CUET Maths Question Papers 2025, Download Question Paper PDF with Answers

CUET Maths Previous Year Question Papers: For CUET 2025 candidates, practicing previous year question papers is an effective way to enhance exam preparation and enhance the prospects of success. Statistically, practicing 10 or more previous year question papers prior to the exam can enhance your performance by as much as 30%. Candidates opting for Mathematics as their subject should incorporate solving CUET 2025 Mathematics question papers as an integral part of their study schedule. The CUET Maths 2025 syllabus consists of major topics like algebra, calculus, integration, differential equations, and many more that are frequently tested. A substantial number of questions in the CUET Maths exam repeat conceptually every 2–3 years, so it is necessary for the candidates to practice these Previous Year Question Papers extensively to gain a better understanding of the subject and sharpen their problem-solving skills.

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1. CUET Maths Previous Year Questions
2. CUET All Subjects Question Papers
3. Download - CUET UG 2025- Mathematics Mock Test with Solution PDF
4. CUET 2025 Exam Structure for Mathematics
5. How to Download CUET 2025 Math Question Paper?

LiveCUET Answer Key 2025 LIVE: NTA CUET UG response sheet soon at cuet.nta.nic.in; result date, cut-off updatesJun 15, 2025 | 12:21 PM IST

The CUET UG 2025 scores are valid only in the colleges/universities that accept the exam scores for admission to their courses.

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This article will walk you through the significance of solving past year CUET Mathematics question papers, summarize the key topics included in the exam, and give tips on how to tackle the questions efficiently. We will also present a thorough analysis of past papers to enable you to recognize patterns, frequently asked questions, and areas of focus in your preparation for CUET 2025.

CUET Maths Previous Year Questions

Solving CUET Maths Previous Year Questions is an essential part of CUET 2025 preparation. They are useful for knowing the pattern of the exam, most-tested topics, and how difficult you are likely to be tested. These questions, upon solving, allow aspirants to not just get a deeper knowledge of main mathematics topics but also enhance problem-solving speed and efficiency.

1. If A and B are symmetric matrices of the same order, then $\mathrm{AB}-\mathrm{BA}$ 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 product $\mathrm{AB}$ and $\mathrm{BA}$ are not generally symmetric, but their difference $\mathrm{AB}-\mathrm{BA}$ is always skew-symmetric. A skew-symmetric matrix is one where $A^T=-A$. This property holds because the transpose of $\mathrm{AB}-\mathrm{BA}$ results in the negative of the matrix, confirming that it is skew-symmetric.

2. If A is a square matrix of order 4 and $|\mathrm{A}|=4$, then $|2\mathrm{A}|$ will be 1

(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 $|2A|=2^4\times |A|=2^4\times 4=16$.

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

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

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

(3) $x=3,y=3$

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

Correct answer: (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 3×2, so B must have 2 rows. Furthermore, the product matrix C is 3×1, 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 namber 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:

The probability of getting a four on a single die throw is $\frac{1}{6}$, 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:

$\mathbb{E}[X]=\frac{1}{6}+\frac{1}{6}=\frac{1}{3}$.

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

Choose the correct answer from the options given below :

(1) A-IV,B-II,C-1,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:

$f^{\prime }(x)=6x^2-18x+12$.

We find the critical points by setting $f^{\prime }(x)=0$, which gives $x=1$ 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 equal to:

(2) 50

(1) 60

(4) 80

(3) 40

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 $ab=25$, we can solve these two equations to find the maximum value of $Z$.

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

To find the area, first determine the points where the lines intersect the x-axis. The line $x+2y=12$ intersects the x-axis at $y=0$, so $x=12$. Thus, the triangle formed has vertices at $(2,0)$, $(6,0)$, and $(12,0)$. Using the formula for the area of a triangle $\text{Area}=\frac{1}{2}\times \text{base}\times \text{height}$, we get an area of 24 square units.

9. A die is rolled thrice. What is the probability of getting a number greater than 4 in the first and the second throw of 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:

The probability of getting a number greater than 4 (i.e., 5 or 6) on a single die is $\frac{2}{6}=\frac{1}{3}$. The probability of getting a number less than 4 (i.e., 1, 2, or 3) is $\frac{3}{6}=\frac{1}{2}$. The total probability of getting a number greater than 4 on the first two rolls and a number less than 4 on the third roll is:

$\mathbb{P}=\frac{1}{3}\times \frac{1}{3}\times \frac{1}{2}=\frac{1}{9}$.

10. The comer 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) $\mathrm{a}=2\mathrm{b}$

(3) $b=2a$

(4) $8b+4=a$

Correct answer: (2) $\mathrm{a}=2\mathrm{b}$

Solution:

The line segment AB determines the boundary of the feasible region. The slope of this line is $-\frac{8}{4}=-2$. For the objective function $Z=ax+by$ to have its maximum on this line, the slope of the objective function must match the slope of the line segment. Therefore, the relation between $a$ and $b$ is $a=2b$.

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

(1) 0

(2) $4t$

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

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

Correct answer: (3) $\frac{4}{3}$

Solution:

The slope of a line is given by the coefficient of $x$ when the equation is written in the form $y=mx+c$, where $m$ is the slope. Rearranging the given equation $4x-3y=12$ into slope-intercept form:

$-3y=-4x+12$,

$y=\frac{4}{3}x-4$.

So, the slope $m$ is $\frac{4}{3}$.

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

(1) $\frac{\pi }{n}{\log }_e\left|\frac{x^n-1}{x^n}\right|+C$

(2) ${\log }_e\left|\frac{x^n+1}{x^n-1}\right|+C$

(3) $\frac{\pi }{n}{\log }_e\left|\frac{x^n+1}{x^n}\right|+C$

(4) $\pi {\log }_e\left|\frac{x^n}{x^n-1}\right|+C$

Correct answer: (3) 5

Solution:

The distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the formula:

$d=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$.

Substituting the coordinates of points A and B:

$d=\sqrt{(5-2{)}^2+(7-3{)}^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5$.

13. The value of ${\int }_0^1\frac{a-b{x}^2}{{(a+b{x}^2)}^2}dx$ 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) $\frac{5}{3}$

Solution:

The sum of the solutions of a quadratic equation $a{x}^2+bx+c=0$ is given by $-\frac{b}{a}$. For the equation $3x^2-5x+2=0$, we have $a=3$, $b=-5$, and $c=2$. Therefore, the sum of the solutions is:

$-\frac{-5}{3}=\frac{5}{3}$.

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

(1) $5^x{\log }_{e}5$

(2) $5^x{({\log }_{e}5)}^2$

(3) $\frac{5^x}{{\log }_{e}5}$

(4) $\frac{5^x}{{({\log }_{e}5)}^2}$

Correct answer: (4) $f^{\prime }(c)=\frac{f(b)-f(a)}{b-a}$

Solution:

This is a statement of the Mean Value Theorem. It states that if a function is continuous on a closed interval $[a,b]$ and differentiable on the open interval $(a,b)$, then there exists at least one point $c\in (a,b)$ such that:

$f^{\prime }(c)=\frac{f(b)-f(a)}{b-a}$.

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

(1) 1

(2) 2

(3) 3

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

Correct answer: (2) 4
Solution:
The formula for the area of a triangle with vertices $(x_1,y_1)$, $(x_2,y_2)$, and $(x_3,y_3)$ is:
$\text{Area}=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|$.
Substituting the coordinates of the vertices $(0,0)$, $(2,0)$, and $(2,4)$:
$\text{Area}=\frac{1}{2}|0(0-4)+2(4-0)+2(0-0)|=\frac{1}{2}|0+8+0|=\frac{1}{2}\times 8=4$.

CUET All Subjects Question Papers

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• CUET Previous Years' Papers

Download - Official Previous Year Question Paper with PDF

We are attaching the official papers from previous years so aspirants can look closely at last year's exams. The exam pattern must be analysed thoroughly to avoid any unnecessary confusion. Of course, the exam pattern keeps changing over the years, so students must always follow the latest exam pattern, CUET 2025.

If students successfully understood the question type and pattern of repeated questions by analysing official papers from the previous year, this technique will benefit students during the CUET 2025 exam.

Download - CUET UG 2025- Mathematics Mock Test with Solution PDF

82% of aspirants feel more motivated when they can evaluate themselves with the help of Mock Tests. Attempting more mock tests ensures more credibility among students to pass the CUET 2025 exam with positive results.CUET Toppers shared this hack with us, stating that during the last week of revisions, students entirely depend on mock test performance.

Career360 also launched an e-book to provide one solution for PYQS, MCQS, and more study resources on one platform.

CUET 2025 Topic-Wise Mathematics Mock Tests

It is highly recommended that the candidates download and go through the mock CUET Mathematics tests designed by the experts of Careers360. The elaborated solutions to each question ensure no residual doubts in the candidates' minds.

Latest: To practice CUET Mathematics mock test paper- Click here

Download - CUET UG 2025- Mathematics Exam Preparation

The e-book includes a vast collection of Previous Year Questions (PYQS) to help students understand exam patterns and frequently asked topics according to the latest exam pattern of CUET 2025.

Advantages of Practicing CUET Previous Year Papers

Practicing CUET Mathematics question papers from the previous year offers several benefits. Firstly, it helps in recognising Frequently Asked Topics for CUET 2025. 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 builds confidence in solving math questions in 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 allows students to identify areas needing improvement in CUET exam preparation.

Understanding the Exam pattern means exposing hidden scoring areas in CUET 2025. Not wasting hours on irrelevant topics gives direction only for High-Priority Topics. If we look at the previous year's papers (2022-2024), they reveal consistent patterns with a good mix of theoretical concepts and practical applications, emphasising critical thinking and logical reasoning.

CUET 2025 Exam Structure for Mathematics

The CUET Mathematics Exam Pattern 2025 consists of two main sections. Section A comprises 35 core mathematics topics, while Section B contains 35 questions on applied mathematics. Students must attempt 25 questions from each section, for 50 questions to be answered. The total exam duration is 60 minutes, with each correct answer earning 5 marks and each incorrect answer resulting in a deduction of 1 mark.

How to Download CUET 2025 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 CUET website

• Look for the Download section

• Select the specific Math question paper you want to download.

• Click on the download link provided.

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

As the CUET Mathematics 2025 exam approaches on 8th May 2025, consistent practice with relevant study materials can help you win the CUET 2025 race. Facing and solving real past questions psychologically prepares you for worst-case papers.