CUET Mathematics Question Paper 2025 (Available)- Download Answer Key and Solution PDF

The feasible region is bounded by the inequalities: \[ 3x + y \geq 90, \quad x + 4y \geq 100, \quad 2x + y \leq 180, \quad x, y \geq 0 \]
If the objective function is \( Z = px + qy \) and \( Z \) is maximized at points \( (6, 18) \) and \( (0, 30) \), then the relationship between \( p \) and \( q \) is:

• (A) \( p = 15, q = 12 \)
• (B) \( p = 12, q = 15 \)
• (C) \( p = 18, q = 10 \)
• (D) \( p = 10, q = 18 \)

If \( A \) is a \( 2 \times 2 \) matrix and \( |A| = 4 \), then \( |A^{-1}| \) is:

• (A) 16
• (B) \( \frac{1}{4} \)
• (C) 4
• (D) 1

For a matrix \( A \) of order \( 3 \times 3 \), which of the following is true?

• (A) \( adj(A) = A^2 \)
• (B) \( adj(A) \neq A^2 \)
• (C) \( adj(A) = A^T \)
• (D) \( adj(A) = A^{-1} \)

If \( A \) is a square matrix such that \( adj(adj(A)) = A \), then \( |A| \) is:

• (A) 1
• (B) 3
• (C) 0
• (D) 9

A person wants to invest at least ₹20,000 in plan A and ₹30,000 in plan B. The return rates are 9% and 10% respectively. He wants the total investment to be \₹80,000 and investment in A should not exceed investment in B. Which of the following is the correct LPP model (maximize return \( Z \))?

• (A) Maximize \( Z = 0.09x + 0.1y \)
• (B) Maximize \( Z = 0.1x + 0.09y \)
• (C) Maximize \( Z = 0.15x + 0.10y \)
• (D) Maximize \( Z = 0.10x + 0.09y \)

The angle between vectors \( \mathbf{a} = \hat{i} + \hat{j} - 2\hat{k} \) and \( \mathbf{b} = 3\hat{i} - \hat{j} + 2\hat{k} \) is:

• (A) \( 60^\circ \)
• (B) \( 90^\circ \)
• (C) \( 45^\circ \)
• (D) \( 30^\circ \)

If vectors \( \mathbf{u}, \mathbf{v}, \) and \( \mathbf{w} \) satisfy \( \mathbf{u} + \mathbf{v} + \mathbf{w} = 0 \), and \( \mathbf{u} \) and \( \mathbf{v} \) are unit vectors, while \( |\mathbf{w}| = \sqrt{3} \), then the angle between \( \mathbf{v} \) and \( \mathbf{w} \) is:

• (A) \( 90^\circ \)
• (B) \( 60^\circ \)
• (C) \( 120^\circ \)
• (D) \( 45^\circ \)

Direction cosines of a vector perpendicular to \( \mathbf{a} = \hat{i} + 2\hat{j} + 3\hat{k} \) and \( \mathbf{b} = 2\hat{i} - \hat{j} + \hat{k} \) are:

• (A) \( \frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{2}{\sqrt{6}} \)
• (B) \( \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}} \)
• (C) \( \frac{1}{\sqrt{5}}, \frac{2}{\sqrt{5}}, \frac{1}{\sqrt{5}} \)
• (D) \( \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \)