MHT CET 2025 15 April Shift 2 Question Paper (Available): Download Question Paper (PCB) with Answers PDF

A sound wave travels through air with a frequency of 500 Hz and a wavelength of 0.68 m. Calculate the speed of sound in air.

• (1) \( 340 \, m/s \)
• (2) \( 500 \, m/s \)
• (3) \( 200 \, m/s \)
• (4) \( 680 \, m/s \)

In a silicon semiconductor at room temperature, the intrinsic carrier concentration is \( 1.5 \times 10^{16} \, m^{-3} \). Calculate the energy band gap of the silicon if the intrinsic carrier concentration is given by: \[ n_i = \sqrt{N_c N_v} e^{-E_g / 2kT} \]
Where:
- \( N_c = 2.8 \times 10^{25} \, m^{-3} \) is the effective density of states in the conduction band,
- \( N_v = 1.04 \times 10^{25} \, m^{-3} \) is the effective density of states in the valence band,
- \( k = 1.38 \times 10^{-23} \, J/K \) is the Boltzmann constant,
- \( T = 300 \, K \) is the temperature.

• (1) \( 1.1 \, eV \)
• (2) \( 0.9 \, eV \)
• (3) \( 2.0 \, eV \)
• (4) \( 0.7 \, eV \)

An ideal gas is contained in a cylinder with a movable piston. The gas undergoes an isothermal expansion from a volume of 2 liters to 8 liters at a temperature of 300 K. If the initial pressure of the gas is \( 2 \times 10^5 \, Pa \), calculate the work done by the gas during this expansion. (Use \( R = 8.31 \, J/mol·K \))

• (1) \( 7200 \, J \)
• (2) \( 3600 \, J \)
• (3) \( 1800 \, J \)
• (4) \( 14400 \, J \)

A concave mirror has a focal length of 20 cm. An object is placed 60 cm in front of the mirror. Find the image distance.

• (1) \( 30 \, cm \)
• (2) \( 40 \, cm \)
• (3) \( 60 \, cm \)
• (4) \( 80 \, cm \)

A projectile is fired with an initial speed of \( 20 \, m/s \) at an angle of \( 30^\circ \) above the horizontal. Find the maximum height reached by the projectile.

• (1) \( 10 \, m \)
• (2) \( 20 \, m \)
• (3) \( 5 \, m \)
• (4) \( 15 \, m \)

The gravitational potential energy of an object of mass 5 kg at a height of 10 m above the surface of the Earth is:

• (1) \( 490 \, J \)
• (2) \( 500 \, J \)
• (3) \( 450 \, J \)
• (4) \( 550 \, J \)

A car of mass 1000 kg is moving in a circular path of radius 50 m with a speed of 20 m/s. Calculate the centripetal force acting on the car.

• (1) \( 4000 \, N \)
• (2) \( 2000 \, N \)
• (3) \( 5000 \, N \)
• (4) \( 10000 \, N \)

Two charges, \( q_1 = +3 \, \mu C \) and \( q_2 = -4 \, \mu C \), are placed 20 cm apart. Calculate the force between the charges. (Use Coulomb's constant \( k = 9 \times 10^9 \, N·m^2/C^2 \))

• (1) \( 1.35 \, N \)
• (2) \( 2.45 \, N \)
• (3) \( 3.5 \, N \)
• (4) \( 4.2 \, N \)

A fluid of density \( 800 \, kg/m^3 \) is flowing through a pipe of varying cross-sectional area. The velocity of the fluid at point A is \( 2 \, m/s \), and the velocity at point B is \( 4 \, m/s \). If the cross-sectional area at point A is \( 1 \, m^2 \), find the cross-sectional area at point B.

• (1) \( 0.5 \, m^2 \)
• (2) \( 1.5 \, m^2 \)
• (3) \( 2.0 \, m^2 \)
• (4) \( 4.0 \, m^2 \)

For the reaction: \[ 2A + B \rightarrow 3C \]
The rate law is given as: \[ Rate = k[A]^2[B] \]
If the concentration of A is doubled and the concentration of B is halved, how does the rate of the reaction change?

• (1) It remains the same.
• (2) It doubles.
• (3) It increases by a factor of 4.
• (4) It decreases by a factor of 2.

The enthalpy of formation of hydrogen chloride (HCl) is \( -92.3 \, kJ/mol \). If 2 moles of HCl are formed from hydrogen and chlorine gas, calculate the total heat released.

