CUET Mathematics 2026 21st May Shift 1 PYQs

Solution of differential equation $\frac{dy}{dx} = \frac{1+x^2}{1+y^2}$ is

If $y = \log_x(x^2+1).\log_{(x^2+1)} x$, then $\frac{dy}{dx}$ is

The points of local maxima and local minima of the $f(x) = x^3 - 6x^2 + 9x + 27$ are

For a matrix $A = \begin{bmatrix} 1 & 4 & 5 \\ 3 & 2 & 6 \\ 0 & 1 & 0 \end{bmatrix}$, where $I$ is identity matrix of order 3 Match List-I with List-II | List-I | List-II | |---|---| | (A) $\left\vert A \right\vert$ | (I) $72$ | | (B) $(\text{adj}A)A$ | (II) $18$ | | (C) $\left\vert 2A \right\vert$ | (III) $9$ | | (D) $2\left\vert A \right\vert$ | (IV) $9I$ | Choose the correct answer from the options given below:

For any 3 ×3 matrix $A$, if $A(adj\,A) = \begin{bmatrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{bmatrix}$, then $2|A|$ is equal to

The function $f(x) = 4x + \frac{1}{x}$ is (A). Increasing in the interval $\left(-\infty, -\frac{1}{2}\right)$ (B). Increasing in the interval $\left(-\frac{1}{2}, 0\right)$ (C). Decreasing in the interval $\left(0, \frac{1}{2}\right)$ (D). Decreasing in the interval $\left(\frac{1}{2}, \infty\right)$ Choose the correct answer from the options given below:

The feasible region for a LPP is shown in the figure. The minimum value of Z = 2x - 3y is <img src="https://balti.afterboards.in/DRY9mOZGxffoEdj" width="400px"/>

If $A = \begin{bmatrix} 4 & -1 & \lambda \\ 2 & 0 & 6 \\ 1 & -2 & 7 \end{bmatrix}$, then $\frac{1}{2}A^{-1}$ exist if

Match List-I with List-II | List-I (Differential Equation) | List-II (Degree) | |---|---| | (A) $2(y'')^2 + 3y = 6$ | (I) 4 | | (B) $2y + 5(y')^4 = 7$ | (II) 1 | | (C) $\log x + (y'')^3 = e^x$ | (III) 2 | | (D) $\sqrt{1-2y'} = 5(y'')^{\frac{1}{4}}$ | (IV) 3 | Choose the correct answer from the options given below:

The value of $\int_{-2}^{3} |x-1|\, dx$ is

If $P(A \cap B) = \frac{1}{2}$, $P(A' \cap B') = \frac{1}{3}$, $P(A) = p$ and $P(B) = 2p$, then value of $p$ is

If $[1 \quad 2 \quad 1] \begin{bmatrix} -1 & 0 & 1 \\ 1 & 2 & -1 \\ 0 & 1 & 3 \end{bmatrix} \begin{bmatrix} 2x \\ x \\ -7 \end{bmatrix} = [0]$, then the value of $x$ is

The area in the first quadrant bounded by $y = 9x^2$, $x = 0$, $y = 1$ and $y = 4$ is :

If $A = [a_{ij}]_{3 \times 3}$ and $a_{ij} = i - j$, then which of the following statements are TRUE? (A). $A$ is scalar matrix (B). $A$ is skew symmetric matrix (C). $|A| = 0$ (D). $a_{21} + a_{12} = 0$ Choose the correct answer from the options given below:

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

A man is known to speak the truth 3 out of 4 times. He throw a die and reports that it is five then the probability that it is actually five is

$\int \frac{dx}{\sin^2 x \cos^2 x} =$

If $x = 3\sin\theta - \sin 3\theta$, $y = 3\cos\theta - \cos 3\theta$, then $\frac{d^2y}{dx^2}$ at $\theta = \frac{\pi}{3}$ is

Given a function $f(x) = ax + \frac{b}{x}$; $a > 0, b > 0$, then Match List-I with List-II | List-I | List-II | |---|---| | (A) $f(x)$ has local maxima at $x$ is equal to | (I) $\sqrt{\frac{b}{a}}$ | | (B) $f(x)$ has local minima at $x$ is equal to | (II) $2\sqrt{ab}$ | | (C) Local Maxima of $f(x)$ | (III) $-\sqrt{\frac{b}{a}}$ | | (D) Local Minima of $f(x)$ | (IV) $-2\sqrt{ab}$ | Choose the correct answer from the options given below:

Value of $\int (e^{2\log x} + e^{x\log 2} + e^{2\log 2})dx$ is

If the lines $\frac{x-1}{2} = \frac{y+1}{\lambda-3} = \frac{z-2}{2}$ and $x = 0, \frac{2y-4}{-2} = \frac{z+1}{2-\lambda}$ are perpendicular, then value of $\lambda$ is

Value of $\int_{1}^{4} \frac{\log_e x}{x^2}\, dx$ is

If $f(x) = \begin{cases} \frac{x^2+3x-10}{x-2}, & x \neq 2 \\ 2k+1, & x = 2 \end{cases}$ is continuous at $x = 2$, then the value of $k$ is

Let A and B be independent events such that $P(A) = \frac{3}{7}$ and $P(B) = \frac{1}{7}$, Then Match List-I with List-II | List-I | List-II | |---|---| | (A) P(A and B) | (I) $\frac{24}{49}$ | | (B) P(A or B) | (II) $\frac{18}{49}$ | | (C) P(A and not B) | (III) $\frac{25}{49}$ | | (D) P(neither A nor B) | (IV) $\frac{3}{49}$ | Choose the correct answer from the options given below:

A problem is given to 3 students A,B and C, whose probabilities of solving are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively, then (A). P(Problem solved) = $\frac{3}{4}$ (B). P(Problem not solved) = $\frac{1}{4}$ (C). P(Problem solved by exactly one student) = $\frac{7}{24}$ (D). P(Problem solved by at least 2 students) = $\frac{17}{24}$ Choose the correct answer from the options given below:

The maximum value of $z = 3x + 4y$ subject to the constraints $x + y \geq 2, 2x + 3y \leq 6, x \geq 0, y \geq 0$ is

The number of corner points of the feasible region determined by the constraints $2x - y \geq 0, x - 3y + 3 \geq 0, x \geq 0, y \geq 0$ is

A pair of dice is thrown. If the two numbers appearing on them are different then the probability that the sum of the number is 6, is.

If $\begin{vmatrix} 2+x & y & z \\ x & 2+y & z \\ x & y & 2+z \end{vmatrix} = 0$, then the value of $x+y+z$ is

If $\vec{a}, \vec{b}, \vec{c}$ are unit vectors such that $\vec{a} + \vec{b} + \vec{c} = 0$. The value of $\vec{a}.\vec{b} + \vec{b}.\vec{c} + \vec{c}.\vec{a}$ is

The solution of the differential equation $e^{\frac{dy}{dx}} = x+1$; $y(0)=5$ is

If $A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 2 & 3 & -1 \end{bmatrix}$, then $A^2$ is equal to

If $\vec{a} = 2\hat{i} - 2\hat{j} + \hat{k}$, then which of the following statements are TRUE? (A) unit vector along $\vec{a}$ is $\frac{1}{3}(2\hat{i}+2\hat{j}-\hat{k})$ (B) $|3\vec{a}| = 9$ (C) $\vec{a}$ is perpendicular to $2\hat{i}+3\hat{j}+2\hat{k}$ (D) Direction Ratios of $\vec{a}$ are 2,-2,1 Choose the correct answer from the options given below:

If $A = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ m & 2 & n \end{bmatrix}$ is a matrix, such that $AA^T = 9I_3$, then the values of $m$ and $n$ are (where $I_3$ is an identity matrix of order 3)

The number of symmetric relations on set $A = \{1,2,3\}$ is

Let $f(x) = |x-1| + |x-2|, x \in R$. Then which of the following statements is/are TRUE? (A) $f$ is continuous everywhere. (B) $f$ is continuous everywhere except at $x = 1$ and $x = 2$ (C) $f$ is not differentiable at $x = 1$ and $x = 2$ (D) $f$ is differentiable at $x = 1$ and $x = 2$ Choose the correct answer from the options given below:

Match List-I with List-II | List-I (Straight Lines) | List-II (Direction Ratios) | |---|---| | (A) $\vec{r} = (\hat{i}+\hat{j}) + \lambda(2\hat{i}-\hat{j}+3\hat{k})$ | (I) 2,1,-3 | | (B) $\frac{x}{2} = \frac{1-y}{-1} = \frac{z+1}{3}$ | (II) -2,1,3 | | (C) $\frac{1-2x}{4} = \frac{y+1}{1} = \frac{2z+3}{6}$ | (III) 2,-1,3 | | (D) $\vec{r} = (2\hat{i}-\hat{k}) + \lambda(2\hat{i}+\hat{j}-3\hat{k})$ | (IV) 2,1,3 | Choose the correct answer from the options given below:

For any invertible matrix $A$, which of the following is NOT true.

General solution of the Differential equation $\frac{dy}{dx} + ay = e^{mx}$ is

Let $\vec{a}$ be any vector such that $\vec{a}.\hat{i} = \vec{a}.(\hat{i}+\hat{j}) = \vec{a}.(\hat{i}+\hat{j}+\hat{k}) = 1$, then $\vec{a}$ is

Area bounded by the curves $y = x|x|$, $x = -1$, $x = 1$ is

If $A = R - \{2\}$ and $B = R - \{1\}$ and function $f: A \rightarrow B$ defined by $f(x) = \frac{x-1}{x-2}$, then $f$ is

If $\Delta = \begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix}$, Then Match List-I with List-II | List-I | List-II | |---|---| | Values of $a, b$ & $c$ | value of $\Delta$ | | (A). $a=b=c=1$ | (I). 2 | | (B). $a=-1,b=1,c=1$ | (II). 0 | | (C). $a=-1,b=-1,c=1$ | (III). -2 | | (D). $a=-1,b=-1,c=-1$ | (IV). 4 | Choose the correct answer from the options given below:

The function $f(x) = \sin x + \cos x$; $0 \leq x \leq 2\pi$ is (A) Increasing in $\left(0, \frac{\pi}{4}\right)$ (B) Decreasing in $(0, \pi)$ (C) Increasing in $\left(\frac{5\pi}{4}, 2\pi\right)$ (D) Decreasing in $\left(\frac{\pi}{4}, \frac{5\pi}{4}\right)$ (E) Neither increasing Nor decreasing in $\left(0, \frac{\pi}{4}\right)$ Choose the correct answer from the options given below:

For the differential equation $\frac{\left[1+\left(\frac{dy}{dx}\right)^2\right]^{\frac{3}{2}}}{\frac{d^2y}{dx^2}} = k, k \neq 0$, which one of the following is TRUE ?

If $A$ and $B$ are matrices of the same order, then $AB^T - BA^T$ is a

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

Value of $\cot\left\{\frac{\pi}{4} - 2\cot^{-1}3\right\}$ is

If $\vec{r} = \vec{a_1} + \lambda\vec{b_1}$ and $\vec{r} = \vec{a_2} + \mu\vec{b_2}$ are two skew lines such that $\vec{b_1} \times \vec{b_2} = 2\hat{i}+3\hat{j}+2\hat{k}$, $\vec{a_1} = \hat{i}+\hat{j}+\hat{k}$ and $\vec{a_2} = 2\hat{i}+3\hat{j}+\hat{k}$, then the shortest distance between the lines is

Let us consider vector $\vec{a} = (c\log_2 x)\hat{i} - 6\hat{j} + 3\hat{k}$ and $\vec{b} = (\log_2 x)\hat{i} + 2\hat{j} + (2c\log_2 x)\hat{k}$, then which of following statements are TRUE? (Where $x \in \mathbb{R}$ (set of real numbers)) (A) Vector $\vec{a}$ and $\vec{b}$ make obtuse angle for any $x \in (0,\infty)$ if $c \in (-1,0)$ (B) Vector $\vec{a}$ and $\vec{b}$ makes obtuse angle for any $x \in \mathbb{R}$ if $c > 0$ (C) Vector $\vec{a}$ and $\vec{b}$ makes obtuse angle for any $x \in (0,\infty)$ if $c \in \left(-\frac{4}{3}, -1\right]$ (D) Vectors $\vec{a}$ and $\vec{b}$ makes obtuse angle for $x \in \mathbb{R}$ if $c \in (1,2)$ Choose the correct answer from the options given below: