CUET Mathematics 2026 22nd May Shift 2 PYQs

The area (in sq. units) of the region in the first quadrant enclosed between the line $x + y = 2$, parabola $y^2 = x$ and the x-axis, is

If $f(x) = \begin{vmatrix} 0 & x+a & x+b \\ x-a & 0 & x+c \\ x-b & x-c & 0 \end{vmatrix}$ then the value of $f(0)$ is equal to:

Match List-I with List-II | List-I | List-II | |---|---| | (A) $\int_{-1}^{1} \lvert x \rvert dx =$ | (I) 3 | | (B) $\int_{-\pi}^{\pi} \cos x \, dx =$ | (II) 1 | | (C) $\int_{-1}^{1} (\lvert x \rvert-1) dx =$ | (III) 0 | | (D) $\int_{-1}^{1} (\lvert x \rvert+1) dx =$ | (IV) -1 | Choose the correct answer from the options given below:

For the function $f(x) = (x+1)^2(x-2)^2$, which of the following statements are TRUE? (A) $f(x)$ is decreasing on $(-\infty,-1)$ (B) $f(x)$ is increasing on $\left(-1,\frac{1}{2}\right)$ (C) $f(x)$ is decreasing on $\left(\frac{1}{2},2\right)$ (D) $f(x)$ is increasing on $(2,\infty)$ Choose the correct answer from the options given below:

A bag contains 8 red and 7 black balls. Two balls are drawn at random. The probability that both the balls are of the same colour is:

The number of diagonal matrices of order 3 with elements either 1 or 2, is:

For a given differential equation $e^{dy/dx} = x + 1; x \in (-1,\infty)$, then which of the following statements are TRUE? (A) Its general solution is $y = x\log_e(x+1) - x + \log_e(x+1) + C$; C is an arbitrary constant. (B) Its particular solution is $y = (x+1)\log_e(x+1) - x + 5; y(0) = 5$ (C) Its general solution is $y = (x-1)\log(x+1) - x + C$; C is an arbitrary constant (D) Its particular solution is $y = (x-1)\log(x+1) - x + 5; y(0) = 5$ Choose the correct answer from the options given below:

If $A^2 = 8A + kI, A = \begin{bmatrix} 1 & 0 \\ -1 & 7 \end{bmatrix}, I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ then value of $k$ is:

If $y^2 = ax + b, a,b \in \mathbb{R}$ where $\mathbb{R}$ is the set of real numbers, then $y\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^2$ is equal to:

The general solution of the differential equation $\frac{dy}{dx} = \frac{3e^{2x}+3e^{4x}}{e^x+e^{-x}}$ is

If the function $f(x)$ defined by $f(x) = x^3 - 3x + 100, (x \in \mathbb{R})$, (Where $\mathbb{R}$ is set of real numbers), then $f(x)$ has

$\int \left\{\frac{1}{\log x} - \frac{1}{(\log x)^2}\right\} dx$ is equal to:(where C is an arbitrary constant)

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

The feasible region represented by the constraints $2x+y \le 12, x+2y \le 12, 4x+5y \ge 20, x,y \ge 0$ of LPP is <img src="https://balti.afterboards.in/F6Aeuqyz9ztpZ7K" width="400px"/>

Match List-I with List-II | List-I | List-II | |---|---| | (A) If $A = [a_{ij}]_{n \times n}$, where $a_{ij} = \begin{cases}0, & i \ne j \\ k, & i=j, k\ne 0\end{cases}$ then A is ___ | (I) Symmetric matrix | | (B) If $A = [a_{ij}]_{2\times 2}$, where $a_{ij} = \begin{cases}1, & i \ne j \\ 0, & i=j\end{cases}$, then $A^2$ is ___ | (II) Skew-Symmetric matrix | | (C) If A and B are matrices of the same order, then $(AB^T - BA^T)$ is ___ | (III) Identity matrix | | (D) If A and B are symmetric matrices of the same order, then $(AB+BA)$ is ___ | (IV) Scalar matrix | Choose the correct answer from the options given below:

$\cos[\tan^{-1}\{\sin(\cot^{-1}x)\}]$ is equal to

If $\int \frac{(\sqrt{x})^5}{(\sqrt{x})^7+x^6} dx = a\log\left|\frac{x^k}{1+x^k}\right| + C$; Where C is an arbitrary constant, then the value of $a.k$ is:

The points on the line $\frac{x+2}{3} = \frac{y+1}{2} = \frac{z-3}{2}$ at a distance of $\sqrt{17}$ from the point (-2, -1, 3) are:

A vector of magnitude 9, which is perpendicular to both the vectors $4\hat{i}-\hat{j}+3\hat{k}$ and $-2\hat{i}+\hat{j}-2\hat{k}$ is:

Two numbers are selected at random from the integers 1 through 19. If the sum is even, then the probability that both are odd numbers is:

Urn A contains 1 white, 2 black and 3 red balls, Urn B contains 2 white, 1 black and 1 red ball and Urn C contains 4 white, 5 black and 3 red balls. One Urn is chosen at random and two balls are drawn. If it is found that there is one white and one red, Then the probability that they come from A is:

If A and B are two independent events such that $P(A) = \frac{4}{7}$ and $P(B) = \frac{2}{7}$ then $P(\overline{A} \cap \overline{B})$ equals

The corner points of the feasible region of a LPP are (0,2), (3,0), (6,0), (6,8) and (0,5). If the objective function is $z = 4x + 6y$, then the sum of maximum and minimum value of z is equal to:

Particular solution of the differential equation $dy = e^{2x+y}dx$, $y(0) = 0$ is:

Consider a function $f:\left[0,\frac{\pi}{2}\right] \to R$, given by $f(x)=\sin x$ and $g:\left[0,\frac{\pi}{2}\right] \to R$, given by $g(x)=\cos x$, Where R is a set of real numbers, Which of the following statements are correct? (A) f and g are one-one (B) f and g are not one-one (C) f+g is not one-one (D) f+g is one-one Choose the correct answer from the options given below:

For the function $f: \mathbb{R} \to \mathbb{R}$ given by $f(x) = \lvert x-3 \rvert + \lvert x+4 \rvert$, Where $\mathbb{R}$ is set of real numbers, which of the following statements are correct? (A) $f(x)$ is continuous as well as differentiable at $x=3$. (B) $f(x)$ is continuous but not differentiable at $x=3$ and $x=-4$ (C) $f(x)$ is neither continuous nor differentiable at $x=3$ (D) $f(x)$ is continuous on $\mathbb{R}$ Choose the correct answer from the options given below:

The relation R on the set A = {1, 2, 3} defined by R = {(1,1), (2,2), (3,3), (1,3), (2,3), (1,2)} is

If $A = \begin{bmatrix}0 & a & -3 \\ 2 & 0 & -1 \\ b & 1 & 0\end{bmatrix}$ is a skew-symmetric matrix, then

If $\begin{bmatrix}3 & 1\\2 & 1\end{bmatrix}P\begin{bmatrix}2 & 1\\3 & 2\end{bmatrix}=\begin{bmatrix}1 & -1\\0 & 1\end{bmatrix}$ then matrix P is

If $A=\begin{bmatrix}0 & b-a & c-a\\a-b & 0 & c-b\\a-c & b-c & 0\end{bmatrix}$ then the value of $\lvert A \rvert$ is

Match List-I with List-II | List-I | List-II | |---|---| | (A) The distance of a point $P(a,b,c)$ from x-axis | (I) $\sqrt{a^2+b^2+c^2}$ | | (B) The distance of a point $P(a,b,c)$ from y-axis | (II) $\sqrt{b^2+c^2}$ | | (C) The distance of a point $P(a,b,c)$ from Z-axis | (III) $\sqrt{a^2+c^2}$ | | (D) The distance of a point $P(a,b,c)$ from origin | (IV) $\sqrt{a^2+b^2}$ | Choose the correct answer from the options given below:

Let A be the area of the triangle with vertices (3, 8), (5, -1) and $(k, 2)$, $k \in \mathbb{Z}$ (set of integers). If $2A = 75$, then k is equal to:

If $A=\begin{bmatrix}k & 2\\2 & k\end{bmatrix}$ such that $\lvert A^3 \rvert = 125$ then which of the following statements are TRUE? (A) $\lvert k.adj(3A) \rvert = 405$ (B) $\lvert k.adj(3A) \rvert = 2025$ (C) $\lvert adj(3A) \rvert = 95$ (D) $\lvert adj(3A) \rvert = 45$ Choose the correct answer from the options given below:

The area (in sq. units) of the region bounded by the curve $x=at^2$, $y=2at$ between the ordinates corresponding to t = 1 and t = 2 is

If $y=\tan^{-1}(x+y)$, then $\frac{d^2y}{dx^2}$ is equal to:

$\int \frac{2\cos 2x \, dx}{(\sin x+\cos x)^2}$ is equal to:(where C is an arbitrary constant)

The area (in sq. units) of the region bounded by the line $2y=3x+6$, x-axis and the ordinates x=-3 and x=1 is:

The shortest distance (in units) between the lines $L_1:\frac{x-1}{2}=\frac{y-2}{3}=\frac{z+4}{6}$ and $L_2:\frac{x-3}{2}=\frac{3-y}{-3}=\frac{z+5}{6}$ is:

If $\vec{a},\vec{b}$ and $\vec{c}$ are three vectors such that $\lvert \vec{a} \rvert=\frac{1}{\sqrt{2}}$, $\lvert \vec{b} \rvert=\frac{1}{\sqrt{3}}$, $\lvert \vec{c} \rvert=\frac{1}{\sqrt{6}}$, $\lvert \vec{a}+\vec{b}+\vec{c} \rvert=1$ and $\vec{c}=\lambda(\vec{a}\times\vec{b})$. The angle between $\vec{a}$ and $\vec{b}$ is

If $A=\begin{bmatrix}5 & 0 & 0\\0 & 5 & 0\\0 & 0 & 5\end{bmatrix}$ such that $A^5=\lambda^2 A$, then the value of $\lambda$ is

Match List-I with List-II | List-I: Linear differential equation | List-II: Integrating factor | |---|---| | (A) $x\frac{dy}{dx}-y=2x^3$ | (I) $e^{-x}$ | | (B) $2x\frac{dy}{dx}+y=3x^2$ | (II) $e^x$ | | (C) $\frac{dy}{dx}+y=\cos x-\sin x$ | (III) $x^{1/2}$ | | (D) $\frac{dy}{dx}-y=e^x$ | (IV) $1/x$ | Choose the correct answer from the options given below:

The area (in sq. units) of the parallelogram whose diagonals are represented by the vectors $\vec{a}=2\hat{i}-\hat{j}+\hat{k}$ and $\vec{b}=3\hat{i}+4\hat{j}-\hat{k}$, is

Let the median of a variable equilateral triangle is increasing at the rate of $2\sqrt{3}$ cm/s. Then the rate at which its each side is increasing is:

If the function $f(x)=\begin{cases}\frac{e^{2\log_e x^2}-1}{x-1}, & x\ne 1\\ a, & x=1\end{cases}$ is continuous at x=1, then the value of a is:

$\int_0^{2\pi} \cos^5 x \, dx$ is equal to

Consider the LPP: Minimize $z=-50x+20y$ subject to $2x-y\ge -5, 3x+y\ge 3, 2x-3y\le 12, x\ge 0, y\ge 0$. Then which of the following statements are TRUE? (A) Corner points of the feasible region of the LPP are (0,5), (0,3), (1,0), (6,0). (B) The optimum value of the objective function is -300 (C) Optimum value does not exist (D) The optimum value of the objective function is 100 Choose the correct answer from the options given below:

A unit vector perpendicular to both the vectors $4\hat{i}-\hat{j}+3\hat{k}$ and $-2\hat{i}+\hat{j}-2\hat{k}$ is:

The interval in which $f(x)=\frac{x}{\log x}$ is increasing, is:

Two dice are thrown simultaneously. If X denotes the number of sixes appearing on two dice, then which of the following are correct? (A) $P(X=0)=\frac{1}{36}$ (B) $P(X=1)=\frac{10}{36}$ (C) $P(X=1)+P(X=0)=\frac{35}{36}$ (D) $P(X=1)+P(X=2)=\frac{11}{36}$ Choose the correct answer from the options given below:

If the local maximum value of the function $f(x)=x^3-2\lambda x^2+\lambda^2 x, \lambda>0$ is 108, Then the local minimum value of the function occurs at