CUET Mathematics 2025 30 May Shift 2 PYQs

The solution of the differential equation $\frac{dy}{dx} = \sqrt\frac{{y}}{x}$ is

For a random variable x, probability distribution P(x) is given by $P(x) = \frac{k}{6}(3-x), x = 0, 1, 2$, then Match List-I with List-II | List-I | List-II | |---|---| | (A) k is equal to | (i) $\frac{1}{2}$ | | (B) P(x = 0) | (ii) 1 | | (C) P(x < 2) | (iii) $\frac{1}{6}$ | | (D) P(1 < x ≤ 2) | (iv) $\frac{5}{6}$ | Choose the correct answer from the options given below:

The function, $f(x) = x - \frac{1}{x}$ is

The area of the region bounded by the parabola $y^2 = 8x$ and its latus rectum in the first quadrant, is

Given a matrix A of order 3x3. If |A|=3 then the value of |A(adj A)| is:

The order of $\sqrt{1 + \left(\frac{dy}{dx}\right)^2} = \left[a \frac{d^2y}{dx^2}\right]^{\frac{1}{2}}$ is

$\int \frac{1}{x(x^5-1)} dx$ is equal to

If $y = 3e^{2x} + 2e^{3x}$, then $\frac{d^2y}{dx^2} + 6y$ is equal to

The value of $\begin{vmatrix} x^2 - x + 1 & x - 1 \\ x + 1 & x + 1 \end{vmatrix}$ is equal to:

If $\begin{bmatrix}2x+1 & 5x \\ 0 & y^2+1\end{bmatrix} = \begin{bmatrix}x+3 & 10 \\ 0 & 26\end{bmatrix}$ then the possible values of x + y are:

For a linear programming problem, the feasible region is shown in the figure by shaded portion, then linear constraints are <img src="https://balti.afterboards.in/rW5MYEPvXEmTawA" width="300px"/>

For $x > 0$, the minimum value of $\frac{x}{\log_e x}$ is

If $A = \begin{bmatrix}1 & -1 \\ 2 & -1\end{bmatrix}$, $B = \begin{bmatrix}a & 1 \\ b & -1\end{bmatrix}$ and $(A + B)^2 = A^2 + B^2$ then

$\int\limits_{\sqrt{log_e 2}}^{\sqrt{log_e 4}} xe^{x^2} dx$ is equal to

For the L.P.P. Maximize z = 10x + 6y subjected to 3x + y ≤ 12, 2x + 5y ≤ 34, x, y ≥ 0. Then the feasible region represented by system of inequalities is

The general solution of the differential equation $x\left(\frac{dy}{dx}\right) = y + x \tan\left(\frac{y}{x}\right)$ is

The value of $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} (\sin|x| + \cos|x|)dx$, is equal to:

If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1 then

If the minimum value of $a$ is $-\frac{k}{2}$ such that the function $f(x) = x^2 + ax + 5$ is increasing in [1, 2]. Then value of $k$ is

If a line makes angles $\alpha, \beta, \gamma$ with the positive directions of the coordinate axes, then the value of $\cos 2\alpha + \cos 2\beta + \cos 2\gamma$ is

A spherical ice ball is melting at the rate of 100 $\pi$ cm³/min. The rate at which its radius is decreasing when its radius is 15 cm, is

Area of the region bounded by the curve $y = \sqrt{x}$ and lines $x + y = 2$, $y = 0$ is

If $ \theta$ is the angle between two unit vectors $\hat{a}$ and $\hat{b}$ then $|\hat{a}-\hat{b}| =$

Two numbers are selected without replacement at random, one at a time from the first six positive integers. Let x denotes the larger of the two numbers. Match List-I with List-II | List-I | List-II | |---|---| | (A) P(x = 2) | (i) $\frac{4}{15}$ | | (B) P(x = 3) | (ii) $\frac{1}{15}$ | | (C) P(x = 4) | (iii) $\frac{2}{15}$ | | (D) P(x = 5) | (iv) $\frac{1}{5}$ | Choose the correct answer from the options given below:

The value of derivative of the function $\cot^{-1}\{(\cos 2x)^{1/2}\}$ at $x = \frac{\pi}{6}$ is

Nitin has taken the subjects mathematics, physics and chemistry. The probability of him getting grade A in these subjects are respectively 0.2, 0.3 and 0.9. Getting grades in different subjects are regarded as independent events. The probability of getting A grade by him, either in mathematics or physics, is

If $y = \left(x + \sqrt{x^2+1}\right)^m$, then $\frac{dy}{dx}$ is

If $x, y, z$ are non-zero numbers, then the inverse of matrix $A = \begin{bmatrix}x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z\end{bmatrix}$ is

The projection vector of the vector $2\hat{i} + 3\hat{j} + \hat{k}$ on $2\hat{i} + \hat{j} - 2\hat{k}$ is

The corner points of the bounded feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Let z = px + qy where p, q > 0. Then the condition on p and q so that the maximum value of z occurs at (15, 15) and (0, 20) is

$\int \frac{\sqrt{16+(\log x)^2}}{x} dx$ is equal to (where C is an arbitrary constant)

The diagonal elements of a skew symmetric matrix are all

The relation R on the set of real numbers defined by $R = \{(a, b): a \leq b^2\}$ is (A) Reflexive (B) Not symmetric (C) Neither reflexive nor transitive (D) Transitive Choose the correct answer from the options given below:

If z-coordinate of a point P on the line joining the points A (2, 2, 1) and B (5, 1, -2) is -1, than x-coordinate of point P is

If $A = [a_{ij}]_{3 \times 2}$ where $a_{ij} = i + j$, then (A) A is a square matrix (B) $a_{21} + a_{32} = 8$ (C) Number of elements in A is 6 (D) Transpose of $A = \begin{bmatrix}2 & 3 \\ 3 & 4 \\ 4 & 5\end{bmatrix}$ Choose the correct answer from the options given below:

Value of $\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \log(\tan x)dx$ is

The linear inequalities satisfying the shaded feasible region given in the figure are <img src="https://balti.afterboards.in/YzPceJq35bcjnXJ" width="300px"/> (A) $x \geq 0$, $y \geq 0$, $2x + y \geq 2$ (B) $x \geq 0$, $y \geq 0$, $2x + y \leq 2$ (C) $x \geq 0$, $y \geq 0$, $2x + y \geq 2$, $x + 2y \leq 8$, $x - y \leq 1$ (D) $x + 2y \geq 8$, $x - y \geq 1$ Choose the correct answer from the options given below:

The simplified form of $\tan^{-1}\left(\frac{\cos x}{1+\sin x}\right)$, $-\frac{\pi}{2} < x < \frac{\pi}{2}$ is

The function $f: \mathbb{R} \rightarrow \mathbb{R}, f(x) = |x|$ ($\mathbb{R}$ is the set of real numbers) is

The coordinates of the image of the point P (5, 4, 2) in the line $\vec{r} = (-\hat{i} + 3\hat{j} + \hat{k}) + \mu(2\hat{i} + 3\hat{j} - \hat{k})$, where $\lambda$ is a parameter, is

For the function $f(x) = e^x + e^{-x}$ (A) $f'(x) = e^x - e^{-x}$ (B) The critical point is $x = 0$ (C) The minimum value is 1 (D) $x = 0$ is the point of local minimum. Choose the correct answer from the options given below:

If A is a singular matrix, then A{adj A} is equal to

The area of region bounded by the curve $y^2 = 4ax$ and the straight line $x = 2a$, $a > 0$ in the first quadrant is:

If $f(x) = \begin{cases}\frac{1- \tan x}{4x-\pi}, & x \neq \frac{\pi}{4} \\ k, & x = \frac{\pi}{4}\end{cases}$ is continuous at $x = \frac{\pi}{4}$, then the value of k is

The sum of order and degree of the differential equation $y = x\frac{dy}{dx} + 2\sqrt{1 + \left(\frac{dy}{dx}\right)^2}$ is

If $|\vec{a} - \vec{r}| = |\vec{a}| = |\vec{r}| = 1$, then angle between $\vec{a}$ and $\vec{r}$ is

A unit vector perpendicular to the vectors $\hat{i} - \hat{j}$ and $\hat{i} + \hat{j}$ is

If A and B are two events such that $P(A) = \frac{1}{2}$, $P(B) = \frac{1}{3}$ and $P(A \cap B) = \frac{1}{4}$, then which of the following statements are true? (A) A and B are independent events (B) $P(A | B) = \frac{3}{4}$ (C) $P(A' | B') = \frac{5}{8}$ (D) $P(A' | B) = \frac{1}{4}$ Choose the correct answer from the options given below:

The value of $\begin{vmatrix}265 & 240 & 219 \\ 240 & 225 & 198 \\ 219 & 198 & 181\end{vmatrix}$ is

If the system of equations $x - 3y + 5z = 3$ $x - 2y + 4z = 4$ $2x - 7y + \lambda z = 5$ has infinite number of solutions, then the value of $\lambda$ is: