CUET Mathematics 2026 25th May Shift 1 PYQs

If $\dfrac{d}{dx}[f(x)] = 5x^4 - \dfrac{2}{x^3}$ such that $f\left(-\dfrac{1}{2}\right) = 0$, then $f(x)$ is equal to

Match the LIST-I with LIST-II | LIST-I | LIST-II | |---|---| | A. If A is an invertible square matrix then $\lvert A^{-1}\rvert =$ | I. $\dfrac{1}{\lvert A\rvert}(\mathrm{adj}\,A)$ | | B. For every square matrix (adj A) A = | II. $\dfrac{1}{\lvert A\rvert}$ | | C. For a square matrix A, if $\lvert A\rvert \neq 0$, then $A^{-1} =$ | III. $B^{-1}A^{-1}$ | | D. If A and B are invertible matrices, then $(AB)^{-1} =$ | IV. $\lvert A\rvert.I$, where I is the identity matrix of same order as A | Choose the correct answer from the options given below:

For a square matrix $A$ of order 3, if $\lvert A\rvert = -3$, then $\lvert 4\,adj A\rvert$ is equal to

General solution of the differential equation $(e^x + e^{-x})dy = (3e^{2x} + 3e^{4x})dx$ is: [Where C is an arbitrary constant]

If $e^y(x+1) = 1$, then $\dfrac{d^2y}{dx^2}$ is equal to

The product of order and degree of the differential equation $x\dfrac{d^3y}{dx^3} = \left(1 + \left(\dfrac{dy}{dx}\right)^2\right)^4$ is

$\displaystyle\int e^{x\log_e 7} e^x\, dx$ is equal to : [where C is an arbitrary constant]

For a two variables linear programming problem (LPP), which of the following statement is correct ?

Which of the following statements are correct ? A. The function $f(x) = a^x$ is increasing on $(-\infty,\infty)$ if $a>1$. B. $f(x) = x^2 - 2x$ is decreasing in $(-\infty,1)$. C. $f(x) = x(x-3)^2$ increases for $1 \le x \le 3$. D. $f(x) = e^{-x}$ decreases in $[0,\infty)$. Choose the correct answer from the options given below:

$\displaystyle\int \dfrac{1}{(x-1)^{3/4}(x+2)^{5/4}}\, dx$ is equal to : [where C is an arbitrary constant]

General solution of the differential equation $\dfrac{3ydx - 2xdy}{y} = 0$ is : [where $c$ is an arbitrary constant]

Let $P(A) = 0.4$, $P(B) = k$, $P(A\cup B) = 0.6$. If A and B are independent events, then the value of 'k' is:

The maximum value of $f(x) = x^{50} - x^{20}$ in the interval $[0,1]$, is

Which of the following statements are TRUE? A. If the product of two matrices is a zero matrix, it is not necessary that one of the matrix is a zero matrix. B. For any three matrices A, B and C, $(AB)C = A(CB)$. C. Diagonal elements of a skew symmetric matrix can be non-zero. D. Multiplication of diagonal matrices of same order is always commutative. Choose the correct answer from the options given below:

If $P = \dfrac{1}{14}\begin{bmatrix} 3 & 2 \\ -4 & 2 \end{bmatrix}$ and $P^{-1} = \begin{bmatrix} x & -2 \\ 4 & y \end{bmatrix}$, then the value of $x$ and $y$ respectively are

If A is a $2 \times 3$ matrix and B is a matrix such that $A^{T}B$ and $BA^{T}$ are both defined. Then order of B is

If $\vec{a} = \hat{i} - 7\hat{j} + 4\hat{k}$ and $\vec{b} = 2\hat{i} - 14\hat{j} - p\hat{k}$ are parallel, then the value of $p$, is:

For two events A and B, if $P(A) = 0.6$, $P(B) = 0.5$ and $P(A\cup B) = 0.8$. Then which of the following statements are TRUE ? A. $P(A\cap B) = 0.3$. B. A and B are independent events. C. $P(A'\cap B') = 0.2$. D. A and B are mutually exclusive events. Choose the correct answer from the options given below:

Two points are moving along the lines : $L_1: \vec{r} = (2\hat{i}+3\hat{j}+\hat{k}) + \lambda(\hat{i}+2\hat{j}+\hat{k})$ $L_2: \vec{r} = (\hat{i}+\hat{j}) + \mu(2\hat{i}+\hat{j}-\hat{k})$ where $\lambda$ and $\mu$ are real parameters , then which of the following statements are correct ? A. The direction ratios of the line perpendicular to both lines are $<-1,1,-1>$. B. The direction cosines of the second line $L_2$ are $<\dfrac{2}{\sqrt6},\dfrac{-1}{\sqrt6},\dfrac{-1}{\sqrt6}>$. C. Angle between two lines is $\pi/3$. D. The lines are skew lines. Choose the correct answer from the options given below:

The area bounded by the curve $y = \tan x$, $x = -\dfrac{\pi}{6}, x = \dfrac{\pi}{6}$ and $y=0$ is

If $\lvert\vec{a}\rvert = 4, \lvert\vec{b}\rvert = 3$ and $\lvert\vec{a}+\vec{b}\rvert = 6$, then $\lvert\vec{a}-\vec{b}\rvert =$

Match the LIST-I with LIST-II | LIST-I Function | LIST-II Value | |---|---| | A. $\tan[\cos^{-1}(\sin(\tan^{-1} 4/3))]$ | I. $1/\sqrt2$ | | B. $\sin\left(2\tan^{-1}\left(\dfrac{3}{4}\right)\right)$ | II. 1 | | C. $\cos\left[\tan^{-1}\left(\dfrac{1}{2}\right)+\tan^{-1}\left(\dfrac{1}{3}\right)\right]$ | III. 24/25 | | D. $\sin\left[\dfrac{\pi}{3} - \sin^{-1}(-1/2)\right]$ | IV. 3/4 | Choose the correct answer from the options given below:

The derivative of $x^{5x}$ with respect to $x$ is

The area (in square units) of the region bounded by the curve $x = y^3, y = -1, y = 2$ and $x = 0$ is:

A four digit number is formed by using the digits 1, 2, 4 and 5 with no repetition. The probability that the number is divisible by 5, is

If $f(x) = x^3 + px^2 + qx - 3$ has a local maxima at $x = 0$ and local minima at $x = 1$, then the values of $p$ and $q$ respectively, are:

Bag A contains 3 red and 4 black balls, and Bag B contains 5 red and 'n' black balls. One ball is drawn at random from one of the bags and it is found to be red. If the probability that it was from bag B is 35/68, then the value of 'n' is:

The value of $\Delta = \begin{vmatrix} 2\sin40^\circ & 2\sin50^\circ \\ -3\cos40^\circ & 3\cos50^\circ \end{vmatrix}$ is:

If $\begin{vmatrix} 2x & 2 \\ 8 & x \end{vmatrix} = \begin{vmatrix} -4 & -2 \\ 4 & -2 \end{vmatrix}$ then $x =$

The rate of change of volume of a sphere with respect to its surface area when radius of the sphere is 4 cm, is

Match the LIST-I with LIST-II | LIST-I | LIST-II | |---|---| | A. Area of triangle determined by vectors $(\hat{i}+\hat{j})$ and $(\hat{i}-2\hat{j}+\hat{k})$ is | I. 0 | | B. The value of $(\hat{i}\times\hat{j}).\hat{j} + (\hat{j}\times\hat{i}).\hat{k} + (\hat{k}\times\hat{i}).\hat{j}$ is | II. $\dfrac{\sqrt{11}}{2}$ | | C. If $(2\lambda-1)\hat{i}+3\hat{j}-\hat{k}$ and $\hat{i}+\lambda\hat{j}+2\hat{k}$ are perpendicular to each other then $\lambda$ is | III. 4 | | D. Projection of $5\hat{i}+\hat{j}+4\hat{k}$ on $2\hat{i}+6\hat{j}+3\hat{k}$ is | IV. 3/5 | Choose the correct answer from the options given below:

The cartesian equation of the line passing through the point $(-4, 3, -2)$ and parallel to the line $\vec{r} = 5\hat{i} - \hat{k} + \lambda(\hat{i}-\hat{j}+2\hat{k})$ is:

If A and B are two non-singular matrices of same order, then which of the following statements are not correct ? A. AB is non singular. B. $(A+B)^{-1} = B^{-1}+A^{-1}$. C. adj (AB) = adj B. adj A. D. AB is not invertible. Choose the correct answer from the options given below:

The points in the interval $[0,2\pi]$, where the function $f(x) = \cos2x + 2\sin x\cos x$, attains its local minima, is/are: A. $\pi/8$ B. $5\pi/8$ C. $13\pi/8$ D. $11\pi/8$ Choose the correct answer from the options given below:

Match the LIST-I with LIST-II | LIST-I Differential equation | LIST-II Integrating factor of the differential equation | |---|---| | A. $\dfrac{dy}{dx} + 2y = xe^{4x}$ | I. $\dfrac{1}{x}$ | | B. $2x\dfrac{dy}{dx} + y = 6x^3$ | II. $\dfrac{1}{y}$ | | C. $ydx - xdy + (\log_e x)dx = 0$ | III. $e^{2x}$ | | D. $ydx - (x+2y^2)dy = 0$ | IV. $\sqrt{x}$ | Choose the correct answer from the options given below:

If $P(A) = \dfrac{3}{10}, P(B) = \dfrac{3}{4}$ and $P(A\cap B) = \dfrac{1}{5}$, then $P(B\mid A)$ is equal to:

The angle between the lines $\dfrac{3-x}{-7} = \dfrac{y+5}{-5} = \dfrac{z}{1}$ and $\dfrac{x}{1} = \dfrac{y}{2} = \dfrac{z}{3}$ is:

$\displaystyle\int_{-2}^{2} \dfrac{x^2}{1+5^x}\, dx$ is equal to:

If $\lvert\vec{a}\rvert = \lvert\vec{b}\rvert = \lvert\vec{a}+\vec{b}\rvert = 1$, then Match List-I with List-II | LIST-I | LIST-II | |---|---| | A. $\lvert\vec{a}-\vec{b}\rvert$ | I. $\dfrac{2\pi}{3}$ | | B. Angle between $\vec{a}$ and $\vec{b}$ | II. $-\dfrac{1}{2}$ | | C. Angle between $\vec{a}$ and $\vec{a}+\vec{b}$ | III. $\sqrt3$ | | D. $\vec{a}.\vec{b}$ | IV. $\dfrac{\pi}{3}$ | Choose the correct answer from the options given below:

If the sum of a matrix A and its transpose is $\begin{bmatrix} -6 & 4 \\ 4 & 10 \end{bmatrix}$, then A is:

For a square matrix $A = \begin{bmatrix} 2 & 1 & 3 \\ 0 & -1 & 4 \\ 1 & 2 & 0 \end{bmatrix}$, which of the following statements is/are TRUE ? A. det (A) = 9. B. $A_{21}.A_{33} = -12$, where $A_{ij}$ is the cofactor of $a_{ij}$ C. det (A) = $a_{11}A_{11} + a_{12}A_{12} + a_{13}A_{31}$. D. $\lvert AA'\rvert \neq \lvert A\rvert^2$ Choose the correct answer from the options given below:

Let $f: \mathbb{N} \to \mathbb{N}$ defined by $f(x) = 3x^2 + 2x + 7$, where $\mathbb{N}$ is set of natural numbers. Then $f(x)$ is:

If $\displaystyle\int \dfrac{\sin^4 x}{\cos^8 x}\, dx = a\tan^7 x + b\tan^5 x + C$, where 'C' is an arbitrary constant then

For the relations $R_1, R_2, R_3, R_4$ defined on the set $A = \{1,2,3\}$, Match the LIST-I with LIST-II | LIST-I | LIST-II | |---|---| | A. $R_1 = \{(1,2),(2,1),(3,3)\}$ | I. Transitive only | | B. $R_2 = \{(1,1),(2,2),(3,3)\}$ | II. Neither reflexive nor symmetric nor transitive | | C. $R_3 = \{(1,2),(2,3),(1,3)\}$ | III. Symmetric but neither reflexive nor transitive | | D. $R_4 = \{(3,3),(3,1),(1,2)\}$ | IV. Equivalence | Choose the correct answer from the options given below:

For the linear programming problem: Minimize $z = 2x - 5y$, subject to the constraints: $x + 2y \ge 10$; $3x + 4y \le 24$; $x,y \ge 0$, then optimal value of $z$ is

Which of the following is a homogeneous differential equation ?

If $x = a(\theta+\sin\theta)$, $y = a(1-\cos\theta)$ then $\dfrac{d^2y}{dx^2}$ is equal to:

Which of the following group of constraints represents the feasible region given as shaded area below ? <img src="https://balti.afterboards.in/n0LrFgidZHaAOQr" width="400px"/>

$\displaystyle\int_{-\pi/3}^{\pi/3} 2x^5\cos^4 x\, dx$ equals

Match the LIST-I with LIST-II | LIST-I | LIST-II | |---|---| | A. $f(x) = \log_e(x^2+1)$ | I. not continuous at all integral values | | B. $f(x) = \lvert x\rvert$ | II. is continuous as well as differentiable at $x=0$ | | C. $f(x) = x^2$ | III. Continuous everywhere | | D. $f(x) = [x]$, $[x]$ is greatest integer function | IV. Continuous everywhere but not differentiable at $x=0$ | Choose the correct answer from the options given below:

Which of the following graph plotted for the months against the three month moving average(3Yr MA) represents the given data correctly ? | Month | January | February (F) | March (M) | April (A) | May | |---|---|---|---|---|---| | Production of items | 15 | 27 | 21 | 27 | 24 | [Four line graphs labelled 1-4, each plotting 3-Yr MA against month, showing different curve shapes and values]

The system of equation $x-y+z=4, x-2y-2z=9, 2x+y+\alpha z=1$ has unique solution then value(/s) of $\alpha$ is (/are) (where $\mathbb{R}$ is set of real numbers)

If $X$ is a random variable such that $X$ can take values 0,1, 2 or 3. Then the expectation of $X$ for the following data is : | $X$ | 0 | 1 | 2 | 3 | |---|---|---|---|---| | $P(X)$ | $k$ | $k^2$ | $1-5k^2$ | $k^2$ | (where $k>0$)

If a random variable X follows poisson's distribution such that $P(X=2) = 9P(X=4) + 90P(X=6)$, then the mean of X is

The supply function for a commodity is $p = 3\sqrt{16+x}$. If 9 units of goods are sold, then producer's surplus is :

A money-lender charges interest at the rate of 10 rupees per 110 rupees semi-annually, payable in advance. Then Match the LIST-I with LIST-II | LIST-I | LIST-II | |---|---| | A. rate per conversion period ($i$) | I. 2 | | B. nominal rate (r)% | II. 21 | | C. number of period in a year (m) | III. 20 | | D. effective rate of interest ($r_e$)% | IV. 0.1 | Choose the correct answer from the options given below:

Meesha takes a loan of ₹ 3,00,000 at an interest of 8% annually for a period of n years. If her monthly EMI using flat rate method is ₹ 7,000, then the number of installments:

For matrix $A = \begin{bmatrix} 2 & -3 \\ 3 & 4 \end{bmatrix}$ the value of $A^2 - 6A$ is equal to:(where I is an identity matrix of order 2)

For the data from the simple random sample as: 5, 8, 10, 7, 18, 12 The point estimate of the population standard deviation is

A company has issued a bond of face value ₹ 90,000 carrying an annual dividend of 7% and maturing in 15 years. If the prevailing market rate of interest is 9% , the value of bond redeemed at par is: (given $(1.09)^{-15} \approx 0.3$)

Integral $I = \displaystyle\int \dfrac{e^{3\log x} - 3x^4}{e^{2\log x} + x^2}\, dx$ (where $x>0$) is equal to

A company produces an item M whose mean sales per shop per month was found to be 84 dozens. After an advertisement, a sample of 26 shops was taken and mean sales was found to be 80 dozens with standard deviation of 9. Based on this data, which of the following is true? (Given $t_{25}(0.05) = 2.06$) [t = t-test statistic]

A particle moves along a curve $3y^2 = 6x^3 + 8$ such that its y-coordinate is changing at the rate of 9 cm/sec at point (1,2). Then the rate of a change of x-coordinate at the same point is :

Consider an investment of ₹ 15,000 whose annual values are given below: | June 1, 2022 | June 1, 2023 | June 1, 2024 | June 1, 2025 | |---|---|---|---| | ₹ 15,000 | ₹ 16,500 | ₹ 19,800 | ₹ 20,790 | then the CAGR % is: (given $(1.386)^{1/3} = 1.115$)

If $x = t^2$ and $y = t\sqrt{t}$, then $\dfrac{d^2y}{dx^2}$ at $t = \dfrac{1}{4}$ is :

Consider the objective function $Z = 3x + 4y$ subject to the following constraints: $x-6y \le 6, x+y-1 \ge 0, x-y+1 \ge 0, x+2y \le 6, x \ge 0, y \ge 0$ . Which of the following inequalities does not contribute to the feasible region?

The least non-negative remainder when $3^{200}$ is divided by 8 is :

In a race of 800 m, A beats B by 80 m and in a race of 600 m, B beats C by 40 m. Then A will beat C in a race of 1000 m by :

For a matrix $A = \begin{bmatrix} a & -1 & b \\ -2 & 1 & -1 \\ 1 & 0 & 2 \end{bmatrix}$, $C_{32} = -1$ and $C_{33} = 3$, where $C_{ij}$ is the cofactor of element $a_{ij}$ in $A$. Then

If $A = \begin{bmatrix} 1 & a \\ b & 2 \end{bmatrix}$ and $B = \begin{bmatrix} a & 1 \\ 2 & -3b \end{bmatrix}$ such that $\lvert AB\rvert = \lvert 2B\rvert$ and $ab \neq -\dfrac{2}{3}$ then: A. $\lvert A\rvert = 2$ B. $\lvert A\rvert = 4$ C. $\lvert B\rvert = 2$ D. $\lvert B\rvert = 4$ Choose the correct answer from the options given below:

A boat goes downstream at a speed of 18 km/hr and upstream at a speed of 'm' km/hr. The boat travelled 90 km downstream in a river and then returned back taking altogether 12.5 hours. Then which of the following are true ? A. $m = 12$ B. $m = 15$ C. Speed of water current is 3 km/hr D. Speed of water current is 1.5 km/hr Choose the correct answer from the options given below:

Let $C(x)$ and $R(x)$ be the cost function and the revenue function for $x$ units of a commodity such that marginal cost of producing 2 units is equal to marginal revenue of selling 1 unit. If $C(x) = ax^3 + bx^2 - 12x + 6$ and $R(x) = 100 + 6ax - bx^2$, then which one of the following is TRUE?

If $\dfrac{x+3}{2x-1} < 1$, then the solution set contains : A. $(-\infty,1/2)$ B. $(-\infty,4)$ C. $(-4,4)$ D. $(4,\infty)$ Choose the correct answer from the options given below:

The mean and variance of a random variable $X$ having a binomial distribution are 1 and 2/3 respectively. Then, Match the LIST-I with LIST-II | LIST-I | LIST-II | |---|---| | A. $P(X=0)$ | I. $1/27$ | | B. $P(X=3)$ | II. $2/9$ | | C. $P(X=2)$ | III. $4/9$ | | D. $P(X=1)$ | IV. $8/27$ | Choose the correct answer from the options given below:

The present value of a sequence of payment of ₹ 1500 made at the end of every 6 months and continuing forever, if money is worth 4% per annum compound semi-annually is

A company makes two types of cakes: type A and type B. it costs ₹ 360 to make a type A cake and ₹ 120 to make a type B cake. The company can make atmost 300 cakes and spend atmost ₹ 72,000 a day, the number of cakes of type B ($y$) cannot exceed the number of type A ($x$) cakes by more than 200. The company makes a profit of ₹ 200 on each type A cake and ₹ 50 on each type B cake. A LPP to maximize the profit (₹) is

Arjun invests ₹ 20,000 in two parts, one part at 8% per annum and the other at 12% per annum interest. His yearly average interest rate comes out to be 9% per annum . Then which of the following are true ? A. He invests ₹ 15,000 @ 8% interest B. He invests ₹ 10,000 @ 12% interest C. He invests ₹ 6000 @ 8% interest D. He invests ₹ 5,000 @ 12% interest Choose the correct answer from the options given below:

The value of t-statistic for the following data as Population mean is 51, Sample mean is 54, Sample size is 10 and sample variance is 36, is:

If m and n are the order and the degree of the differential equation : $x\dfrac{d^2y}{dx^2} = \left[1+\left(\dfrac{dy}{dx}\right)^2\right]^{1/3}$ then which one of the following is TRUE?

The value of $\begin{vmatrix} 1 & a & a^2 \\ 1 & b & b^2 \\ 1 & c & c^2 \end{vmatrix}$ is equal to

Two pipes A and B can fill a tank in 10 minutes & 16 minutes respectively whereas a waste pipe can empty 3 litres per minute. All the three pipes working together can fill the tank in 8 minutes, then the capacity of the tank is:

If X is a random variable which can take values 0,1,2,3 such that $E(X^2) = 2E(X)$. If $P(X=0) = P(X=1) = m\ \&\ P(X=2) = 2m$, then which of the following are TRUE? A. $P(X=1) = \dfrac{1}{13}$ B. $P(X=3) = \dfrac{1}{13}$ C. $E(X) = \dfrac{18}{13}$ D. $P(X=2) = \dfrac{6}{13}$ Choose the correct answer from the options given below:

If the critical points (extreme values) of the function $f(x)$ given by $f(x) = -\dfrac{3}{4}x^4 - ax^3 - \dfrac{bx^2}{2} + 15$ are -3 and -5, then the value of $f''(-1)$ is :

An asset costing ₹ 1,50,000 is expected to have useful life of 5 years and scrap value of ₹ 30,000. Using linear depreciation method which of the following are TRUE? A. Annual depreciation is ₹ 24,000 B. Depreciation rate is 20% per annum C. Depreciation rate is 24% per annum D. Annual depreciation is ₹ 22,000 Choose the correct answer from the options given below:

A simple random sample of 49 items from a population with standard deviation 10 resulted in a sample mean of 25. Then the 95% confidence interval for population mean are : (Given $z_{\alpha/2} = 1.96$ where $\alpha = 0.05$)