List of top Questions asked in MHT CET

Volume of a gas at NTP is \( 1.12 \times 10^{-7} \, \text{cm}^3 \). The number of molecules in it is:

If the length of the body diagonal of a FCC unit cell is \( x \, \text{Å} \), the distance between two octahedral voids in the cell in \( \text{Å} \) is:

A battery of \( 6 \, \text{V} \) is connected to the circuit as shown below. The current \( I \) drawn from the battery is:

The electrostatic potential due to an electric dipole at a distance \( r \) varies as:

A closed organ pipe (closed at one end) is excited to support the third overtone. It is found that air in the pipe has:

If \( M \) is the mass of water that rises in a capillary tube of radius \( r \), then the mass of water which will rise in a capillary tube of radius \( 2r \) is:

A big drop is formed by coalescing 1000 small droplets of water. The surface energy will become:

An electric field is given by \( \vec{E} = (6\hat{i} + 5\hat{j} + 3\hat{k}) \, \text{N/C} \). The electric flux through a surface area \( 30\hat{i} \, \text{m}^2 \) lying in the YZ-plane (in SI units) is:

\( \sigma \) is the uniform surface charge density of a thin spherical shell of radius \( R \). The electric field at any point on the surface of the spherical shell is:

The velocity of sound in a gas in which two wavelengths \( 4.08 \, \text{m} \) and \( 4.16 \, \text{m} \) produce 40 beats in 12 seconds will be:

A liquid is allowed to flow into a tube of truncated cone shape. Identify the correct statement:

When two soap bubbles of radii \( a \) and \( b \) (\( b>a \)) coalesce, the radius of curvature of the common surface is:

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 logic performed by the circuit shown in the figure is equivalent to:

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:

If \( n \) is the number density and \( d \) is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e., mean free path) is represented by:

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: