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: