The CUET Mathematics 2025 exam was held from 13th May to 3rd June, and the question paper, answer key, and solution PDF are available for download here. The Mathematics paper in CUET evaluates a student's understanding of algebra, calculus, trigonometry, coordinate geometry, probability, statistics, and other core mathematical concepts.
As per the revised exam pattern, students had to attempt all 50 questions within 60 minutes, with the paper carrying a total of 250 marks. Each correct answer earns +5 marks, while every incorrect answer results in a –1 mark deduction.
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CUET 2025 Question Paper with Solution PDF
CUET Mathematics Question Paper with Solution PDF
| CUET Mathematics 2025 Question Paper with Solutions PDF | Download PDF | Check Solutions |
Let A = \( [a_{ij}]_{n x n} \) be a matrix. Then Match List-I with List-II
List-I
(A) \(A^{T}\) = A
(B) \(A^{T}\) = -A
(C) |A| = 0
(D) |A| \(\neq\) 0
List-II
(I) A is a singular matrix
(II) A is a non-singular matrix
(III) A is a skew symmetric matrix
(IV) A is a symmetric matrix
Choose the correct answer from the options given below:
then the matrix AB is equal to 
If A is a square matrix and I is the identity matrix of same order such that \(A^{2}\) = I, then \( (A - I)^{3}\) + \((A + I)^{3}\) - 3A is equal to
If 
, then |adj A| is equal to
If y = \(3e^{2x} + 2e^{3x}\), then \(\frac{d^2y}{dx^2} + 6y\) is equal to
The interval, on which the function f(x) = \( x^{2} e^{-x}\) is increasing, is equal to
If the maximum value of the function f(x) = \(\frac{\log_e x}{x}\), x \(>\) 0 occurs at x = a, then \(a^{2}f''\)(a) is equal to
\(\int_{1}^{4} |x - 2| dx\) is equal to
The integral I = \(\int \frac{e^{5\log_e x} - e^{4\log_e x}}{e^{3\log_e x} - e^{2\log_e x}} dx\) is equal to
The area (in sq. units) of the region bounded by the parabola \(y^{2}\) = 4x and the line x = 1 is
Which of the following are linear first order differential equations?
(A) \(\frac{dy}{dx} + P(x)y = Q(x)\)
(B) \(\frac{dx}{dy} + P(y)x = Q(y)\)
(C) \((x - y)\frac{dy}{dx} = x + 2y\)
(D) \((1 + x^2)\frac{dy}{dx} + 2xy = 2\)
Choose the correct answer from the options given below:
The solution of the differential equation \(\log_e(\frac{dy}{dx}) = 3x + 4y\) is given by
The probability distribution of a random variable X is given by
If a \(>\) 0, then P(0 \(<\) x \(\le\) 2) is equal to
The corner points of the feasible region associated with the LPP: Maximise Z = px + qy, p, q \(>\) 0 subject to 2x + y \(\le\) 10, x + 3y \(\le\) 15, x,y \(\ge\) 0 are (0, 0), (5, 0), (3, 4) and (0, 5). If optimum value occurs at both (3, 4) and (0, 5), then
Consider the LPP: Minimize Z = x + 2y subject to 2x + y \(\ge\) 3, x + 2y \(\ge\) 6, x, y \(\ge\) 0. The optimal feasible solution occurs at
Let f: R \(\rightarrow\) R be defined as f(x) = 10x. Then (Where R is the set of real numbers)
Let A = {1, 2, 3}. Then, the number of relations containing (1, 2) and (1, 3), which are reflexive and symmetric but not transitive, is
for \(|x| < 1\), \(sin(tan^{-1}x)\) equal to
Let 
and Mij, Aij respectively denote the minor, co-factor of an element aij of matrix A, then which of the following are true?
(A) M22 = -1
(B) A23 = 0
(C) A32 = 3
(D) M23 = 1
(E) M32 = -3
Choose the correct answer from the options given below:
Let 
. If \(A^{T} + A = I\), then
If A and B are skew-symmetric matrices, then which one of the following is NOT true?
If A and B are invertible matrices then which of the following statement is NOT correct?
Let A = [aij]2x3 and B = [bij]3x2, then |5AB| is equal to
Let AX = B be a system of three linear equations in three variables. Then the system has
(A) a unique solution if |A| = 0
(B) a unique solution if |A| \(\neq\) 0
(C) no solutions if |A| = 0 and (adj A) B \(\neq\) 0
(D) infinitely many solutions if |A| = 0 and (adj A)B = 0
Choose the correct answer from the options given below:
If the function 
is continuous at x = \(\frac{\pi}{2}\), then k is equal to
Match List-I with List-II
Choose the correct answer from the options given below:
Let y = sin(cos(x2)), then the value of \(\frac{dy}{dx}\) at x = \(\frac{\sqrt{\pi}}{2}\) is equal to
Match List-I with List-II
Choose the correct answer from the options given below:
The function f(x) = tanx - x
The rate of change of area of a circle with respect to its circumference when radius is 4cm, is
\(\int_{\pi/6}^{\pi/3} \frac{\tan x}{\tan x + \cot x} dx\) is equal to
Match List-I with List-II
Choose the correct answer from the options given below:
The integral I = \(\int e^x (\frac{x-1}{3x^2}) dx\) is equal to
The area (in sq. units) of the region bounded by the curve y = x5, the x-axis and the ordinates x = -1 and x = 1 is equal to
The area (in sq. units) of the region bounded by y = \(2\sqrt{1-x^2}\), x \(\in\) [0,1] and x-axis is equal to
The integrating factor of the differential equation \((x \log_e x) \frac{dy}{dx} + y = 2\log_e x\) is
Consider the differential equation, \(x \frac{dy}{dx} = y(\log_e y - \log_e x + 1)\), then which of the following are true?
(A) It is a linear differential equation
(B) It is a homogenous differential equation
(C) Its general solution is \(\log_e(\frac{y}{x}) = Cx\), where C is constant of integration
(D) Its general solution is \(\log_e(\frac{x}{y}) = Cy\), where C is constant of integration
(E) If y(1) = 1, then its particular solution is y = x
Choose the correct answer from the options given below:
If \(\hat{i}\), \(\hat{j}\) and \(\hat{k}\) are unit vectors along co-ordinates axes OX, OY and OZ respectively, then which of the following is/are true?
(A) \(\hat{i} \times \hat{i} = \vec{0}\)
(B) \(\hat{i} \times \hat{k} = \hat{j}\)
(C) \(\hat{i} \cdot \hat{i} = 1\)
(D) \(\hat{i} \cdot \hat{j} = 0\)
Choose the correct answer from the options given below:
If the points A, B, C with position vectors \(20\hat{i} + \lambda\hat{j}\), \(5\hat{i} - \hat{j}\) and \(10\hat{i} - 13\hat{j}\) respectively are collinear, then the value of \(\lambda\) is
If \(\vec{a} + \vec{b} + \vec{c} = \vec{0}\) and \(|\vec{a}| = 3, |\vec{b}| = 5, |\vec{c}| = 7\), then the angle between \(\vec{a}\) and \(\vec{b}\) is
Let \(\vec{a} = \hat{i} + 4\hat{j}\), \(\vec{b} = 4\hat{j} + \hat{k}\) and \(\vec{c} = \hat{i} - 2\hat{k}\). If \(\vec{d}\) is a vector perpendicular to both \(\vec{a}\) and \(\vec{b}\) such that \(\vec{c} \cdot \vec{d} = 16\), then \(|\vec{d}|\) is equal to
If a line makes angles \(\alpha, \beta, \gamma\) with the positive directions of x-axis, y-axis and z-axis respectively, then \(\sin^2\alpha + \sin^2\beta + \sin^2\gamma\) is equal to
Consider the line \(\vec{r} = (\hat{i} - 2\hat{j} + 4\hat{k}) + \lambda(-\hat{i} + 2\hat{j} - 4\hat{k})\)
Match List-I with List-II
Choose the correct answer from the options given below:
The shortest distance between the lines \(\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4}\) and \(\frac{x-2}{4} = \frac{y-4}{6} = \frac{z-5}{8}\) is equal to
Which one of the following set of constraints does the given shaded region represent?
The corner points of the feasible region of the LPP:
Minimize \( Z = -50x + 20y \) subject to \( 2x - y \geq -5 \), \( 3x + y \geq 3 \), \( 2x - 3y \leq 12 \), and \( x, y \geq 0 \)
are:
If A and B are any two events such that P(B) = P(A and B), then which of the following is correct
If A is any event associated with sample space and if E1, E2, E3 are mutually exclusive and exhaustive events. Then which of the following are true?
(A) \(P(A) = P(E_1)P(E_1|A) + P(E_2)P(E_2|A) + P(E_3)P(E_3|A)\)
(B) \(P(A) = P(A|E_1)P(E_1) + P(A|E_2)P(E_2) + P(A|E_3)P(E_3)\)
(C) \(P(E_i|A) = \frac{P(A|E_i)P(E_i)}{\sum_{j=1}^{3} P(A|E_j)P(E_j)}, i=1,2,3\)
(D) \(P(A|E_i) = \frac{P(E_i|A)P(E_i)}{\sum_{j=1}^{3} P(E_i|A)P(E_j)}, i=1,2,3\)
Choose the correct answer from the options given below:
Let A and B are two events such that P(A) = 0.8, P(B) = 0.5, P(B|A) = 0.4
Match List-I with List-II
Choose the correct answer from the options given below:
A black and a red die are rolled simultaneously. The probability of obtaining a sum greater than 9, given that the black die resulted in a 5 is
If P, Q and R are three singular matrices given by 
and 
, then the value of \((2a + 6b + 17c)\) is
Let A be a non-singular matrix of order 3 and \(|A| = 15\), then \(|adj A|\) is equal to
If 
and \(AX = B\), then the value of the \(\alpha\) is
Which of the following statements is incorrect?
Match List-I with List-II
Choose the correct answer from the options given below:
If X = 11 and Y = 3, then X mod Y = (X + aY) mod Y holds
The least non-negative remainder when \(3^{128}\) is divided by 7 is:
A tub contains 60 litres of milk. From this tub, 6 litres of milk was taken out and replaced with water. This whole process was repeated further two more times. How much milk is there in the tub now?
A person can row a boat in still water at the rate of 5 km/hr. It takes him 4 times as long to row upstream of a river as to row downstream to cover same distance in the same river. The speed of flow of the stream is
Two runners, Ajay and Vijay complete a 600 m race in 38 seconds and 48 seconds respectively. By how many meters will Ajay defeat Vijay?
Which of the following inequalities holds true?
If \(e^y = \log x\), then which of the following is true?
The total cost C(x) in Rupees associated with the production of x units of an item is given by C(x) = \(0.007x^3 - 0.003x^2 + 15x + 400\). The marginal cost when 10 items are produced is:
The slope of the normal to the curve y = \(2x^2\) at x = 1 is:
If \(\int \frac{(1 + x \log x)}{xe^{-x}} dx = e^x f(x) + C\), where C is constant of integration, then f(x) is
Let \(e^{\alpha y} + e^{\beta y} + \gamma x^2 + \delta \log|x| + C = 0\), where \(C \in \mathbb{R}\) be a particular solution of the differential equation \(x(e^{2y} - 1)dy + (x^2 - 1)e^y dx = 0\) and passes through the point (1, 1). The value of \((\alpha + \beta + \gamma + \delta - C)\) is
The probability distribution of the random variable X is given by
The variance of the random variable X is
How many minimum number of times must a man toss a fair coin so that the probability of having at least one head is more than 90%?
Let F(Z) be the cumulative density function of the standard normal variate Z, then which of the following are correct?
What is the mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on 1 face?
For the given 5 values, 15, 18, 21, 27, 39; the three year moving averages are:
Which of the following are correct?
Which of the following is not a component of the time series?
If \(y = a + b(x - 2022)\) is a straight line trend using the least square method for the following data
. Then the value of \(\frac{a}{b}\) is:
Match List-I with List-II
Choose the correct answer from the options given below:
Which of the following are the assumptions underlying the use of t-distribution?
If a 95% confidence interval for a population mean was reported to be 132 to 160 and sample standard deviation s = 50, then the size of the sample in the study is:
(Given \(Z_{0.025}\) = 1.96)
An annuity in which the periodic payment begin on a fixed date and continue forever is called
Which of the following are correct about the Sinking Fund?
A person wishes to purchase a house for Rupess 39,65,000 with a down payment of Rupees 5,00,000 and balance in equal monthly installments (EMI) for 25 years. If bank charges 6% per annum compounded monthly, then EMI on reducing balance payment method is:
[Given \((1.005)^{300} = 4.465\)]
The original value of an asset minus the accumulated depreciation at a given date is known as
A sofa set costing Rupees 36000 has a useful life of 10 years. If the annual depreciation is Rupees 3000, then the scrap value by linear method is:
A person invested Rupees 10000 in a stock of a company for 6 years. The value of his investment at the end of each year is given in the following table:
The compound annual growth rate (CAGR) of his investment is:
Given \((1.4)^{1/6} \approx 1.058\)
Which of the following is NOT a basic requirement of the linear programming problem (LPP)?
Which of the following statements are correct in reference to the linear programming problem (LPP):
Maximize Z = 5x + 2y
subject to the following constraints
3x + 5y \(\le\) 15,
5x + 2y \(\le\) 10,
x \(\ge\) 0, y \(\ge\) 0.
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