MHT CET 2025 25 April Shift 1 Question Paper (Available): Download Question Paper (PCM) with Answers PDF

A body of mass 0.2 kg is attached to a light string of length 1 m and revolved in a vertical circle. What is the minimum speed at the lowest point so that the body can complete the circular motion? (Take \( g = 10 \, m/s^2 \))

• (a) 2 m/s
• (b) 4.47 m/s
• (c) 5 m/s
• (d) 6.32 m/s

A coil of 100 turns, carrying a current of 5A, is placed in a magnetic field of 2T. The area of each turn is 0.01 m\(^2\). What is the magnetic moment of the coil?

• (a) 0.5 Am\(^2\)
• (b) 1 Am\(^2\)
• (c) 2 Am\(^2\)
• (d) 5 Am\(^2\)

The electric field at a point in space is \( 2 \times 10^3 \, N/C \) and the potential at the same point is 100 V. What is the potential energy of a charge of 5 μC placed at that point?

• (a) 0.5 mJ
• (b) 1.0 mJ
• (c) 2.0 mJ
• (d) 5.0 mJ

In an LC circuit, the inductance \( L \) is 2 H and the capacitance \( C \) is 4 μF. What is the frequency of oscillation of the circuit?

• (a) 100 Hz
• (b) 50 Hz
• (c) 25 Hz
• (d) 200 Hz

A body of mass 5 kg is placed on a frictionless inclined plane of angle 30°. What is the component of the weight of the body along the plane?

• (1) 25 N
• (2) 50 N
• (3) 45 N
• (4) 75 N

A 0.5 m long solenoid has 100 turns and carries a current of 3A. What is the magnetic field at the center of the solenoid?

• (1) \( 2 \times 10^{-2} \, T \)
• (2) \( 4 \times 10^{-2} \, T \)
• (3) \( 6 \times 10^{-2} \, T \)
• (4) \( 8 \times 10^{-2} \, T \)

A particle is moving with a constant velocity of 5 m/s in a circular path of radius 2 m. What is the centripetal acceleration of the particle?

• (a) 1.25 m/s\(^2\)
• (b) 2.5 m/s\(^2\)
• (c) 5 m/s\(^2\)
• (d) 10 m/s\(^2\)

What is the moment of inertia of a solid sphere of mass \( M \) and radius \( R \) about its diameter?

• (a) \( \frac{2}{5} M R^2 \)
• (b) \( \frac{1}{2} M R^2 \)
• (c) \( \frac{3}{5} M R^2 \)
• (d) \( M R^2 \)

A galvanometer has resistance \( G = 100 \, \Omega \) and shows full-scale deflection at \( I_q = 1 \, mA \). To convert it into a voltmeter of range 5 V, what resistance should be connected in series?

• (a) 400 \( \Omega \)
• (b) 4900 \( \Omega \)
• (c) 490 \( \Omega \)
• (d) 5000 \( \Omega \)

A body of mass 2 kg is moving in a circular path of radius 3 m with a constant speed of 6 m/s. What is the centripetal force acting on the body?

• (a) 4 N
• (b) 8 N
• (c) 24 N
• (d) 12 N

A force of 20 N is applied to a body at an angle of \( 30^\circ \) to the horizontal, moving the body a distance of 5 m. What is the work done by the force?

• (a) 100 J
• (b) 50 J
• (c) 200 J
• (d) 150 J

Two point charges \( +2 \, muC \) and \( -3 \, muC \) are placed 10 cm apart in vacuum. What is the electrostatic force between them?

• (a) 4.5 N
• (b) 9 N
• (c) 18 N
• (d) 2.25 N

A body of mass 10 kg is at a height of 5 m above the surface of the Earth. What is the gravitational potential energy of the body? (Take \( g = 10 \, m/s^2 \))

• (a) 50 J
• (b) 500 J
• (c) 100 J
• (d) 250 J

A gas expands from a volume of 2 m³ to 4 m³ against a constant pressure of 5 atm. How much work is done by the gas during expansion? (1 atm = \( 1.01 \times 10^5 \, Pa \))

• (a) \( 2.02 \times 10^5 \, J \)
• (b) \( 1.01 \times 10^5 \, J \)
• (c) \( 5.02 \times 10^5 \, J \)
• (d) \( 1.02 \times 10^5 \, J \)

A coil has 200 turns and an area of \( 0.01 \, m^2 \). If the magnetic field changes from 0 to 0.5 T in 0.1 seconds, what is the induced emf in the coil?

• (a) 1 V
• (b) 0.5 V
• (c) 2 V
• (d) 5 V

A concave mirror has a focal length of 15 cm. An object is placed 30 cm from the mirror. What is the image distance?

• (a) 30 cm
• (b) 45 cm
• (c) 60 cm
• (d) 20 cm

A water tank is open at the top and has a hole of area \( 10^{-4} \, m^2 \) at the bottom. The height of the water column is 5 m. What is the speed of the water flowing out of the hole? (Take \( g = 10 \, m/s^2 \))

• (a) 5 m/s
• (b) 10 m/s
• (c) 15 m/s
• (d) 20 m/s

If \( \mathbf{a} = \frac{1}{\sqrt{10}} (4\hat{i} - 3\hat{j} + \hat{k}) \) and \( \mathbf{b} = \frac{1}{5} (\hat{i} + 2\hat{j} + 2\hat{k}) \), then the value of \[ (2\mathbf{a} - \mathbf{b}) \cdot \left[ (\mathbf{a} \times \mathbf{b}) \times (\mathbf{a} + 2\mathbf{b}) \right] \]

• (1) 5
• (2) -3
• (3) -5
• (4) 3

Evaluate the integral: \[ \int \sqrt{x^2 + 3x} \, dx \]

If \( P(A \cap B) = \frac{2}{25} \) and \( P(A \cup B) = \frac{8}{25} \), then find the value of \( P(A) \).

• (1) \( \frac{4}{15} \)
• (2) \( \frac{4}{5} \)
• (3) \( \frac{3}{8} \)
• (4) \( \frac{2}{5} \)

Find the smallest angle of the triangle whose sides are \( 6 + \sqrt{12}, \sqrt{48}, \sqrt{24} \).

• (a) \( \frac{\pi}{4} \)
• (b) \( \frac{\pi}{2} \)
• (c) \( \frac{\pi}{6} \)
• (d) \( \frac{\pi}{3} \)

Evaluate the integral: \[ \int \frac{x^2 + 2x}{\sqrt{x^2 + 1}} \, dx \]

• (1) \( \frac{1}{3} \left( x^2 + 1 \right)^{3/2} \)
• (2) \( \frac{1}{2} \left( x^2 + 1 \right)^{3/2} \)
• (3) \( \frac{1}{2} \left( x^2 + 1 \right)^{5/2} \)
• (4) \( \frac{1}{3} \left( x^2 + 1 \right)^{5/2} \)

Find the value of the following expression: \[ \sin^2(30^\circ) + \cos^2(60^\circ) \]

• (1) \( \frac{1}{2} \)
• (2) \( 1 \)
• (3) \( \frac{3}{4} \)
• (4) \( \frac{1}{4} \)

If two dice are rolled, what is the probability of getting a sum of 7?

• (1) \( \frac{1}{6} \)
• (2) \( \frac{1}{36} \)
• (3) \( \frac{5}{36} \)
• (4) \( \frac{1}{3} \)

If \( \mathbf{a} = 3\hat{i} + 4\hat{j} \) and \( \mathbf{b} = 2\hat{i} - \hat{j} \), find \( \mathbf{a} \cdot \mathbf{b} \) (the dot product).

• (1) 6
• (2) 4
• (3) 10
• (4) 12

Find the roots of the quadratic equation \( x^2 - 5x + 6 = 0 \).

• (1) 2 and 3
• (2) 3 and -2
• (3) -2 and -3
• (4) 1 and 6

A bag contains 5 red balls, 7 green balls, and 8 blue balls. One ball is drawn at random. What is the probability that the ball is either red or green?

• (1) \( \frac{5}{20} \)
• (2) \( \frac{7}{20} \)
• (3) \( \frac{12}{20} \)
• (4) \( \frac{5}{10} \)

In the reaction \( 2H_2 + O_2 \rightarrow 2H_2O \), if 4 moles of hydrogen react with excess oxygen, how many moles of water are produced?

• (1) 2 moles
• (2) 4 moles
• (3) 8 moles
• (4) 1 mole

What is the pH of a solution with a hydrogen ion concentration of \( 1 \times 10^{-5} \, mol/L \)?

• (1) 5
• (2) 10
• (3) 7
• (4) 4

Which of the following elements has the highest electronegativity?

• (1) Fluorine (F)
• (2) Oxygen (O)
• (3) Nitrogen (N)
• (4) Chlorine (Cl)

The enthalpy change for the reaction \( N_2(g) + 3H_2(g) \rightarrow 2NH_3(g) \) is \( -92.4 \, kJ/mol \). What is the enthalpy change when 4 moles of nitrogen react?

• (1) \( -92.4 \, kJ \)
• (2) \( -184.8 \, kJ \)
• (3) \( -46.2 \, kJ \)
• (4) \( -368.4 \, kJ \)

What is the volume occupied by 2 moles of an ideal gas at standard temperature and pressure (STP)?

• (1) 22.4 L
• (2) 44.8 L
• (3) 11.2 L
• (4) 48.8 L

In the reaction \( Zn + 2Ag^+ \rightarrow Zn^{2+} + 2Ag \), what is the oxidation state of zinc in \( Zn \) and \( Zn^{2+} \)?

• (1) \( 0 \) in \( Zn \), \( +2 \) in \( Zn^{2+} \)
• (2) \( +2 \) in \( Zn \), \( 0 \) in \( Zn^{2+} \)
• (3) \( +2 \) in \( Zn \), \( +1 \) in \( Zn^{2+} \)
• (4) \( 0 \) in \( Zn \), \( 0 \) in \( Zn^{2+} \)