MHT-CET 2024 previous year paper practice · PYQ-pattern set

MHT-CET 2024 PYQ-pattern questions

Showing 10 of the 16 PYQ-pattern questions in this set — freshly worded in that year's pattern, not the original questions. Answers and solutions open under each question.

1. Q1 · Motion in a Straight Line and Plane (Class 11 — ~20% weight)

   A particle moves along a straight line such that its displacement x at time t is given by x = 4t² – 2t + 5 (all in SI units). The acceleration of the particle is:

   • A. 4 m/s²
   • B. 8 m/s²
   • C. 2 m/s²
   • D. 6 m/s²
   Answer and solution

   Answer: B

   Acceleration is the second derivative of displacement. Differentiating x = 4t² – 2t + 5 twice gives a = d²x/dt² = 8 m/s².

2. Q2 · Thermodynamics — Basics (Class 11 — ~20% weight)

   In an isothermal process for an ideal gas:

   • A. Temperature remains constant
   • B. Pressure remains constant
   • C. Volume remains constant
   • D. Internal energy increases
   Answer and solution

   Answer: A

   Isothermal process is defined as a process in which the temperature of the system remains constant throughout.

3. Q3 · Oscillations (Class 11 — ~20% weight)

   A particle executes simple harmonic motion with amplitude 8 cm. At what displacement from the mean position will its kinetic energy be equal to its potential energy?

   • A. 2√2 cm
   • B. 4√2 cm
   • C. 4 cm
   • D. 8 cm
   Answer and solution

   Answer: B

   For KE = PE in SHM, the particle must be at displacement x = A/√2. With A = 8 cm, x = 8/√2 = 4√2 cm.

4. Q4 · Wave Theory of Light

   In Young's double-slit experiment, the distance between two consecutive bright fringes is 0.5 mm. If the wavelength of light used is 600 nm and the distance of the screen from the slits is 1.5 m, what is the slit separation?

   • A. 1.2 mm
   • B. 1.8 mm
   • C. 2.4 mm
   • D. 3.0 mm
   Answer and solution

   Answer: B

   Fringe width β = λD/d. Rearranging, d = λD/β = (600×10⁻⁹ × 1.5) / (0.5×10⁻³) = 1.8 × 10⁻³ m = 1.8 mm.

5. Q5 · Current Electricity (Class 12)

   A potentiometer wire of length 5 m and resistance 10 Ω is connected to a 3 V battery. A cell of emf 1.5 V gives null deflection at 2.5 m. The internal resistance of the cell if it is shunted by 5 Ω resistance and null point shifts to 2.0 m is

   • A. 1.25 Ω
   • B. 2.5 Ω
   • C. 0.5 Ω
   • D. 1.0 Ω
   Answer and solution

   Answer: A

   Using the relation for shunted cell: r = S(L₁ - L₂)/L₂, where S = 5 Ω, L₁ = 2.5 m, L₂ = 2.0 m. Thus r = 5(2.5 - 2.0)/2.0 = 1.25 Ω.

6. Q6 · Electromagnetic Waves (Class 12)

   The frequency of electromagnetic wave which best suits for radar systems used in aircraft navigation is

   • A. Infrared waves
   • B. Microwaves
   • C. Radio waves
   • D. X-rays
   Answer and solution

   Answer: B

   Microwaves (frequency 10⁹ to 10¹¹ Hz) are used for radar systems because they have suitable wavelength for detecting objects and penetrating clouds.

7. Q7 · Semiconductor Electronics (Class 12)

   In an intrinsic semiconductor at room temperature, if the number density of electrons is 1.5 × 10¹⁶ per m³, what is the number density of holes?

   • A. 0.75 × 10¹⁶ per m³
   • B. 1.5 × 10¹⁶ per m³
   • C. 3.0 × 10¹⁶ per m³
   • D. Zero
   Answer and solution

   Answer: B

   In an intrinsic semiconductor, electron density equals hole density, so the answer is 1.5 × 10¹⁶ per m³.

8. Q8 · Structure of Atom (Class 11 — ~20% weight)

   Calculate the wavelength (in nm) of light emitted when an electron in a hydrogen atom transitions from n = 3 to n = 1. (Rydberg constant Rₕ = 1.097 × 10⁷ m⁻¹)

   • A. 102 nm
   • B. 121 nm
   • C. 156 nm
   • D. 434 nm
   Answer and solution

   Answer: A

   Using 1/λ = Rₕ(1/1² - 1/3²) = 1.097×10⁷(8/9), we obtain λ ≈ 102 nm.

9. Q9 · Hydrogen and s-Block Elements (Class 11 — ~20% weight)

   Which of the following alkali metals reacts most vigorously with cold water?

   • A. Lithium
   • B. Sodium
   • C. Potassium
   • D. Rubidium
   Answer and solution

   Answer: D

   Reactivity of alkali metals with water increases down the group due to decreasing ionization energy. Hence Rb reacts most vigorously among the given options.

10. Q10 · Surface Chemistry (Class 12)

    Which one of the following gases will be adsorbed to the maximum extent by activated charcoal at the same temperature and pressure?

    • A. H₂
    • B. N₂
    • C. NH₃
    • D. CH₄
    Answer and solution

    Answer: C

    NH₃ has the highest critical temperature among the given gases, making it most easily liquefiable and thus most readily adsorbed on activated charcoal.