BITSAT 2025 Question Paper 27th May Shift 2 (Available): Download Solutions with Answer Key

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

• (A) 121
• (B) 144
• (C) 100
• (D) 196

If \( f(x) = \sin^{-1}(2x\sqrt{1 - x^2}) \), then \( f'(x) \) is:

• (A) \( \frac{2(1 - 2x^2)}{\sqrt{1 - 4x^2(1 - x^2)}} \)
• (B) \( \frac{2x(1 - 2x^2)}{\sqrt{1 - 4x^2(1 - x^2)}} \)
• (C) \( \frac{1 - 2x^2}{\sqrt{1 - 4x^2(1 - x^2)}} \)
• (D) \( \frac{2x\sqrt{1 - x^2}}{1 - x^2} \)

If \( y = \tan^{-1}\left(\frac{2x}{1 - x^2}\right) \), then \( \frac{dy}{dx} \) is:

• (A) \( \frac{2}{1 + x^2} \)
• (B) \( \frac{1 - x^2}{1 + x^2} \)
• (C) \( \frac{2}{(1 - x^2)^2} \)
• (D) \( \frac{2}{1 - x^2} \)

If the roots of the quadratic equation \( x^2 + 4x + k = 0 \) are real and equal, then the value of \( k \) is:

• (A) 2
• (B) 4
• (C) 8
• (D) 16

If \( f(x) = x^2 + 3x \), then \( f'(x) \) is:

• (A) \( x + 3 \)
• (B) \( 2x + 3 \)
• (C) \( x^2 + 3 \)
• (D) \( 2x \)

Find the slope of the line passing through the points \( (1, 2) \) and \( (3, 6) \):

• (A) 3
• (B) 2
• (C) 4
• (D) 1

A body starts from rest and moves with constant acceleration. If it covers a distance of \( 40 \, m \) in 4 seconds, then its acceleration is:

• (A) \( 5 \, m/s^2 \)
• (B) \( 2.5 \, m/s^2 \)
• (C) \( 10 \, m/s^2 \)
• (D) \( 4 \, m/s^2 \)

If a force of \( 10 \, N \) displaces a body by \( 5 \, m \) in the direction of the force, the work done is:

• (A) \( 2 \, J \)
• (B) \( 50 \, J \)
• (C) \( 0 \, J \)
• (D) \( 5 \, J \)

A block of mass \( 5\, kg \) is placed on a rough horizontal surface. A horizontal force of \( 25\, N \) is applied. If the coefficient of friction is \( 0.4 \), what is the acceleration of the block? (Take \( g = 10\, m/s^2 \))

• (A) \( 1\, m/s^2 \)
• (B) \( 2\, m/s^2 \)
• (C) \( 3\, m/s^2 \)
• (D) \( 4\, m/s^2 \)

Three resistors of \( 2\, \Omega \), \( 3\, \Omega \), and \( 6\, \Omega \) are connected in parallel. What is the equivalent resistance of the combination?

• (A) \( 1\, \Omega \)
• (B) \( 2\, \Omega \)
• (C) \( 3\, \Omega \)
• (D) \( 4\, \Omega \)

How many moles are present in \( 22\, g \) of carbon dioxide (CO\(_2\))? (Molar mass of CO\(_2\) = \( 44\, g/mol \))

• (A) 0.25 mol
• (B) 0.5 mol
• (C) 1 mol
• (D) 2 mol

Which of the following elements has the highest electronegativity?

• (A) Sodium
• (B) Fluorine
• (C) Oxygen
• (D) Chlorine

Which of the following molecules has a linear shape?

• (A) H\(_2\)O
• (B) CO\(_2\)
• (C) NH\(_3\)
• (D) SO\(_2\)

Which of the following is a strong acid?

• (A) CH\(_3\)COOH
• (B) HCl
• (C) NH\(_4^+\)
• (D) H\(_2\)CO\(_3\)

Which of the following is an alkene?

• (A) C\(_2\)H\(_6\)
• (B) C\(_2\)H\(_4\)
• (C) C\(_3\)H\(_8\)
• (D) C\(_4\)H\(_{10}\)