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

The CUET 2025 exam was conducted from 13th May to 3rd June. The CUET Mathematics Question Paper 2025 with Answer Key and Solution PDF is available here for download. The CUET Mathematics paper was moderate to difficult in terms of difficulty level.

As per the exam pattern, the CUET Mathematics exam will consist of 50 questions for 250 marks to be attempted in 60 minutes. 5 marks will be awarded for each correct answer, and 1 mark will be deducted for incorrect answer.

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CUET 2025 Question Paper with Solution PDF

CUET Mathematics Question Paper 2025 with Answer Key

CUET Mathematics Question Paper 2025	Download PDF	Check Solution

Question 1:

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) \( p = 10, q = 18 \)

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Question 2:

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

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Question 3:

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) \( adj(A) = A^{-1} \)

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Question 4:

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

(A) 1
(B) 3
(C) 0
(D) 9

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Question 5:

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 \( Z = 0.10x + 0.09y \)

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Question 6:

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) \( 30^\circ \)

View Solution

Question 7:

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) \( 45^\circ \)

View Solution

Question 8:

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) \( \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \)

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CUET Mathematics Sectional weightage

CUET Mathematics 2025 paper has three sections:

Section A: Core Maths (40%), including core subject matter such as Calculus & Integration, Probability & Linear Programming, Algebra, and Differential Equations.

Section B1: Higher Mathematics (25%), with emphasis on higher-level concepts such as Relations & Functions and Vectors & 3D Geometry

Section B2: Applied Mathematics (35%), with a focus on practical application via Financial Mathematics & Quantification and Index Numbers & Data Analysis.

Section	Topic	Important Subtopics	Expected Weightage
Section A: Core Mathematics	Calculus & Integration	Differentiation, Integration Techniques, Definite and Indefinite Integrals, Applications of Integrals	8–10 questions
	Probability & Linear Programming	Probability Distributions, Conditional Probability, Linear Programming Problems, Graphical Solutions	3–4 questions
	Algebra	Quadratic Equations, Sequences and Series, Matrices, Determinants	2–3 questions
	Differential Equations	First-Order Differential Equations, Linear Differential Equations, Applications	2–3 questions
Section B1: Advanced Mathematics	Relations & Functions	Types of Functions, Inverse Functions, Composite Functions, Graph Transformations	6–7 questions
	Vectors & 3D Geometry	Vector Operations, Scalar and Vector Products, Lines and Planes in 3D, Distance and Angle Calculations	4–5 questions
Section B2: Applied Mathematics	Financial Mathematics & Quantification	Simple and Compound Interest, Annuities, Time Value of Money, Quantifying Data	8–10 questions
	Index Numbers & Data Analysis	Index Numbers, Weighted Averages, Measures of Central Tendency, Data Interpretation	6–7 questions

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CUET Questions

1.
A simple random sample consists of five observations: 4, 5, 9, 10 & 12. What is the point estimate of population standard deviation?

View Solution

2.
For the function \[ f(x)=ax+\frac{b}{x}, \qquad a>0,\; b>0, \] which of the following statements are correct?

(A) Function \(f(x)\) is increasing on \[ \left(\sqrt{\frac{b}{a}},\,\infty\right) \]

(B) Function \(f(x)\) is increasing on \[ (-\infty,\infty) \]

(C) Function \(f(x)\) is decreasing on \[ \left(-\sqrt{\frac{b}{a}},\,\sqrt{\frac{b}{a}}\right) \]

(D) Function \(f(x)\) is increasing on \[ \left(-\infty,\,-\sqrt{\frac{b}{a}}\right) \]

(A), (B) and (D) only
(A) and (C) only
(A), (C) and (D) only
(A) and (D) only

View Solution

3.
A function \[ f(x)=12x^{4/3}-6x^{1/3}, \qquad x\in[-1,1] \] is given. Then, which of the following are TRUE?

(A) \(f(x)\) has a critical point at \(x=\dfrac{1}{8}\)
(B) Absolute maximum value of \(f(x)\) is \(18\)
(C) Absolute maximum value of \(f(x)\) is \(6\)
(D) Absolute minimum value of \(f(x)\) is \(-\dfrac{9}{4}\)

(A), (C) and (D) only
(A) and (B) only
(A), (B) and (D) only
(C) and (D) only

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4.
If \( P(A) = \frac{3}{5} \), \( P(\overline{B}) = \frac{4}{7} \), and \( P(A \cup B) = \frac{2}{3} \), which of the following are correct?

(A) \( P(A \cap B) = \frac{17}{105} \)
(B) \( P(A \mid B) = \frac{17}{45} \)
(C) A and B are independent events
(D) \( P(B \mid A) = \frac{17}{36} \)

(A), (B) and (D) only
(B) and (C) only
(A) and (D) only
(A) and (B) only

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5.
The function \[ f(x)=\sum_{k=1}^{7}(x-k)^2 \] has a minimum value at \(x=a\). Then, \(a\) is equal to:

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6.
A pump can fill a tank in 2 hours. Because of a leak, it took \( 2 \frac{1}{3} \) hours (or 7/3 hours) to fill the tank. In how many hours can the leak drain all the water?

14 hours
7/3 hours
3/7 hours
7 hours

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

CUET Mathematics Question Paper 2025 with Answer Key

CUET Mathematics Sectional weightage

CUET Questions

1.
A simple random sample consists of five observations: 4, 5, 9, 10 & 12. What is the point estimate of population standard deviation?

4.
If \( P(A) = \frac{3}{5} \), \( P(\overline{B}) = \frac{4}{7} \), and \( P(A \cup B) = \frac{2}{3} \), which of the following are correct?

(A) \( P(A \cap B) = \frac{17}{105} \)
(B) \( P(A \mid B) = \frac{17}{45} \)
(C) A and B are independent events
(D) \( P(B \mid A) = \frac{17}{36} \)

5.
The function \[ f(x)=\sum_{k=1}^{7}(x-k)^2 \] has a minimum value at \(x=a\). Then, \(a\) is equal to:

6.
A pump can fill a tank in 2 hours. Because of a leak, it took \( 2 \frac{1}{3} \) hours (or 7/3 hours) to fill the tank. In how many hours can the leak drain all the water?

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CUET Mathematics Question Paper 2025 with Answer Key

CUET Mathematics Sectional weightage

CUET Questions

1.A simple random sample consists of five observations: 4, 5, 9, 10 & 12. What is the point estimate of population standard deviation?

4.If \( P(A) = \frac{3}{5} \), \( P(\overline{B}) = \frac{4}{7} \), and \( P(A \cup B) = \frac{2}{3} \), which of the following are correct? (A) \( P(A \cap B) = \frac{17}{105} \) (B) \( P(A \mid B) = \frac{17}{45} \) (C) A and B are independent events (D) \( P(B \mid A) = \frac{17}{36} \)

5. The function \[ f(x)=\sum_{k=1}^{7}(x-k)^2 \] has a minimum value at \(x=a\). Then, \(a\) is equal to:

6.A pump can fill a tank in 2 hours. Because of a leak, it took \( 2 \frac{1}{3} \) hours (or 7/3 hours) to fill the tank. In how many hours can the leak drain all the water?

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1.
A simple random sample consists of five observations: 4, 5, 9, 10 & 12. What is the point estimate of population standard deviation?

4.
If \( P(A) = \frac{3}{5} \), \( P(\overline{B}) = \frac{4}{7} \), and \( P(A \cup B) = \frac{2}{3} \), which of the following are correct?

(A) \( P(A \cap B) = \frac{17}{105} \)
(B) \( P(A \mid B) = \frac{17}{45} \)
(C) A and B are independent events
(D) \( P(B \mid A) = \frac{17}{36} \)

5.
The function \[ f(x)=\sum_{k=1}^{7}(x-k)^2 \] has a minimum value at \(x=a\). Then, \(a\) is equal to:

6.
A pump can fill a tank in 2 hours. Because of a leak, it took \( 2 \frac{1}{3} \) hours (or 7/3 hours) to fill the tank. In how many hours can the leak drain all the water?