CUET Maths Important Questions with Solutions

To do well on the CUET Maths Important Questions, you need to do more than just study; you need to know what the most important questions are and how much weight each chapter has. Knowing which topics are worth the most points helps you plan your study time and focus on the most important ones.

The marking scheme for the CUET exam math question paper is clear: each correct answer gets 5 points, and each wrong answer loses 1 point. It's important to practice CUET math questions based on trends from the previous year because you will lose points for mistakes. By looking at these patterns, you can get better at what you do, get a higher final score, and deal with being called names.

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CUET Maths Important Questions Pattern 2026

Before looking into the questions, you must understand the unique structure of the CUET exam maths question paper. Unlike other subjects, the Mathematics paper is divided into specific sections to cater to both Core and Applied Mathematics students.

The total duration for the CUET Math paper is 60 minutes, providing slightly more time than other domain subjects due to the calculation-intensive nature of the subject.

High-Weightage CUET Maths Important Questions

Analysis of the CUET Math previous year question paper shows that certain units consistently carry more weight. To maximise your score, prioritise the following areas:

1. Calculus (10–12 Questions)

Calculus is the backbone of the CUET Maths questions. Expect a heavy focus on:

• Continuity and Differentiability: Questions on the chain rule and logarithmic differentiation.

• Application of Derivatives: Focus on Tangents, Normals, and finding Maxima/Minima.

• Integrals: Practice definite integrals using properties, as these are common in the CUET exam maths question paper.

2. Algebra: Matrices and Determinants (7–9 Questions)

This is often considered the most scoring section. Important question types include:

• Finding the inverse of a matrix using the Adjoint method.

• Solving systems of linear equations using Cramer’s Rule or Matrix Method.

• Properties of Determinants (e.g.,  |kA| = k^n|A| ).

3. Vectors and 3D Geometry (6–8 Questions)

These topics are highly visual and formula-driven.

• Vectors: Focus on dot and cross products and the projection of one vector on another.

• 3D Geometry: Learn the shortest distance between two lines and the equation of a plane.

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CUET Maths Important Questions with Solutions

To excel in the questions section, you must practice a variety of problems that test both speed and logic. Based on the CUET exam maths question paper trends from previous years, here are 10 important questions across different chapters.

1. Relations and Functions

If a set  A = \{1, 2, 3\} , how many different relations can be defined on set  A ?

• Solution: The number of elements in  A \times A  is  3 \times 3 = 9 . The total number of relations is  2^n , where  n  is the number of ordered pairs. So, total relations =  2^9 = 512 .

2. Inverse Trigonometric Functions

Find the principal value of  \sin^{-1}(\frac{\sqrt{3}}{2}) + \cos^{-1}(-\frac{1}{2}) .

• Solution:  \sin^{-1}(\frac{\sqrt{3}}{2}) = \frac{\pi}{3} . For  \cos^{-1}(-\frac{1}{2}) , we use  \pi - \cos^{-1}(\frac{1}{2}) = \pi - \frac{\pi}{3} = \frac{2\pi}{3} . Total value =  \frac{\pi}{3} + \frac{2\pi}{3} = \pi .

3. Matrices

If  A  is a square matrix such that  A^2 = A , then find the value of  (I + A)^3 - 7A .

• Solution: Expand  (I + A)^3 = I^3 + 3I^2A + 3IA^2 + A^3 . Since  A^2 = A  and  A^3 = A \cdot A^2 = A , the expression becomes  I + 3A + 3A + A - 7A = I + 7A - 7A = I .

4. Determinants

Find the area of a triangle whose vertices are  (2, 0), (4, 5),  and (6, 3) using determinants.

• Solution: Area = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| .

• \frac{1}{2} |2(5-3) + 4(3-0) + 6(0-5)| = \frac{1}{2} |4 + 12 - 30| = \frac{1}{2} |-14| = 7 sq units.

5. Continuity and Differentiability

Find the derivative of \log(\sin x) with respect to x .

• Solution: Using the chain rule, let u = \sin x . The derivative is \frac{1}{\sin x} \cdot \frac{d}{dx}(\sin x) = \frac{\cos x}{\sin x} = \cot x 

6. Application of Derivatives

Find the slope of the tangent to the curve y = x^3 - x at x = 2 .

• Solution: \frac{dy}{dx} = 3x^2 - 1. Substituting  x = 2 , we get 3(2)^2 - 1 = 12 - 1 = 11.

7. Integrals

Evaluate the definite integral \int_{0}^{\pi/2} \sin^2 x \, dx.

• Solution: Using the property \int_{0}^{a} f(x) dx = \int_{0}^{a} f(a-x) dx, we get 2I = \int_{0}^{\pi/2} (\sin^2 x + \cos^2 x) dx = \int_{0}^{\pi/2} 1 \, dx = \frac{\pi}{2}. Thus, I = \frac{\pi}{4}.

8. Differential Equations

Find the order and degree of the differential equation:  (\frac{d^2y}{dx^2})^2 + (\frac{dy}{dx})^3 = e^x .

• Solution: The highest order derivative is \frac{d^2y}{dx^2} , so the Order is 2. The power of this derivative is 2, so the Degree is 2.

9. Vector Algebra

Find the projection of vector \vec{a} = 2\hat{i} + 3\hat{j} + 2\hat{k} on vector \vec{b} = \hat{i} + 2\hat{j} + \hat{k}.

• Solution: Projection = \frac{\vec{a} \cdot \vec{b}}{|\vec{b}|} = \frac{(2\cdot1) + (3\cdot2) + (2\cdot1)}{\sqrt{1^2 + 2^2 + 1^2}} = \frac{10}{\sqrt{6}}.

10. Matrices

If A is a 3 \times 3 matrix and |A| = 4, find the value of |3A|.

• Solution: Using the property |kA| = k^n|A|, where n is the order.

• |3A| = 3^3 \times |A| = 27 \times 4 = 108.

11. Relations and Functions

Let R be a relation on the set of real numbers defined by aRb if 1 + ab > 0. Is this relation transitive?

• Solution: By testing values (e.g., a=1, b=0.5, c=-2), you can determine if the property holds. These types of theoretical questions test your fundamental clarity.

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Benefits of Practising CUET Maths Important Questions

• You get a clear idea of the specific types of problems that appear in the actual exam.

• Regular practice builds the confidence you need to solve difficult equations without stress.

• It helps you increase your speed and accuracy so you can finish the paper on time.

• Solving these questions makes your understanding of complex math concepts much stronger.

• You can easily find and fix your weak spots to improve your overall score.

Read More: CUET Weightage Chapter Wise 2026

CUET Maths Important Questions FAQs

Q1. How many questions are mandatory in the CUET maths paper?

Section A, consisting of 15 questions, is mandatory for all students. Thereafter, you must choose 25 questions from either Section B1 or Section B2, making a total of 40 attempted questions.

Q2. Is there a difference between the CUET math paper from the previous year's Core and Applied?

The papers share Section A. However, the B1 section focuses on Core topics like Vectors and 3D Geometry, while B2 focuses on Applied topics like Financial Mathematics and Probability Distributions.

Q3. Which unit carries the highest weightage in important CUET maths questions?

Calculus (Differentiation and integration) typically holds the highest weightage, often accounting for 25% to 30% of the total marks in the exam.

Q4. Why should I practise the CUET Maths previous year paper?

If you practice the CUET Maths previous year paper, you'll get a better idea of how the test works, what kinds of questions are on it, and how hard it is. It also helps you manage your time better and shows you which topics are most important and often asked about. You can find out what you're not good at and feel more confident for the real test by doing these papers regularly.