• (1) \( -184.6 \, kJ \)
• (2) \( -92.3 \, kJ \)
• (3) \( 92.3 \, kJ \)
• (4) \( 184.6 \, kJ \)

For the equilibrium reaction: \[ N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) \]
At a certain temperature, the equilibrium constant \( K_c \) is 4.0. If the concentrations of \( N_2 \), \( H_2 \), and \( NH_3 \) are 0.2 M, 0.6 M, and 0.4 M, respectively, calculate the reaction quotient \( Q_c \) and determine whether the reaction is at equilibrium.

• (1) \( Q_c = 1.2 \), the reaction will shift to the left.
• (2) \( Q_c = 4.0 \), the reaction is at equilibrium.
• (3) \( Q_c = 2.0 \), the reaction will shift to the right.
• (4) \( Q_c = 0.5 \), the reaction will shift to the left.

The freezing point depression constant (\( K_f \)) for water is \( 1.86 \, °C·kg/mol \). If 0.5 moles of a non-volatile solute is dissolved in 1 kg of water, calculate the freezing point depression.

• (1) \( 0.93 \, °C \)
• (2) \( 1.86 \, °C \)
• (3) \( 3.72 \, °C \)
• (4) \( 2.79 \, °C \)

The energy of the nth orbit of the hydrogen atom is given by: \[ E_n = - \frac{13.6}{n^2} \, eV \]
What is the energy of the second orbit (n = 2) of the hydrogen atom?

• (1) \( - 3.4 \, eV \)
• (2) \( - 13.6 \, eV \)
• (3) \( - 6.8 \, eV \)
• (4) \( - 1.36 \, eV \)

In the reaction: \[ Zn(s) + CuSO_4(aq) \rightarrow ZnSO_4(aq) + Cu(s) \]
Which of the following is the correct oxidation half-reaction?

• (1) \( Zn \rightarrow Zn^{2+} + 2e^- \)
• (2) \( Cu^{2+} + 2e^- \rightarrow Cu \)
• (3) \( Zn^{2+} + 2e^- \rightarrow Zn \)
• (4) \( Cu \rightarrow Cu^{2+} + 2e^- \)

Which of the following is the primary function of the human respiratory system?

• (1) To transport oxygen to tissues and carbon dioxide to the lungs.
• (2) To remove waste products from the body.
• (3) To facilitate digestion and absorption of nutrients.
• (4) To maintain homeostasis by regulating blood pH.

In a monohybrid cross between two heterozygous pea plants (Pp x Pp), what is the expected phenotypic ratio of the offspring?

• (1) 3:1
• (2) 1:2:1
• (3) 1:1
• (4) 4:0

Which of the following is an example of a primary consumer in an ecosystem?

• (1) Grasshopper
• (2) Snake
• (3) Fox
• (4) Deer

Which part of the human brain is primarily responsible for regulating basic life functions, such as heart rate and breathing?

• (1) Cerebrum
• (2) Cerebellum
• (3) Medulla Oblongata
• (4) Hypothalamus

Which of the following is the correct equation for photosynthesis?

• (1) \( 6CO_2 + 6H_2O + light energy \rightarrow C_6H_{12}O_6 + 6O_2 \)
• (2) \( C_6H_{12}O_6 + 6O_2 \rightarrow 6CO_2 + 6H_2O + energy \)
• (3) \( 6CO_2 + 6H_2O \rightarrow C_6H_{12}O_6 + 6O_2 + light energy \)
• (4) \( C_6H_{12}O_6 + 6O_2 \rightarrow 6CO_2 + 6H_2O + light energy \)

Which organelle is primarily responsible for producing ATP in a cell?

• (1) Nucleus
• (2) Mitochondria
• (3) Endoplasmic Reticulum
• (4) Golgi Apparatus

In a DNA molecule, which of the following base-pairings is correct?

• (1) Adenine pairs with Cytosine.
• (2) Thymine pairs with Guanine.
• (3) Adenine pairs with Thymine.
• (4) Cytosine pairs with Uracil.

Which of the following processes occurs during the second meiotic division (Meiosis II)?

• (1) Homologous chromosomes are separated.
• (2) Sister chromatids are separated.
• (3) DNA replication occurs.
• (4) Crossing over occurs.

Which of the following factors does NOT affect the rate of an enzyme-catalyzed reaction?

• (1) Temperature
• (2) pH
• (3) Substrate concentration
• (4) Color of the enzyme