CUET Mathematics 2026 30th May Shift 1 PYQs

Let $y(x)$ be the solution curve of the differential equation $\frac{dy}{dx} + 2y^2 = 0, y(1) = 1$, then $y\left(\frac{3}{4}\right)$ is equal to:

A box has 5 blue and 4 red balls. One ball is drawn at random and not replaced. Its colour is also not noted, then another ball is drawn at random. The probability of second ball being red is

If E and F are two events such that P(E) = 0.8, P(F) = 0.7 and P(E ∩ F) = 0.6 then $P(\bar{E}/\bar{F})$ is:

The corner points of the bounded feasible region determined by the system of linear constraints of an LPP are (0, 0), (0, 8), (5, 0) and (4, 10). Let $z = 3x - 4y$ be the objective function, then the minimum value of $z$ is:

Let $f(x) = (x-a)^2+(x-b)^2+(x-c)^2$ then $f(x)$ has a minimum value at $x =$

The value (/s) of $x$ satisfying the matrix equation: $x\begin{bmatrix}2x & 2\\3 & x\end{bmatrix}+2\begin{bmatrix}8 & 5x\\4 & 4x\end{bmatrix}=2\begin{bmatrix}(x^2+8) & 24\\10 & 6x\end{bmatrix}$ is/are:

The function $f(x) = -x^3 + 12x^2 - 36x + 21$ is A. Increasing on $(-\infty, 2)$ B. Decreasing on $(-\infty, 2)$ C. Increasing on $(2, 6)$ D. Decreasing on $(6, \infty)$ Choose the correct answer from the options given below:

The area of the region lying in the first quadrant and bounded by $y=8x^2, x=0, y=1$ and $y=4$ is:

Let A, B be square matrices of order $3\times3$. Then $|A.adj(A).B|$ is

Match the LIST-I with LIST-II | | LIST-I<br>Differential equation | | LIST-II<br>Sum of the order and the degree of the differential equation | |---|---|---|---| | A. | $\dfrac{d}{dx}\left(\dfrac{dy}{dx}\right) = 1$ | I. | $2$ | | B. | $4 + \left(\dfrac{dy}{dx}\right)^4 = 7\left(\dfrac{d^2y}{dx^2}\right)^3$ | II. | $3$ | | C. | $x^3\left(\dfrac{d^2y}{dx^2}\right)^2 + x\left(\dfrac{dy}{dx}\right)^4 + 1 = 0$ | III. | $5$ | | D. | $\dfrac{dy}{dx} = x^4 e^{-3y}$ | IV. | $4$ | Choose the correct answer from the options given below:

If A and B are two symmetric matrices of the same order, then

Which of the following is/are correct? A. $\int e^x\left[\frac{1}{(x-2)}-\frac{1}{(x-2)^2}\right]dx=\frac{e^x}{(x-2)}+C$, where C is an arbitrary constant. B. $\int e^x\left[\frac{1}{(x-2)^3}-\frac{3}{(x-2)^4}\right]dx=\frac{e^x}{(x-2)^2}+C$, where C is an arbitrary constant. C. $\int e^x\left[\frac{x-4}{(x-2)^3}\right]dx=\frac{e^x}{(x-2)^2}+C$, where C is an arbitrary constant. D. $\int e^x\left[\frac{1}{x+2}-\frac{3}{(x+2)^2}\right]dx=\frac{e^x}{(x+2)^2}+C$, where C is an arbitrary constant. Choose the correct answer from the options given below:

Let $f(x)=\begin{cases}\frac{1-\cos4x}{x^2}, & \text{if } x<0\\2\lambda, & \text{if } x=0\\\frac{\sqrt{x}}{\sqrt{16+\sqrt{x}}-4}, & \text{if } x>0\end{cases}$ such that $f$ continuous at $x=0$. Then, the value of $\lambda$ is equal to:

$\int e^x\left(\log x+\frac{1}{x^2}\right)dx$ is equal to: (consider $\log x=\log_e x$) [C is an arbitrary constant]

Match the LIST-I with LIST-II | | LIST-I<br>(Matrix) | | LIST-II<br>(Type of matrix) | |---|---|---|---| | A. | $A = [a_{ij}]_{m \times m}$ where $a_{ij} = 0\ \forall\, i \neq j$ | I. | Scalar matrix | | B. | $A = [a_{ij}]_{m \times 1}$ | II. | Diagonal matrix | | C. | $A = [a_{ij}]_{1 \times n}$ | III. | Column matrix | | D. | $A = [a_{ij}]_{m \times m}$ where $a_{ij} = 0\ \forall\, i \neq j$ and $a_{ij} = k\ \forall\, i = j, k \neq 0$ | IV. | Row matrix | Choose the correct answer from the options given below:

In reference to a linear programming problem (LPP), which of the following statements are true? A. The optimal value of the objective function is attained at the points given by intersections of inequation with the axes only. B. The objective function of a LPP is a linear function to be optimized. C. Every LPP admits an optimal solution. D. The region represented by the inequation system, $x, y\geq0$, $x+2y\leq4, 3x+y\geq3, 4x+3y\geq6$ is bounded in the first quadrant. Choose the correct answer from the options given below:

The area bounded by the y-axis, $y=\cos x$ and $y=\sin x$, when $0\leq x\leq\frac{\pi}{4}$, is

Let $A=\begin{bmatrix}1 & \sin\theta & 1\\-\sin\theta & 1 & \sin\theta\\-1 & -\sin\theta & 1\end{bmatrix}$, where $\theta\in[0,2\pi]$ then which of the following statements are correct? A. $|A|=2+2\sin^2\theta$ B. Maximum value of $|A|$ is 1. C. Maximum value of $|A|$ is –1. D. $|A|\in[2,4]$ Choose the correct answer from the options given below:

The value of the determinant $\Delta=\begin{vmatrix}\cos\alpha\cos\beta & \cos\alpha\sin\beta & -\sin\alpha\\-\sin\beta & \cos\beta & 0\\\sin\alpha\cos\beta & \sin\alpha\sin\beta & \cos\alpha\end{vmatrix}$ is:

For a LPP, the objective function is $z=4x+3y$ and the feasible region determined by a set of linear constraints is shown in the graph as a shaded portion. Which one of the following statement is true ? <img src="https://balti.afterboards.in/MlHK4OHrR07hALc" width="400px"/>

Which of the following statements are correct? A. The unit vector in the direction of the vector $\vec{a}=\hat{i}+\hat{j}+2\hat{k}$ is $\frac{1}{\sqrt{6}}\hat{i}+\frac{1}{\sqrt{6}}\hat{j}+\frac{2}{\sqrt{6}}\hat{k}$. B. A vector in the direction of the vector $5\hat{i}-\hat{j}+2\hat{k}$ which has magnitude 8 units is $40\hat{i}-8\hat{j}+16\hat{k}$. C. The vector joining the points P(2, 3, 0) and Q(–1, –2, –4) directed from P to Q is $-3\hat{i}-5\hat{j}-4\hat{k}$. D. The position vector of the mid-point of the vector joining the points P(2, 3, 4) and Q(4, 1, –2) is $3\hat{i}+2\hat{j}-\hat{k}$. Choose the correct answer from the options given below:

If $A=\begin{bmatrix}2 & 3\\1 & 2\end{bmatrix}, I=\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}$ and $A^2=\alpha A+\beta I$, for some constant $\alpha$ and $\beta$ then the value of $\alpha$ and $\beta$ respectively:

Integrating factor of the differential equation $x\log x\frac{dy}{dx}+y=2\log x$ is equal to: (Consider $\log x=\log_e x$)

The relation R in the set of real numbers, defined as R = {(a, b): 1 + ab > 0}, is:

Which of the following statements are correct ? A. If $\vec{a}$ and $\vec{b}$ are two adjacent sides of a triangle, then the area of the triangle is $\frac{1}{2}|\vec{a}\times\vec{b}|$ B. If $\vec{a}$ and $\vec{b}$ are two adjacent sides of a triangle, then the area of the triangle is $\frac{1}{2}|\vec{a}.\vec{b}|$ C. If $\vec{a}$ and $\vec{b}$ are two adjacent sides of a parallelogram, then its area is $|\vec{a}\times\vec{b}|$ D. If $\vec{a}$ and $\vec{b}$ are two adjacent sides of a parallelogram, then its area is $|\vec{a}.\vec{b}|$ Choose the correct answer from the options given below:

The signum function $f:R\to R$, defined by $f(x)=\begin{cases}-1, & x<0\\0, & x=0\\1, & x>0\end{cases}$ is: (Where R is set of real numbers)

If A and B are two independent events such that P(A) = 0.5, P(B) = 0.3 then Match the LIST-I with LIST-II | LIST-I | LIST-II | |---|---| | A. $P(A/B)$ | I. 0.35 | | B. $P(B/A)$ | II. 0.5 | | C. $P(A\cap B)$ | III. 0.3 | | D. $P(\bar{A}\cap\bar{B})$ | IV. 0.15 | Choose the correct answer from the options given below:

A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimeters of gas per second. The rate at which the radius of the balloon increases when the radius is 15 cm, is:

If the function $f(x)=\begin{cases}\frac{x^3-1}{x-1}, & x<1\\a, & x=1\\\frac{b\sin(x-1)}{x-1}, & x>1\end{cases}$ is continuous at $x=1$, then which of the following statements are correct ? A. $a=b$ B. $a+b$ is a multiple of 4 C. $2a-b$ is a multiple of 3 D. $a+4b$ is divisible by 5 Choose the correct answer from the options given below:

$\int\frac{\tan^5\sqrt{x}.\sec^2\sqrt{x}}{\sqrt{x}}dx$ is equal to:

Given a line $L:\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$, then Match the LIST-I with LIST-II | LIST-I | LIST-II | |---|---| | A. The foot of perpendicular from point (1, 6, 3) on line L | I. $2\sqrt{13}$ | | B. Perpendicular distance from point (1, 6, 3) to line L | II. (1, 0, 7) | | C. Image of point (1, 6, 3) with respect to line L | III. (1, 3, 5) | | D. Distance between points (1, 6, 3) and (1, 0, 7) | IV. $\sqrt{13}$ | Choose the correct answer from the options given below:

The value of $\int_{-\pi/3}^{\pi/3}\frac{1}{1+e^{\tan x}}dx$ is:

In a sphere of radius $r$, a right circular cone of height $h$ having a maximum curved surface area is inscribed. The expression for the curved surface area of the cone is

Match the LIST-I with LIST-II | | LIST-I<br>Number of the elements in a matrix | | LIST-II<br>Number of matrices of possible order | |---|---|---|---| | A. | $17$ | I. | $8$ | | B. | $8$ | II. | $2$ | | C. | $12$ | III. | $6$ | | D. | $24$ | IV. | $4$ | Choose the correct answer from the options given below:

If $x\sqrt{1+y}+y\sqrt{1+x}=0, x>-1$ and $x\neq y$, then $(1+x)^2\frac{dy}{dx}$ is equal to

A bag contains 17 tickets numbered from 1 to 17. A ticket is drawn, and then another ticket is drawn without replacing the first one. Then the probability that both the tickets show at least one even number, is

The area bounded by an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and the lines $x=0, x=ae$ and the $x$-axis in the first quadrant, where $e$ is the eccentricity of the ellipse, is:

The shortest distance between lines $L_1:\frac{x+3}{-4}=\frac{6-y}{-3}=\frac{z}{2}$ and $L_2:\frac{x+2}{-4}=\frac{y}{1}=\frac{z-7}{1}$ is:

The value of $\int_{-\pi/2}^{\pi/2}(\sin|x|+\cos|x|)dx$ equals:

The general solution of the differential equation $\frac{dy}{dx}-\frac{y}{x}+\text{cosec}\left(\frac{y}{x}\right)=0$ is (Consider $\log x=\log_e x$)

if $x=\sqrt{a^{\tan^{-1}t}}$ and $y=\sqrt{a^{\cot^{-1}t}}$ then which one of the following is true?

The vectors from origin to the points A and B are $\vec{a}=2\hat{i}-3\hat{j}+2\hat{k}$ and $\vec{b}=2\hat{i}+3\hat{j}+\hat{k}$ respectively, then the area (in Sq. unit) of triangle OAB is:

The value of $2\sec^2(\tan^{-1}2)+3\text{cosec}^2(\cot^{-1}3)$ is:

Probabilities of solving a specific mathematical problem independently by three students are $\frac{1}{2},\frac{1}{3}$ and $\frac{1}{4}$. If all the three students try to solve the problem independently, the probability that the problem is solved, is:

The Cartesian equation of a line is $6x-2=3y+1=2z-2$. Then its vector from is:

The function $f(x)=\cot^{-1}x+x$ increases in the interval:

The value of $\begin{vmatrix}1 & \log_ba\\\log_ab & 1\end{vmatrix}$ is:

Let $L_1$ and $L_2$ lines such that $L_1:\vec{r}=\hat{i}+\hat{j}+\lambda(2\hat{i}-\hat{j}+\hat{k})$, $L_2:\vec{r}=2\hat{i}+\hat{j}-\hat{k}+\mu(4\hat{i}-2\hat{j}+2\hat{k})$ and $\theta$ be the acute angle between $L_1$ and $L_2$, then Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | $\cos\theta$ | I. | $\dfrac{\sqrt{66}}{6}$ | | B. | $\sin\theta$ | II. | $3$ | | C. | the shortest distance (in units) between $L_1$ and $L_2$ | III. | $1$ | | D. | (sum of squares of direction cosines of $L_1$) $+2$ | IV. | $0$ | Choose the correct answer from the options given below:

If $A=\begin{bmatrix}1 & 2\\2 & 1\end{bmatrix}$ and $f(x)=x^2-2x-3$, then $f(A)$ is equal to

A company manufactured a product through 4 units. A, B, C and D. The probability that a product is manufactured are $\frac{3}{10},\frac{1}{5},\frac{1}{10}$ and $\frac{2}{5}$ by units A, B, C and D respectively. The probability that it will be defective are $\frac{1}{4},\frac{1}{3}$ and $\frac{1}{12}$ if it is produced by A, B, C respectively and there is no defective from unit D. A product is chosen, it is found to be defective. Match the LIST-I with LIST-II | LIST-I | LIST-II | |---|---| | A. The Probability that the defective product is from A | I. 4/9 | | B. The Probability that the defective product is from B | II. 0 | | C. Probability of defective product | III. 1/2 | | D. Probability that the defective product is from D | IV. 3/20 | Choose the correct answer from the options given below:

A box containing 10 wall clocks has three defective pieces in it. If random sample of two clocks is taken from the box, then the probability distribution of defective clocks is:

In reference to the Inferential Statistics, which of the following statements are correct? A. The number of degrees of freedom of a statistic is the number of independent varieties used to compute the statistic. B. A confidence interval is a range that could be expected to contain the population parameter of interest. C. In a hypothesis test, the significance level is the probability of making wrong decision when the null hypothesis is true. D. The confidence level of the sampling distribution of a statistic is known as its standard error. Choose the correct answer from the options given below:

Amayra takes a loan of ₹5,00,000 at an interest of 10% per annum for a period of three years. The equated monthly installment (EMI) by using flat rate method, she has to pay is:

Match the LIST-I with LIST-II | LIST-I | LIST-II | |---|---| | A. The present value of a perpetuity of ₹3120 payable at the beginning of each year, if money is worth 6% effective. | I. ₹2,00,000 | | B. The present value of a perpetuity of ₹5,000 payable at the end of each year, if money is worth 5% compounded annually | II. ₹1,50,000 | | C. The present value of a sequence of payments of ₹3,000 payable at the end of each 6 months and continuing forever, if money is worth 4% compounded semi-annually. | III. ₹1,00,000 | | D. The present value of a perpetuity of ₹3,000 payable at the end of each quarter, if money is worth 6% compounded quarterly | IV. ₹55,120 | Choose the correct answer from the options given below:

On a multiple choice examination with four possible answers (out of which only one is correct) for each of five questions, what is the probability that a candidate would get four or more correct answers just by guessing?

In reference to the financial mathematics, which of the following statements are correct? A. Sinking fund is an annuity created for accumulating money that can be used for paying off a financial obligation at some future pre-decided date. B. The compound annual growth rate (CAGR) is calculated by dividing the cumulative return by the number of years. C. The average annual growth rate (AAGR) is linear measure that does not account for the effects of compounding. D. Sinking fund is created to deposit surplus money which can be used for any future need. Choose the correct answer from the options given below:

If $A$ is a square matrix of order 3 and $|A|=6$, then the value of $|2A^T|$ is:

Match the LIST-I with LIST-II | | LIST-I<br>(Inequality) | | LIST-II<br>(Solution Set) | |---|---|---|---| | A. | $\vert 3x-5 \vert \geq 4$ | I. | $(-\infty,-1] \cup \left[\dfrac{7}{3},\infty\right)$ | | B. | $\vert 3x \vert \geq \vert 6-3x \vert$ | II. | $(-\infty,-4] \cup [2,\infty)$ | | C. | $\vert x+1 \vert \geq 3$ | III. | $[1,\infty)$ | | D. | $\vert 2-3x \vert \geq 5$ | IV. | $\left(-\infty,\dfrac{1}{3}\right] \cup [3,\infty)$ | Choose the correct answer from the options given below:

$\int_{-2}^{1}|x^2-1|dx$ equals:

An electric bike costs ₹42,000 and has a useful life of 10 years. If annual depriciation is ₹3,000, then the scrap value by using linear method of depriciation is:

The number of telephone calls made daily in a certain community between 8 P.M. and 9 P.M. has a mean of 352 and standard deviation of 31. What percentage of time will there be more than 400 telephone calls made in this community between 8 P.M. to 9 P.M.? [Given that: $P(0\leq Z\leq1.55)=0.4394$, where $Z$ is the standard normal variate]

In reference to the Time Series Analysis, which of the following statements are correct? A. Variations which generally occur due to the general tendency of the data to increase or decrease, are known as secular variations. B. Variations which occur due to change in climate, wheather conditions, festivals etc. are known as seasonal variations. C. Variations which occur due to some unpredictable forces are known as cyclic variations. D. Variations which occur due to booms and depressions are known as irregular variations. Choose the correct answer from the options given below:

The function $f(x)=17-9x+6x^2-x^3$ is strictly increasing in the interval, is:

Which of the following statements are correct about the linear programming problem (LPP)? A. Every point in the feasible region is a feasible solution of the given LPP. B. An optimal solution of an LPP, if it exists, occurs at one of the extreme points of the convex set of the feasible solutions. C. The feasible region for an LPP is always a convex set. D. If an LPP admits two optimal solutions, it has an infinite number of optimal solutions. Choose the correct answer from the options given below:

The speed of a boat in still water is 15 km/hr. It takes twice as long to go upstream to a point as to return downstream to the starting point. The speed of the stream is:

The point at which the maximum value of the function $Z=x+y$, subject to the constraints $x+2y\leq70$, $2x+y\leq95$, $x,y\geq0$, is obtained, is:

If $A$ is a square matrix of order 3 such that $A(adj\,A)=\begin{bmatrix}-3 & 0 & 0\\0 & -3 & 0\\0 & 0 & -3\end{bmatrix}$, then which of the following is NOT correct?

Let $y_t=a+b(x_i-2021)$ be the straight line trend for the following data by least squares method: | Year($x_i$) | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | 2024 | |---|---|---|---|---|---|---|---| | Production in Lakh tonnes($y_i$) | 32 | 34 | 30 | 35 | 38 | 39 | 42 | the trend value for the year 2025 approximately is:

Match the LIST-I with LIST-II | LIST-I | LIST-II | |---|---| | A. The percentage of all possible samples that can be expected to include the true population parameter | I. Standard error | | B. The statistical measures computed from the sample observations alone | II. Null hypothesis | | C. Assumtion made about a population parameter | III. Statistic | | D. Standard deviation of the sampling distribution of a statistic | IV. Confidence level | Choose the correct answer from the options given below:

If the matrix $\begin{bmatrix}0 & \alpha & 2\\2 & \beta & 1\\\gamma & -1 & 0\end{bmatrix}$ is skew-symmetric, then $(\beta-\alpha-\gamma)$ equals

A pump can fill a water tank in 4 hours but because of the leakage in the tank it took $4\frac{1}{4}$ hours to fill the tank. How much time will it take for the leakage to drain all the water of the full tank?

The set of values of $x$ satisfying $x\equiv12(\mod5)$ is: (Where $I$ is set of integer)

Match the LIST-I with LIST-II | LIST-I<br>(Financial data) | LIST-II<br>(Nominal rate of return) | |---|---| | A. Original investment value = ₹3,50,000; Current market value of investment = ₹4,37,500 | I. 66.66% | | B. Original investment value = ₹2,50,000; Current market value of investment = ₹3,25,000 | II. 33.33% | | C. Original investment value = ₹3,00,000; Current market value of investment = ₹4,00,000 | III. 30% | | D. Original investment value = ₹3,00,000; Current market value of investment = ₹5,00,000 | IV. 25% | Choose the correct answer from the options given below:

If the total cost function is given by $C(x)=\frac{x^3}{3}-2x^2+9x-70$ and the selling price per unit is ₹6, then for what value of $x$ will the profit be maximum?

A sinking fund is created for the redemption of debentures of ₹2,00,000 at the end of 25 years. How much money should be provided out of profits each year for the sinking fund, if investment can earn interest 5% per annum? [Given $(1.05)^{25}\approx3.4$]

A box contains 8 red and 2 white balls. If three balls are drawn, one by one, at random without replacement, then the variance of the number of white balls drawn is:

Let $x=at^2, y=2at$. If $\frac{d^2y}{dx^2}+\frac{dy}{dx}=0$ at $t=3$, then $a$ is equal to:

In a 900 meters race, A gives B a start of 150 meters and defeats him by 50 seconds. If the speed of A is 4.5 m/sec, then speed of B is:

In what ratio water be added to dilute honey costing ₹120 per litre so that the resulting syrup would be worth ₹100 per litre?

A company has been producing steel tubes of mean inner diameter of 2 cm. A sample of 10 tubes gives an inner diameter of 2.01 cm and a standard deviation of 0.063 cm. If $t_9(0.05)=2.262$, then which of the following is NOT correct?

If the manufacturer's marginal cost function is $100\left(\frac{1}{\sqrt{x}}+50\right)$, then the cost involved to increase production from 25 units to 100 units is:

Which of the following statements are correct? A. If $P$ and $Q$ are square matrices of same order, then $(PQ^T-QP^T)$ is a skew symmetric matrix. B. The number of all possible matrices of order $3\times2$ with each entry either –1 or 1, is 64. C. If $P$ is an invertible matrix, then $P^T$ is also invertible. D. If $P$ and $Q$ are square matrices of the same order, then $|PQ|=|P|+|Q|$. Choose the correct answer from the options given below:

$\int\frac{x-1}{x(x-\log x)}dx$ equals: (consider: $\log x=\log_e x$)

For what values of $\lambda$ and $\mu$, the following system of linear equations: $x+y+2z=1, 2x+y-z=4, x+2y+\lambda z=\mu$ have infinitely many solution?

The particular solution of the differential equation $\frac{dy}{dx}=x(2\log x+1)$, given that $y=0$ when $x=2$, is: (consider $\log x=\log_e x$)