MHT CET 2025 23 April Shift 1 Question Paper (Available): Download Question Paper (PCM) with Answers PDF

A car accelerates uniformly from rest to a velocity of \( 25 \, m/s \) in \( 10 \, seconds \). What is the acceleration of the car?

• (1) \( 2.5 \, m/s^2 \)
• (2) \( 5 \, m/s^2 \)
• (3) \( 10 \, m/s^2 \)
• (4) \( 15 \, m/s^2 \)

A block of mass \( 5 \, kg \) is placed on a horizontal surface. The coefficient of friction between the block and the surface is \( 0.4 \). What is the force of friction acting on the block?

• (1) \( 10 \, N \)
• (2) \( 15 \, N \)
• (3) \( 20 \, N \)
• (4) \( 25 \, N \)

In a Young's double-slit experiment, the distance between the slits is \( 0.2 \, mm \) and the distance between the screen and the slits is \( 2 \, m \). If the wavelength of the light used is \( 600 \, nm \), calculate the distance between the two adjacent bright fringes.

• (1) \( 0.3 \, mm \)
• (2) \( 0.6 \, mm \)
• (3) \( 1.2 \, mm \)
• (4) \( 1.5 \, mm \)

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

• (1) \( 100 \, Hz \)
• (2) \( 50 \, Hz \)
• (3) \( 25 \, Hz \)
• (4) \( 200 \, Hz \)

A thin spherical shell of radius \( 0.5 \, m \) and mass \( 2 \, kg \) is rotating about its axis of symmetry with an angular velocity of \( 10 \, rad/s \). What is its moment of inertia?

• (1) \( 0.5 \, kg \cdot m^2 \)
• (2) \( 1.0 \, kg \cdot m^2 \)
• (3) \( 2.0 \, kg \cdot m^2 \)
• (4) \( 4.0 \, kg \cdot m^2 \)

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?

• (1) \( 1.25 \, m/s^2 \)
• (2) \( 2.5 \, m/s^2 \)
• (3) \( 5 \, m/s^2 \)
• (4) \( 10 \, m/s^2 \)

A body of mass \( 5 \, kg \) is placed on a frictionless inclined plane of angle \( 30^\circ \). What is the component of the weight of the body along the plane?

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

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 \( 5 \, muC \) placed at that point?

• (1) \( 0.5 \, mJ \)
• (2) \( 1.0 \, mJ \)
• (3) \( 2.0 \, mJ \)
• (4) \( 5.0 \, mJ \)

A 0.5 m long solenoid has 400 turns and carries a current of \( 3 \, A \). 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 photon has an energy of \( 3.2 \times 10^{-19} \, J \). What is the frequency of the photon?

• (1) \( 5.0 \times 10^{14} \, Hz \)
• (2) \( 4.0 \times 10^{14} \, Hz \)
• (3) \( 3.0 \times 10^{14} \, Hz \)
• (4) \( 6.0 \times 10^{14} \, Hz \)

A satellite is orbiting the Earth at a height of \( 10^4 \, km \) above the Earth's surface. If the radius of the Earth is \( 6.4 \times 10^6 \, m \), calculate the orbital speed of the satellite. (Gravitational constant \( G = 6.67 \times 10^{-11} \, N \cdot m^2/kg^2 \) and Earth's mass \( M = 6 \times 10^{24} \, kg \))

• (1) \( 7.0 \, km/s \)
• (2) \( 8.0 \, km/s \)
• (3) \( 9.0 \, km/s \)
• (4) \( 10.0 \, km/s \)

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

• (1) \( 0.5 \, A \cdot m^2 \)
• (2) \( 1.0 \, A \cdot m^2 \)
• (3) \( 2.0 \, A \cdot m^2 \)
• (4) \( 5.0 \, A \cdot m^2 \)

The pH of a solution is 3. What is the concentration of \( H^+ \) ions in the solution?

• (1) \( 1 \times 10^{-3} \, mol/L \)
• (2) \( 3 \times 10^{-3} \, mol/L \)
• (3) \( 1 \times 10^{-6} \, mol/L \)
• (4) \( 3 \times 10^{-6} \, mol/L \)

What is the oxidation state of chromium in \( K_2Cr_2O_7 \)?

• (1) +2
• (2) +3
• (3) +6
• (4) +7

What is the molecular geometry of \( SO_3 \)?

• (1) Linear
• (2) Trigonal planar
• (3) Tetrahedral
• (4) Octahedral

What is the mass of sodium chloride (\( NaCl \)) formed when 0.5 moles of sodium (\( Na \)) reacts with excess chlorine (\( Cl_2 \))?

• (1) \( 29 \, g \)
• (2) \( 35.5 \, g \)
• (3) \( 58 \, g \)
• (4) \( 70 \, g \)

Calculate the oxidation number of sulfur in \( H_2SO_4 \).

• (1) +4
• (2) +6
• (3) +2
• (4) 0

A sample of an ideal gas occupies 10 liters at a pressure of 2 atm and a temperature of 300 K. What is the volume of the gas at 1 atm pressure and 300 K temperature?

• (1) 5 L
• (2) 10 L
• (3) 20 L
• (4) 40 L

What is the total number of orbitals in the third energy level (n = 3)?

• (1) 9
• (2) 16
• (3) 4
• (4) 3

What is the value of the ionization energy of hydrogen in joules? (Given that the ionization energy of hydrogen is \( 13.6 \, eV \))

• (1) \( 2.18 \times 10^{-18} \, J \)
• (2) \( 1.6 \times 10^{-18} \, J \)
• (3) \( 3.2 \times 10^{-19} \, J \)
• (4) \( 1.0 \times 10^{-19} \, J \)

What is the empirical formula of a compound containing 40% sulfur and 60% oxygen by mass?

• (1) \( SO_2 \)
• (2) \( SO_3 \)
• (3) \( S_2O_3 \)
• (4) \( SO \)

What is the standard electrode potential for the half-reaction \( Cu^{2+} + 2e^- \rightarrow Cu \)?

• (1) +0.34 V
• (2) -0.34 V
• (3) +1.10 V
• (4) 0 V

What is the percentage composition of nitrogen in ammonium nitrate (\( NH_4NO_3 \))?

• (1) 18.5%
• (2) 28.0%
• (3) 35.0%
• (4) 42.5%

What is the total number of moles of gas in a 5 L container at 300 K and 2 atm pressure (Use the ideal gas law)?

• (1) 0.4 mol
• (2) 0.6 mol
• (3) 1.0 mol
• (4) 2.0 mol

A solution contains 10 g of NaOH dissolved in 500 mL of water. What is the molarity of the NaOH solution?

• (1) 0.25 M
• (2) 0.5 M
• (3) 1.0 M
• (4) 2.0 M

The enthalpy change for the reaction \( C + O_2 \rightarrow CO_2 \) is \( -393.5 \, kJ/mol \). What is the heat released when 2 moles of carbon react with excess oxygen?

• (1) \( -393.5 \, kJ \)
• (2) \( -787 \, kJ \)
• (3) \( -196.75 \, kJ \)
• (4) \( 0 \, kJ \)

Find the roots of the quadratic equation \( 2x^2 - 4x - 6 = 0 \).

• (1) \( x = 1 \, or \, x = -3 \)
• (2) \( x = -1 \, or \, x = 3 \)
• (3) \( x = 2 \, or \, x = -1 \)
• (4) \( x = 3 \, or \, x = -2 \)

Find the area of a triangle with vertices \( A(2, 3) \), \( B(5, 11) \), and \( C(8, 7) \).

• (1) 15
• (2) 18
• (3) 20
• (4) 25

Solve for \( x \): \( \log_2 (x-1) = 3 \).

• (1) \( x = 9 \)
• (2) \( x = 7 \)
• (3) \( x = 8 \)
• (4) \( x = 6 \)

Find the derivative of the function \( f(x) = 3x^2 - 5x + 7 \).

• (1) \( 6x - 5 \)
• (2) \( 6x + 5 \)
• (3) \( 3x^2 + 5 \)
• (4) \( 3x^2 - 5 \)

Find the value of the determinant \( \begin{vmatrix} 2 & 3
4 & 5 \end{vmatrix} \).

• (1) 2
• (2) 1
• (3) 0
• (4) -1

Solve the system of equations: \[ x + y = 5 \] \[ 2x - y = 4 \]

• (1) \( x = 3, y = 2 \)
• (2) \( x = 2, y = 3 \)
• (3) \( x = 4, y = 1 \)
• (4) \( x = 1, y = 4 \)

If \( \log_2 x = 5 \), what is the value of \( x \)?

• (1) \( x = 32 \)
• (2) \( x = 25 \)
• (3) \( x = 20 \)
• (4) \( x = 16 \)

Find the length of the diagonal of a rectangle with length 6 cm and breadth 8 cm.

• (1) 10 cm
• (2) 12 cm
• (3) 14 cm
• (4) 8 cm

Solve the system of equations: \[ x + y = 10 \] \[ 3x - y = 5 \]

• (1) \( x = 5, y = 5 \)
• (2) \( x = 4, y = 6 \)
• (3) \( x = 3, y = 7 \)
• (4) \( x = 6, y = 4 \)

Find the sum of the first 20 terms of the arithmetic progression: \( 2, 5, 8, 11, \dots \).

• (1) 400
• (2) 420
• (3) 440
• (4) 460

Find the value of \( x \) if \( \sin(2x) = 1 \).

• (1) \( x = \frac{\pi}{4} \)
• (2) \( x = \frac{\pi}{2} \)
• (3) \( x = \frac{\pi}{6} \)
• (4) \( x = \frac{3\pi}{4} \)

Find the value of \( \log_3 81 \).

• (1) 3
• (2) 4
• (3) 2
• (4) 1