MHT CET 2025 17 April Shift 2 Question Paper (Available): Download Question Paper (PCB) with Answers PDF

MHT CET 2025 April 17 Shift 2 Questions with Solutions

Question 1:

In a semiconductor, the intrinsic carrier concentration is \( 1.5 \times 10^{10} \, cm^{-3} \) at room temperature. If the energy band gap of the semiconductor is \( 1.1 \, eV \), calculate the intrinsic carrier concentration at a temperature of \( 500 \, K \). The intrinsic carrier concentration at room temperature (\( 300 \, K \)) is known to vary with temperature according to the relation: \[ n_i(T) = n_{i0} \left( \frac{T}{T_0} \right)^{3/2} \exp \left( -\frac{E_g}{2k} \left( \frac{1}{T} - \frac{1}{T_0} \right) \right) \]
Where:
- \( n_{i0} = 1.5 \times 10^{10} \, cm^{-3} \),
- \( T_0 = 300 \, K \),
- \( E_g = 1.1 \, eV \),
- \( k = 8.617 \times 10^{-5} \, eV/K \),
- \( T = 500 \, K \).

• (1) \( 3.0 \times 10^{12} \, cm^{-3} \)
• (2) \( 6.2 \times 10^{12} \, cm^{-3} \)
• (3) \( 8.5 \times 10^{13} \, cm^{-3} \)
• (4) \( 1.2 \times 10^{14} \, cm^{-3} \)

A 1.0 kg sample of water at \( 80^\circ C \) is placed in thermal contact with a 2.0 kg sample of water at \( 20^\circ C \). If the system is insulated, what will be the final equilibrium temperature of the system? Assume no heat loss to the surroundings, and the specific heat capacity of water is \( 4.18 \, J/g^\circ C \).

• (1) \( 40^\circ C \)
• (2) \( 45^\circ C \)
• (3) \( 50^\circ C \)
• (4) \( 60^\circ C \)

In an electromagnetic wave traveling in a vacuum, the electric field amplitude is \( 3.0 \times 10^3 \, V/m \). What is the magnetic field amplitude of the wave? Assume the speed of light in vacuum is \( c = 3.0 \times 10^8 \, m/s \).

• (1) \( 1.0 \times 10^{-5} \, T \)
• (2) \( 1.0 \times 10^{-3} \, T \)
• (3) \( 1.0 \times 10^{-6} \, T \)
• (4) \( 1.0 \times 10^{-4} \, T \)

A capacitor of capacitance \( 10 \,  \) is charged to a potential difference of \( 100 \, V \). What is the energy stored in the capacitor?

• (1) \( 0.5 \, J \)
• (2) \( 5.0 \, J \)
• (3) \( 50.0 \, J \)
• (4) \( 0.05 \, J \)

A photon has an energy of \( 5.0 \, eV \). What is its wavelength? (Planck's constant \( h = 6.626 \times 10^{-34} \, J \cdot s \), speed of light \( c = 3.0 \times 10^8 \, m/s \))

• (1) \( 400 \, nm \)
• (2) \( 500 \, nm \)
• (3) \( 600 \, nm \)
• (4) \( 700 \, nm \)

What is the entropy change when 1.0 kg of water at \( 100^\circ C \) is converted to steam at the same temperature? The latent heat of vaporization of water is \( 2.25 \times 10^6 \, J/kg \).

• (1) \( 2.25 \times 10^3 \, J/K \)
• (2) \( 2.25 \times 10^6 \, J/K \)
• (3) \( 2.25 \times 10^9 \, J/K \)
• (4) \( 2.25 \times 10^7 \, J/K \)

A current of \( 2.0 \, A \) is passed through a conductor for \( 10 \, minutes \). How much charge passes through the conductor?

• (1) \( 1.2 \times 10^3 \, C \)
• (2) \( 1.0 \times 10^3 \, C \)
• (3) \( 2.0 \times 10^3 \, C \)
• (4) \( 3.0 \times 10^3 \, C \)

What is the wavelength of a sound wave that has a frequency of \( 500 \, Hz \) and travels at a speed of \( 343 \, m/s \)?

• (1) \( 0.5 \, m \)
• (2) \( 1.0 \, m \)
• (3) \( 2.0 \, m \)
• (4) \( 3.0 \, m \)

A radioactive substance has a half-life of \( 10 \, hours \). If the initial amount of the substance is \( 200 \, g \), how much of the substance remains after \( 30 \, hours \)?

• (1) \( 25 \, g \)
• (2) \( 50 \, g \)
• (3) \( 100 \, g \)
• (4) \( 12.5 \, g \)

What is the pH of a solution with a hydrogen ion concentration of \( 3.0 \times 10^{-4} \, mol/L \)?

• (1) \( 3.52 \)
• (2) \( 3.00 \)
• (3) \( 4.52 \)
• (4) \( 2.52 \)

What is the molarity of a solution prepared by dissolving \( 5.0 \, g \) of sodium chloride (\( NaCl \)) in \( 250 \, mL \) of water? (Molar mass of NaCl = \( 58.5 \, g/mol \))

• (1) \( 0.34 \, M \)
• (2) \( 0.50 \, M \)
• (3) \( 1.0 \, M \)
• (4) \( 2.0 \, M \)

What is the volume of \( 1.0 \, mol \) of an ideal gas at standard temperature and pressure (STP)? (STP is \( 0^\circ C \) and \( 1.0 \, atm \), and the ideal gas constant \( R = 0.0821 \, L·atm/mol·K \))

• (1) \( 22.4 \, L \)
• (2) \( 24.0 \, L \)
• (3) \( 20.0 \, L \)
• (4) \( 25.0 \, L \)

What is the molar mass of a gas if \( 2.5 \, g \) of the gas occupies \( 1.0 \, L \) at \( 300 \, K \) and a pressure of \( 1.0 \, atm \)? (Use the ideal gas law, \( R = 0.0821 \, L·atm/mol·K \))

• (1) \( 32 \, g/mol \)
• (2) \( 28 \, g/mol \)
• (3) \( 36 \, g/mol \)
• (4) \( 44 \, g/mol \)

What is the pH of a \( 0.01 \, M \) solution of hydrochloric acid (\( HCl \))?

• (1) \( 1.0 \)
• (2) \( 2.0 \)
• (3) \( 0.5 \)
• (4) \( 3.0 \)

What is the concentration of \( NaOH \) in a solution if \( 25.0 \, mL \) of \( 0.100 \, M \) \( HCl \) is neutralized by \( 50.0 \, mL \) of \( NaOH \)?

• (1) \( 0.05 \, M \)
• (2) \( 0.10 \, M \)
• (3) \( 0.20 \, M \)
• (4) \( 0.25 \, M \)

What is the molarity of a solution made by dissolving \( 2.5 \, g \) of potassium chloride (\( KCl \)) in \( 500 \, mL \) of water? (Molar mass of \( KCl = 74.5 \, g/mol \))

• (1) \( 0.10 \, M \)
• (2) \( 0.25 \, M \)
• (3) \( 0.50 \, M \)
• (4) \( 1.00 \, M \)