $ p$-region because:

Two identical particles each of mass $ m $ go around a circle of radius $ a $ under the action of their mutual gravitational attraction. The angular speed of each particle will be:

Two vessels $ A $ and $ B $ are of the same size and are at the same temperature. Vessel $ A $ contains $ 1 \, \text{g} $ of hydrogen and vessel $ B $ contains $ 1 \, \text{g} $ of oxygen. $ P_A $ and $ P_B $ are the pressures of the gases in $ A $ and $ B $ respectively. Then $ \frac{P_A}{P_B} $ is:

A steel wire with mass per unit length $ 7.0 \times 10^{-3} \, \text{kg/m} $ is under a tension of $ 70 \, \text{N} $. The speed of transverse waves in the wire will be:

A current-carrying rectangular loop PQRS is made of uniform wire. The length PR = QS = $ 5 \, \text{cm} $ and PQ = RS = $ 100 \, \text{cm} $. If the ammeter current reading changes from $ I $ to $ 2I $, the ratio of magnetic forces per unit length on the wire PQ due to wire RS in the two cases respectively $ F^{I}_{PQ} : F^{2I}_{PQ} $ is:

The ratio of the mass densities of nuclei of $ ^{40}\text{Ca} $ and $ ^{16}\text{O} $ is close to:

An ice cube has a bubble inside. When viewed from one side, the apparent distance of the bubble is $ 12 \, \text{cm} $. When viewed from the opposite side, the apparent distance of the bubble is $ 4 \, \text{cm} $. If the side of the ice cube is $ 24 \, \text{cm} $, the refractive index of the ice cube is:

A proton, an electron, and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as:

A solid metallic cube having total surface area $ 24 \, \text{m}^2 $ is uniformly heated. If its temperature is increased by $ 10^\circ \, \text{C} $, calculate the increase in volume of the cube.
$ \text{(Given: } \alpha = 5.0 \times 10^{-4} \, \text{C}^{-1} \text{)} $

The magnetic flux through a coil perpendicular to its plane is varying according to the relation $ \phi = 5t^3 + 4t^2 + 2t - 5 $. If the resistance of the coil is $ 5 \, \Omega $, then the induced current through the coil at $ t = 2 \, \text{sec} $ will be:

The value of acceleration due to gravity at Earth's surface is $ 9.8 \, \text{m/s}^2 $. The altitude above its surface at which the acceleration due to gravity decreases to $ 4.9 \, \text{m/s}^2 $ is close to: (Radius of Earth $ R = 6.4 \times 10^6 \, \text{m} $)

A current of $ 200 \, \mu\text{A} $ deflects the coil of a moving coil galvanometer through $ 60^\circ $. The current to cause deflection through $ \frac{\pi}{10} \, \text{radian} $ is:

A monkey of mass 50 kg climbs on a rope which can withstand the tension $ T = 350 \, \text{N} $. If the monkey initially climbs down with an acceleration of $ 4 \, \text{m/s}^2 $ and then climbs up with an acceleration of $ 5 \, \text{m/s}^2 $, choose the correct option ($ g = 10 \, \text{m/s}^2 $):

Light emerges out of a convex lens when a source of light is kept at its focus. The shape of the wavefront of the light is:

A real gas within a closed chamber at $ 27^\circ \text{C} $ undergoes the cyclic process as shown in the figure. The gas obeys the equation $ PV^3 = RT $ for the path A to B. The net work done in the complete cycle is (assuming $ R = 8 \, \text{J/molK} $):