MHT CET 2025 19 April Shift 2 Question Paper (Available): Download Question Paper (PCM) with Answers PDF

The value of the definite integral \( \int_0^{\pi} \sin^2 x \, dx \) is:

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

The distance between the points \( A(3, 4) \) and \( B(-1, -2) \) is:

• (1) \( 5 \)
• (2) \( 6 \)
• (3) \( 7 \)
• (4) \( 8 \)

A bag contains 5 red balls and 3 green balls. If two balls are drawn at random without replacement, what is the probability that both balls drawn are red?

• (1) \( \frac{5}{28} \)
• (2) \( \frac{5}{21} \)
• (3) \( \frac{3}{14} \)
• (4) \( \frac{1}{3} \)

If \( \tan \theta = 2 \), then the value of \( \sec^2 \theta \) is:

• (1) \( 5 \)
• (2) \( 4 \)
• (3) \( 3 \)
• (4) \( 2 \)

If the roots of the quadratic equation \( x^2 - 7x + 12 = 0 \) are \( \alpha \) and \( \beta \), then the value of \( \alpha + \beta \) is:

• (1) \( 7 \)
• (2) \( 12 \)
• (3) \( 5 \)
• (4) \( 6 \)

The general solution of the differential equation \( \frac{dy}{dx} = 3x^2 \) is:

• (1) \( y = x^3 + C \)
• (2) \( y = 3x^3 + C \)
• (3) \( y = \frac{3}{2} x^3 + C \)
• (4) \( y = x^3 + 3C \)

If \( A = \begin{bmatrix} 2 & 1
3 & 4 \end{bmatrix} \), then the determinant of matrix \( A \) is:

• (1) \( 4 \)
• (2) \( 5 \)
• (3) \( 7 \)
• (4) \( 10 \)

The limit of \( \lim_{x \to 0} \frac{\sin x}{x} \) is:

• (1) \( 1 \)
• (2) \( 0 \)
• (3) \( \infty \)
• (4) Does not exist

If \( \vec{A} = 2\hat{i} + 3\hat{j} \) and \( \vec{B} = 4\hat{i} - \hat{j} \), then the dot product \( \vec{A} \cdot \vec{B} \) is:

• (1) \( 5 \)
• (2) \( 6 \)
• (3) \( 7 \)
• (4) \( 8 \)

The maximum value of the function \( f(x) = -2x^2 + 4x + 1 \) occurs at:

• (1) \( x = 1 \)
• (2) \( x = -1 \)
• (3) \( x = 0 \)
• (4) \( x = 2 \)

The value of the integral \( \int_0^1 x^2 \, dx \) is:

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

If \( z = 3 + 4i \), then the modulus of \( z \) is:

• (1) \( 5 \)
• (2) \( 7 \)
• (3) \( 9 \)
• (4) \( 10 \)

A die is rolled. What is the probability of getting a number less than or equal to 4?

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

In how many ways can 5 people be arranged in a row?

• (1) \( 120 \)
• (2) \( 60 \)
• (3) \( 24 \)
• (4) \( 10 \)

The feasible region of the linear programming problem is determined by the system of inequalities: \[ x + y \leq 6, \quad x \geq 0, \quad y \geq 0. \]
What is the maximum value of \( x + y \) in the feasible region?

• (1) \( 6 \)
• (2) \( 5 \)
• (3) \( 4 \)
• (4) \( 3 \)

A car accelerates uniformly from rest and attains a velocity of \( 20 \, m/s \) in 10 seconds. What is the acceleration of the car?

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

A force of \( 10 \, N \) acts on a body and moves it through a displacement of \( 5 \, m \) in the direction of the force. What is the work done by the force?

• (1) \( 50 \, J \)
• (2) \( 25 \, J \)
• (3) \( 10 \, J \)
• (4) \( 5 \, J \)

Two charges of \( +2 ) and \( -2 ) are placed 1 meter apart. What is the force between them?

• (1) \( 9 \times 10^9 \, N \)
• (2) \( 18 \times 10^9 \, N \)
• (3) \( 4 \times 10^9 \, N \)
• (4) \( 0 \, N \)

A gas expands from an initial volume of \( V_1 = 1 \, m^3 \) to a final volume of \( V_2 = 3 \, m^3 \) under constant pressure of \( P = 2 \, atm \). What is the work done by the gas during this expansion?

• (1) \( 6 \times 10^5 \, J \)
• (2) \( 4 \times 10^5 \, J \)
• (3) \( 2 \times 10^5 \, J \)
• (4) \( 1 \times 10^5 \, J \)

A convex lens has a focal length of \( 20 \, cm \). An object is placed at a distance of \( 30 \, cm \) from the lens. What is the position of the image formed?

• (1) \( 60 \, cm \)
• (2) \( 15 \, cm \)
• (3) \( 10 \, cm \)
• (4) \( 25 \, cm \)

A body moves in a circle of radius \( r = 5 \, m \) with a constant speed of \( v = 10 \, m/s \). What is the centripetal acceleration of the body?

• (1) \( 2 \, m/s^2 \)
• (2) \( 5 \, m/s^2 \)
• (3) \( 10 \, m/s^2 \)
• (4) \( 20 \, m/s^2 \)

A fluid flows through a pipe with a varying cross-sectional area. If the velocity of the fluid is \( v_1 = 4 \, m/s \) at a point where the cross-sectional area is \( A_1 = 2 \, m^2 \), and the velocity at another point where the cross-sectional area is \( A_2 = 1 \, m^2 \) is \( v_2 \), what is the velocity \( v_2 \)?

• (1) \( 8 \, m/s \)
• (2) \( 4 \, m/s \)
• (3) \( 2 \, m/s \)
• (4) \( 1 \, m/s \)

A mass of \( 0.5 \, kg \) is attached to a spring with a spring constant \( k = 200 \, N/m \). The mass is displaced by \( 0.1 \, m \) from its equilibrium position. What is the potential energy stored in the spring?

• (1) \( 1 \, J \)
• (2) \( 0.5 \, J \)
• (3) \( 2 \, J \)
• (4) \( 0.25 \, J \)

Two bodies of masses \( m_1 = 5 \, kg \) and \( m_2 = 10 \, kg \) are placed 2 meters apart. What is the gravitational force between them?

• (1) \( 1.67 \times 10^{-7} \, N \)
• (2) \( 6.67 \times 10^{-11} \, N \)
• (3) \( 3.34 \times 10^{-7} \, N \)
• (4) \( 2.00 \times 10^{-10} \, N \)

A charge of \( 2 ) is placed in an electric field of intensity \( 4 \times 10^3 \, N/C \). What is the force experienced by the charge?

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

In the reaction \( 2 \, H_2 + O_2 \to 2 \, H_2O \), if 4 moles of hydrogen react completely with oxygen, how many moles of water will be produced?

• (1) \( 2 \, mol \)
• (2) \( 4 \, mol \)
• (3) \( 8 \, mol \)
• (4) \( 1 \, mol \)

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

• (1) 1
• (2) 2
• (3) 3
• (4) 4

What is the molarity of a solution prepared by dissolving 10 grams of NaOH in 250 mL of water? (Molar mass of NaOH = 40 g/mol)

• (1) 0.1 M
• (2) 0.5 M
• (3) 1.0 M
• (4) 2.0 M

What is the pH of a 0.1 M NaOH solution?

• (1) 12
• (2) 13
• (3) 14
• (4) 11

Which of the following gases is produced when zinc reacts with dilute hydrochloric acid?

• (1) Oxygen
• (2) Hydrogen
• (3) Nitrogen
• (4) Carbon dioxide

Which of the following is an example of a redox reaction?

• (1) NaCl dissolving in water
• (2) 2H\(_2\)O\(_2\) (aq) \(\to\) 2H\(_2\)O (l) + O\(_2\) (g)
• (3) NaOH dissolving in water
• (4) CaCO\(_3\) (s) \(\to\) CaO (s) + CO\(_2\) (g)

Which of the following elements does not have a completely filled outermost shell in its ground state?

• (1) Neon
• (2) Helium
• (3) Oxygen
• (4) Argon

Which of the following compounds is an example of an ionic bond?

• (1) H\(_2\)O
• (2) CO\(_2\)
• (3) NaCl
• (4) Cl\(_2\)

Which of the following is the correct electron configuration for the ion \(Fe^{3+}\)?

• (1) [Ar] 3d\(^6\)
• (2) [Ar] 3d\(^5\)
• (3) [Ar] 4s\(^2\) 3d\(^3\)
• (4) [Ar] 3d\(^8\)

Which of the following gases is most soluble in water?

• (1) Oxygen
• (2) Nitrogen
• (3) Carbon dioxide
• (4) Hydrogen