VITEEE 2025 22 April Shift 2 Question Paper (Available): Download Solutions with Answer Key

Find the derivative of \( f(x) = 3x^2 - 4x + 7 \).

• (1) \( 6x - 4 \)
• (2) \( 6x - 7 \)
• (3) \( 3x - 4 \)
• (4) \( 3x + 4 \)

Solve for \( x \) in the equation \( \frac{2x - 3}{4} = 5 \).

• (1) \( x = 13 \)
• (2) \( x = 14 \)
• (3) \( x = 15 \)
• (4) \( x = 16 \)

Find the value of \( \log_2 32 \).

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

Find the value of \( x \) in the equation \( 4(x - 2) = 3(x + 5) \).

• (1) \( x = 23 \)
• (2) \( x = 3 \)
• (3) \( x = 7 \)
• (4) \( x = -7 \)

Find the derivative of \( f(x) = 4x^3 - 6x^2 + 2x - 5 \).

• (1) \( 12x^2 - 12x + 2 \)
• (2) \( 12x^2 - 10x + 2 \)
• (3) \( 12x^2 - 12x + 5 \)
• (4) \( 12x^2 - 10x + 3 \)

What is the area of a triangle with base \( 12 \, cm \) and height \( 8 \, cm \)?

• (1) \( 48 \, cm^2 \)
• (2) \( 60 \, cm^2 \)
• (3) \( 40 \, cm^2 \)
• (4) \( 36 \, cm^2 \)

A body of mass 10 kg is moving with a velocity of 20 m/s. What is the kinetic energy of the body?

• (1) \( 2000 \, J \)
• (2) \( 1000 \, J \)
• (3) \( 4000 \, J \)
• (4) \( 5000 \, J \)

A capacitor is charged with a voltage of 100 V. If the capacitance of the capacitor is \( 10 \, muF \), what is the charge on the capacitor?

• (1) \( 1 \, C \)
• (2) \( 10 \, C \)
• (3) \( 100 \, C \)
• (4) \( 0.1 \, C \)

A ball is dropped from a height of 20 m. What is its velocity just before hitting the ground? (Take \( g = 9.8 \, m/s^2 \))

• (1) \( 10 \, m/s \)
• (2) \( 14 \, m/s \)
• (3) \( 20 \, m/s \)
• (4) \( 18 \, m/s \)

A force of \( 10 \, N \) acts on a body of mass \( 2 \, kg \). What is the acceleration of the body?

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

A parallel plate capacitor has a capacitance of \( 4 \, muF \). If the dielectric constant of the material between the plates is \( 5 \), what will be the new capacitance?

• (1) \( 20 \, muF \)
• (2) \( 15 \, muF \)
• (3) \( 8 \, muF \)
• (4) \( 10 \, muF \)

A body is thrown vertically upwards with an initial velocity of \( 10 \, m/s \). How high will the body rise? (Take \( g = 10 \, m/s^2 \))

• (1) \( 5 \, m \)
• (2) \( 10 \, m \)
• (3) \( 20 \, m \)
• (4) \( 50 \, m \)

A body of mass 5 kg is moving with a velocity of 15 m/s. What is its momentum?

• (1) \( 75 \, kg \cdot m/s \)
• (2) \( 50 \, kg \cdot m/s \)
• (3) \( 25 \, kg \cdot m/s \)
• (4) \( 10 \, kg \cdot m/s \)

What is the wavelength of a sound wave with a frequency of \( 500 \, Hz \) in air? (Take the speed of sound in air as \( 340 \, m/s \))

• (1) \( 0.68 \, m \)
• (2) \( 0.68 \, cm \)
• (3) \( 1.7 \, m \)
• (4) \( 1.5 \, m \)

What is the molecular mass of \( K_2SO_4 \)?

• (1) \( 174 \, g/mol \)
• (2) \( 132 \, g/mol \)
• (3) \( 144 \, g/mol \)
• (4) \( 94 \, g/mol \)

Which of the following gases has the highest density at STP?

• (1) \( CO_2 \)
• (2) \( O_2 \)
• (3) \( N_2 \)
• (4) \( CH_4 \)

What is the pH of a \( 0.01 \, M \) solution of \( HCl \)?

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

Which of the following compounds has the highest boiling point?

• (1) \( H_2O \)
• (2) \( CH_4 \)
• (3) \( NH_3 \)
• (4) \( CO_2 \)

What is the oxidation number of sulfur in \( H_2SO_4 \)?

• (1) \( +6 \)
• (2) \( +2 \)
• (3) \( 0 \)
• (4) \( -2 \)

What is the pH of a \( 0.01 \, M \) solution of \( NaOH \)?

• (1) \( 12 \)
• (2) \( 13 \)
• (3) \( 14 \)
• (4) \( 11 \)