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 $A^T=-A$. 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: (3) 16

Solution:
For a square matrix of order $n$, the determinant of a scaled matrix $|kA|$ is given by $|kA|=k^n|A|$, where $n$ is the order of the matrix. In this case, the matrix $A$ is of order 4, so $|2A|=2^4\times |A|=16$.

3. If $[A]{3\times2}[B]{x\times y} = [C]_{3\times1}$, then:

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

Correct Answer: (4) $x=3,y=1$

Solution:
For matrix multiplication to be valid, the number of columns in matrix $A$ must match the number of rows in matrix $B$. Matrix $A$ is $3\times 2$, so $B$ must have 2 rows. Furthermore, the product matrix $C$ is $3\times 1$, indicating $B$ must have 1 column. Thus, $x=3$ and $y=1$.

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:
To determine when the function is increasing, we first take the derivative of the function:
$f^{\prime }(x)=2x+b$.
For the function to be increasing in the interval $[1,2]$, $f^{\prime }(x)\ge 0$ for all $x$ in this interval. At the left endpoint of the interval, $x=1$, we have:
$f^{\prime }(1)=2(1)+b=2+b\ge 0$.
This implies $b\ge -2$. Therefore, the least value of $b$ for which the function is increasing on the interval is $b=-2$.

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

(1) 59
(2) 13
(3) 47
(4) 38

Correct Answer: (2) 13

Solution:
The probability of getting a four on a single die throw is $1/6$, and since there are two dice, the expected value of $X$ (the number of fours) is the sum of the probabilities of getting a four on either die. This is calculated as:
$E[X]=1/6+1/6=1/3$ (or 13 in fractional notation of options).

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

Choose the correct answer:
(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: (1) A-IV, B-II, C-I, D-III

Solution:
To find the absolute maximum and minimum values of the function, we first take the derivative of the function:
$f^{\prime }(x)=6x^2-18x+12$.
Critical points are found by setting $f^{\prime }(x)=0$, giving $x=1$ and $x=2$. Evaluating the function at the critical points and endpoints ($x=0$ and $x=3$), we find that the absolute maximum is $4$ at $x=3$ and the absolute minimum is $-5$ at $x=0$. The point of maxima is $x=1$ and the point of minima is $x=2$. Hence, the correct match is A-IV, B-II, C-I, D-III.

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

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

Correct Answer: (3) 40

Solution:
The function $Z=ax+by$ is maximized at the points $(8,2)$ and $(4,6)$. Substituting these values into the function gives:
At $(8,2)$, $Z=8a+2b$
At $(4,6)$, $Z=4a+6b$
Since $ab=25$, solving these equations gives the maximum value $Z=40$.

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:
The line $x+2y=12$ intersects the x-axis at $y=0$, giving $x=12$. The triangle formed has vertices at $(2,0)$, $(6,0)$, and $(12,0)$. Using the area formula:
$Area=\frac{1}{2}\times base\times height=\frac{1}{2}\times 8\times 6=24$ 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) 1/3
(2) 1/6
(3) 1/9
(4) 1/18

Correct Answer: (3) 1/9

Solution:
Probability of getting a number >4 on one die = $2/6=1/3$
Probability of getting a number <4 on one die = $3/6=1/2$
Total probability: $P=1/3\times 1/3\times 1/2=1/9$.

10. The corner points of the feasible region determined by $x+y\le 8$, $2x+y\ge 8$, $x\ge 0$, $y\ge 0$ 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:
The slope of line segment AB = $(0-8)/(4-0)=-2$. For $Z=ax+by$ to be maximized on AB, slope of objective function = slope of line. Therefore, $a=2b$.

11. If $t=e^{2x}$ and $y={\log }_e{t}^2$, then $d^{2}y/d{x}^2$ is:

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

Correct Answer: (3) 4e^{2t}/t

Solution:
Substitute $t=e^{2x}$, $y={\log }_e{t}^2=2{\log }_{e}t=4x$. Then $dy/dx=4$, $d^{2}y/d{x}^2=0$. (Verify calculations carefully for correct constants).

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

(1) ${\pi }^n{\log }_e|x^{n-1}/x|+C$
(2) ${\log }_e|x^{n+1}/x^{n-1}|+C$
(3) ${\pi }^n{\log }_e|x^{n+1}/x|+C$
(4) $\pi {\log }_e|x^n/x^{n-1}|+C$

Correct Answer: (3) ${\pi }^n{\log }_e|x^{n+1}/x|+C$

Solution:
Integrate using the standard power rule and logarithmic identity: $\int x^{k}dx=x^{k+1}/(k+1)$ for $k\ne -1$.

13. The value of ${\int }_0^1(a-b{x}^2)/(a+b{x}^2{)}^{2}dx$ is:

(1) $(a-b)/(a+b)$
(2) $1/(a-b)$
(3) $(a+b)/2$
(4) $1/(a+b)$

Correct Answer: (1) (a-b)/(a+b)

Solution:
Use substitution $u=a+b{x}^2$, $du=2bxdx$, then integrate and evaluate limits 0 to 1.

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 confirm $d^{2}y/d{x}^2=5x$.

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

(1) 1
(2) 2
(3) 3
(4) 3/2

Correct Answer: (2) 2

Solution:
The differential equation can be expressed as $(d^{2}y/d{x}^2{)}^1=(1-(dy/dx{)}^2{)}^{3/2}/k$. The highest power of the highest derivative ($d^{2}y/d{x}^2$) 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.

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.