CUET Maths Question Papers, Download Mathematics Previous Year Papers PDF

CUET 2026 Exam Pattern for Mathematics

The CUET Exam Pattern 2026 for mathematics consists of two main sections. Section A comprises core mathematics topics, while Section B contains questions on applied mathematics. The total exam duration is 60 minutes. Each correct answer earns 5 marks, and each incorrect answer results in a 1-mark deduction.

CUET Maths Previous Year Questions

Solving CUET Maths Previous Year Questions is an essential part of CUET 2026 preparation. They help you know the pattern of the exam, the most-tested topics, and how difficult you are likely to be tested. Solving these questions allows aspirants not only to gain a deeper understanding of the main mathematics topics but also to enhance their problem-solving speed and efficiency.

1. If A and B are symmetric matrices of the same order, then AB−BA is a:

(1) symmetric matrix
(2) zero matrix
(3) skew-symmetric matrix
(4) Identity matrix

Correct Answer: (3) skew-symmetric matrix

Solution:
For symmetric matrices A and B, the products AB and BA are not generally symmetric, but their difference AB−BA is always skew-symmetric. A skew-symmetric matrix is one where AT=−A. This property holds because the transpose of AB−BA results in the negative of the matrix, confirming that it is skew-symmetric.

2. If $A$ is a square matrix of order $4$ and $|A| = 4$, then $|2A|$ will be:

(1) $8$
(2) $64$
(3) $16$
(4) $4$

Correct Answer: (2) $64$

Solution:
For a square matrix of order $n$:
$|kA| = k^n |A|$

Here $n = 4$, so:
$|2A| = 2^4 \times 4 = 16 \times 4 = 64$

3. If $[A]{3 \times 2}[B]{x \times y} = [C]_{3 \times 1}$, then:

(1) $x = 1, y = 3$
(2) $x = 2, y = 1$
(3) $x = 3, y = 3$
(4) $x = 3, y = 1$

Correct Answer: (2) $x = 2, y = 1$

Solution:
For matrix multiplication:
Number of columns of $A$ = number of rows of $B$

So, $2 = x \Rightarrow x = 2$

Resultant matrix is $3 \times 1$, so $y = 1$

4. If a function $f(x) = x^2 + bx + 1$ is increasing in the interval $[1,2]$, then the least value of $b$ is:

(1) $5$
(2) $0$
(3) $-2$
(4) $-4$

Correct Answer: (3) $-2$

Solution:
$f'(x) = 2x + b$

For increasing function:
$f'(x) \geq 0$ on $[1,2]$

At $x = 1$:
$2(1) + b \geq 0 \Rightarrow b \geq -2$

Least value: $b = -2$

5. Two dice are thrown simultaneously. If $X$ denotes the number of fours, then the expectation of $X$ will be:

(1) $\frac{5}{9}$
(2) $\frac{1}{3}$
(3) $\frac{4}{7}$
(4) $\frac{3}{8}$

Correct Answer: (2) $\frac{1}{3}$

Solution:
Probability of getting a four on one die $= \frac{1}{6}$

For two dice:
$E(X) = \frac{1}{6} + \frac{1}{6} = \frac{1}{3}$

6. For the function $f(x) = 2x^3 - 9x^2 + 12x - 5$, $x \in [0,3]$, match List-I with List-II:

List-I
(A) Absolute maximum value
(B) Absolute minimum value
(C) Point of maxima
(D) Point of minima

List-II
(I) $3$
(II) $0$
(III) $-5$
(IV) $4$

(1) A-IV, B-II, C-I, D-III
(2) A-II, B-III, C-I, D-IV
(3) A-IV, B-III, C-II, D-I
(4) A-IV, B-III, C-I, D-II

Correct Answer: (3) A-IV, B-III, C-II, D-I

Solution:
$f'(x) = 6x^2 - 18x + 12 = 6(x-1)(x-2)$

Critical points: $x = 1, 2$

Evaluate at $x = 0, 1, 2, 3$:
$f(0) = -5$, $f(1) = 0$, $f(2) = -1$, $f(3) = 4$

Absolute maximum = $4$ at $x = 3$
Absolute minimum = $-5$ at $x = 0$

7. An objective function $Z = ax + by$ is maximum at points $(8,2)$ and $(4,6)$. If $a \geq 0$, $b \geq 0$ and $ab = 25$, then the maximum value of the function is:

(1) $60$
(2) $50$
(3) $40$
(4) $80$

Correct Answer: (3) $40$

Solution:
At $(8,2)$: $Z = 8a + 2b$
At $(4,6)$: $Z = 4a + 6b$

For maximum at both points:
$8a + 2b = 4a + 6b$

$\Rightarrow 4a = 4b \Rightarrow a = b$

Given $ab = 25$:
$a^2 = 25 \Rightarrow a = b = 5$

$Z = 8(5) + 2(5) = 40$

8. The area of the region bounded by the lines $x + 2y = 12$, $x = 2$, $x = 6$ and the $x$-axis is:

(1) $34$ sq units
(2) $20$ sq units
(3) $24$ sq units
(4) $16$ sq units

Correct Answer: (3) $24$ sq units

Solution:
From $x + 2y = 12$:
$y = \frac{12 - x}{2}$

Area = $\int_{2}^{6} \frac{12 - x}{2} , dx$

$= \frac{1}{2} \int_{2}^{6} (12 - x), dx$

$= \frac{1}{2} \left[12x - \frac{x^2}{2}\right]_{2}^{6}$

$= \frac{1}{2} \left[(72 - 18) - (24 - 2)\right]$

$= \frac{1}{2} (54 - 22) = \frac{32}{2} = 16$

Correct area = $16$ sq units

9. A dice is rolled thrice. What is the probability of getting a number greater than 4 in the first and second throw of the dice, and a number less than 4 in the third throw?

(1) $\frac{1}{3}$
(2) $\frac{1}{6}$
(3) $\frac{1}{9}$
(4) $\frac{1}{18}$

Correct Answer: (3) $\frac{1}{9}$

Solution:
Probability of getting a number $>4$ on one die $= \frac{2}{6} = \frac{1}{3}$
Probability of getting a number $<4$ on one die $= \frac{3}{6} = \frac{1}{2}$

Total probability:
$P = \frac{1}{3} \times \frac{1}{3} \times \frac{1}{2} = \frac{1}{9}$

10. The corner points of the feasible region determined by $x + y \leq 8$, $2x + y \geq 8$, $x \geq 0$, $y \geq 0$ are $A(0,8)$, $B(4,0)$ and $C(8,0)$. If the objective function $Z = ax + by$ has its maximum value on the line segment $AB$, then the relation between $a$ and $b$ is:

(1) $8a + 4 = b$
(2) $a = 2b$
(3) $b = 2a$
(4) $8b + 4 = a$

Correct Answer: (2) $a = 2b$

Solution:
Slope of line segment $AB = \frac{0 - 8}{4 - 0} = -2$

For $Z = ax + by$ to be maximized on $AB$, slope of objective function must equal slope of $AB$:
$-\frac{a}{b} = -2 \Rightarrow a = 2b$

11. If $t = e^{2x}$ and $y = \log_e t^2$, then $\frac{d^2 y}{dx^2}$ is:

(1) $0$
(2) $4t$
(3) $\frac{4e^{2t}}{t}$
(4) $\frac{e^{2t}(4t - 1)}{t^2}$

Correct Answer: (1) $0$

Solution:
$y = \log_e (t^2) = 2 \log_e t$

Since $t = e^{2x}$,
$y = 2 \cdot (2x) = 4x$

$\frac{dy}{dx} = 4$
$\frac{d^2 y}{dx^2} = 0$

12. $\int \frac{\pi x^n + 1}{x} , dx =$

(1) $\pi^n \log_e \left|\frac{x^n - 1}{x}\right| + C$
(2) $\log_e \left|\frac{x^{n+1}}{x^{n-1}}\right| + C$
(3) $\pi^n \log_e \left|\frac{x^n + 1}{x}\right| + C$
(4) $\pi \log_e \left|\frac{x^n}{x^{n-1}}\right| + C$

Correct Answer: (3) $\pi^n \log_e \left|\frac{x^n + 1}{x}\right| + C$

Solution:
Use standard integration rules and logarithmic properties:
$\int x^k dx = \frac{x^{k+1}}{k+1}, ; k \neq -1$

13. The value of $\int_0^1 \frac{a - bx^2}{(a + bx^2)^2} , dx$ is:

(1) $\frac{a - b}{a + b}$
(2) $\frac{1}{a - b}$
(3) $\frac{a + b}{2}$
(4) $\frac{1}{a + b}$

Correct Answer: (1) $\frac{a - b}{a + b}$

Solution:
Let $u = a + bx^2$

Then $du = 2bx , dx$

Apply substitution and evaluate limits from $0$ to $1$ to obtain:
$\frac{a - b}{a + b}$

14. The second-order derivative of which of the following functions is $5x$?

(1) $5x \log_e 5$
(2) $5x (\log_e 5)^2$
(3) $5x \log_e 5$
(4) $5x (\log_e 5)^2$

Correct Answer: (4) $5x (\log_e 5)^2$

Solution:
Differentiate twice and verify:
$\frac{d^2 y}{dx^2} = 5x$

15. The degree of the differential equation $(1 - (\frac{dy}{dx})^2)^{3/2} = k \frac{d^2 y}{dx^2}$ is:

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

Correct Answer: (2) $2$

Solution:
Remove the fractional power by squaring:

$\left(1 - \left(\frac{dy}{dx}\right)^2\right)^3 = k^2 \left(\frac{d^2 y}{dx^2}\right)^2$

The highest power of the highest order derivative $\frac{d^2 y}{dx^2}$ is $2$.

Download CUET Math Previous Year Question Paper PDF

We are attaching the official papers from previous years so that aspirants can review last year's exams closely. The exam pattern must be analysed thoroughly to avoid any unnecessary confusion. Of course, the exam pattern changes over the years, so students must always follow the latest exam pattern, which is CUET 2026.

If students successfully understand the question type and pattern of repeated questions by analysing official papers from the previous year, this technique will benefit students during the CUET 2026 exam.

CUET 2026 Mathematics Mock Test with Solution PDF Download

82% of aspirants feel more motivated when they can evaluate themselves with the help of Mock Tests. Conducting more mock tests helps students gain credibility and achieve positive results in the CUET 2026 exam. CUET Toppers shared this hack with us, stating that during the last week of revisions, students entirely depend on mock test performance.

Careers360 has launched this e-book to provide a single solution for PYQS, MCQS, and other study resources on one platform.

CUET 2026 Topic-Wise Mathematics Mock Tests

It is highly recommended that candidates download and review the CUET 2026 Mock Test Mathematics designed by Careers360 experts. The elaborated solutions to each question ensure that there are no residual doubts in the candidates' minds.

CUET 2026 Exam Preparation

The e-book features a comprehensive collection of Previous Year Questions (PYQs) to help students understand exam patterns and frequently asked topics, according to the latest CUET 2026 exam pattern.

Advantages of Practising CUET Previous Year Papers

Practising CUET Mathematics question papers from the previous year offers several benefits. Firstly, it helps in recognising Frequently Asked Topics for CUET 2026. Students benefit by sharpening their conceptual clarity by focusing on essential topics only. Solving past papers Increases Confidence among students for the real exam.

Familiarity with the concepts: It helps students understand the CUET exam format and types of questions.

Builds confidence: Regular practice helps build confidence in solving math questions on the CUET exam.

Time Management: It improves speed and efficiency in answering CUET questions within the time limit.

Improves understanding of the concepts: Repeated exposure to various topics strengthens knowledge of the concepts in the CUET exam.

Identifying Weaknesses: It enables students to pinpoint areas that require improvement in CUET exam preparation.

Understanding the Exam pattern means exposing hidden scoring areas in CUET 2026. Not wasting hours on irrelevant topics gives direction only for High-Priority Topics. If we look at the previous year's papers (2022-2025), they reveal consistent patterns with a good mix of theoretical concepts and practical applications, emphasising critical thinking and logical reasoning.

How to Download CUET 2026 Math Question Paper?

Students often analyse previous years' maths CUET question papers to identify important topics and patterns in the exam. To download the CUET Math question paper, follow these steps:

• Visit the official NTA website

• Look for the Download section

• Select the specific year, exam name, subject, whose question paper you want to download.

• Click on search.

• Click on the download link provided.

• Save the PDF file to your device for future reference.

As the CUET Mathematics 2026 exam approaches next year, consistent practice with relevant study materials can help you win the CUET 2026 race. Facing and solving real past questions psychologically prepares you for worst-case papers.

How to Use CUET Maths Previous Year Papers Effectively

Solving CUET Maths previous year question papers strategically is one of the most effective ways to prepare for CUET 2026. Practicing these papers helps students improve their problem-solving speed, accuracy, and understanding of important concepts while familiarizing them with the exam pattern.

Step-by-Step Approach to Solving Papers

Start your preparation with sectional practice, focusing on chapters like Algebra, Calculus, or Vectors individually. Begin by attempting easier questions to build confidence, then move on to moderate and difficult problems. This approach ensures better time management and helps identify recurring question types and high-weightage topics, which can significantly improve your CUET 2026 score.

Simulate Exam Conditions

Solve previous year papers under timed, exam-like conditions to replicate the pressure of the actual CUET exam. Time-bound practice not only enhances speed and accuracy but also builds endurance and reduces exam stress, giving you an edge on test day.

Analyze Mistakes and Weak Areas

After each practice session, carefully review your mistakes to identify weak areas. Maintaining a mistake log allows you to track recurring errors and revisit challenging concepts. Focusing on these weak spots ensures continuous improvement and strengthens your overall preparation.

Combine with NCERT and Reference Books

Align your practice with NCERT chapters and standard reference books for conceptual clarity. Focus on application-based questions from NCERT, as these are frequently tested in CUET Maths. Reinforcing difficult topics through repeated practice of previous year questions and reference material ensures a solid grasp of all essential concepts for CUET 2026.

Best Books for CUET 2026 Maths Preparation

Choosing the right books is not just about quantity—it’s about picking resources that actually match the CUET 2026 exam pattern, difficulty level, and syllabus coverage. A mix of NCERT-based conceptual clarity, objective practice, and CUET-specific preparation material is essential for balanced preparation.

This section will contain a carefully curated list of the best CUET Maths books, along with their key features, suitability for different preparation levels, and how each book helps in concept building, practice, and revision for CUET 2026.

Common Mistakes to Avoid in CUET 2026 Preparation

Avoiding common mistakes in the CUET exam can significantly improve your CUET 2026 Mathematics score and save you from unnecessary stress during preparation and the actual CUET exam day.

• Starting preparation too late - Begin at least 6 months before the exam, not 2-3 months. Late start leads to incomplete syllabus coverage and increased stress.

• Ignoring previous year papers - Start solving them after completing 50% syllabus. They reveal actual exam patterns and frequently asked topics.

• Not analysing mock test results - Spend equal time analysing mistakes as solving papers. Identify the CUET exam pattern and focus on areas for improvement.

• Poor question selection during exam - Scan the entire paper first, attempt easy questions initially, and save difficult ones for later.

• Rote learning formulas - Understand the logic behind formulas instead of just memorising them. This helps in applying them correctly during the exam.