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:

If a 99% confidence interval states that the population mean is greater than 100 and less than 400. Then the sample mean and margin of error respectively are:

If $x = -4$ is a root of $\begin{vmatrix}x & 2 & 3 \\ 1 & x & 1 \\ 3 & 2 & x\end{vmatrix} = 0$, then the sum of the other 2 roots is

In an LPP, the feasible region represented by the set off constraints $2x + 3y \leq 18$, $x + y \leq 10$, $x \geq 0$, $y \geq 0$ is <img src="https://balti.afterboards.in/MsDd5yO8dQQKuwR" width="300px"/>

The equation of tangent line to $y = 2x^2 + 7$, which is parallel to the line $4x - y + 3 = 0$ is

The effective rate of return equivalent to a nominal rate of 12% per annum compounded quarterly is: [Given that: $(1.03)^4 ≈ 1.1255$]

If $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, then $\frac{d^2y}{dx^2}$ is equal to

The minimum value of $\begin{vmatrix}2 & 2 & 2 \\ 2 & 2+x & 2 \\ 2 & 2 & 2+x\end{vmatrix}$, $x \in R$ is

The speed of water current is half the speed of a motor boat. The motor boat travels 15 km downstream in 1 hour. Then the time taken to return to the starting point is:

The probability of a shooter of hitting the target is $\frac{1}{4}$. The minimum number of fire needed so that the probability of hitting the target atleast once is greater than $\frac{7}{16}$ is:

Two pipes A and B can fill a tank respectively in 30 min and 45 min. Both A and B are opened together for some time and then pipe B is turned off. If the tank is filled in 20 min, then find after how many minutes the pipe B is turned off?

In reference to Inferential Statistics, if $\bar{x}$ is a sample mean of random data $\{x_i\}_{i=1}^n$ and $n$ is the sample size, then the formula $\frac{1}{n-1}\sum_{i=0}^n(x_i - \bar{x})^2$ represents

If $A = \begin{bmatrix}2 & 3 & 1 \\ 2 & -1 & 0\end{bmatrix}$ and $B^T = \begin{bmatrix}4 & 4 \\ 6 & -2 \\ 2 & 0\end{bmatrix}$, then $4A + B$ is

The digit in the unit's place of $6^{500}$ is:

Mean and variance of a binomial distribution are 6 and 2 respectively. The probability of 2 successes will be

For the given five values, 3.6, 4.3, 4.3, 3.4, 4.4, the three years moving averages are:

Match List-I with List-II | List-I | List-II | |---|---| | (A) The measurable characteristic of a population is called | (i) Sample | | (B) The measurable characteristic of a sample is called | (ii) Alternative hypothesis | | (C) A smaller group of a population selected to represent a population is called | (iii) Parameter | | (D) The assumption made opposite to the null hypothesis is called | (iv) Statistic | Choose the correct answer from the options given below:

An investment of ₹ 3,00,000 becomes ₹ 4,50,000 in 5 years, then the compound annual growth rate (CAGR) is equal to: [Given that: $(1.5)^{1/5} = 1.084$]

The solution set of the inequality $\frac{2x+3}{x-1} < 0$ is:

$\int_1^{\sqrt{3}} \frac{1}{1+x^2} dx$ is equal to:

Let $A$ and $B$ be square matrices of order 3, then det $[(A - A^T) + (B - B^T)]$ is equal to

At what rate of interest will the present value of a perpetuity of ₹ 600 payable at the end of every 3 months be ₹ 18,000?

Probability distribution of random variable X is | X | -2 | -1 | 0 | 1 | 2 | |---|---|---|---|---|---| | P(X) | 2/11 | 1/11 | 4/11 | 3/11 | 1/11 | Then the value of E(X) is

If the cost function of a product is given by $C(x) = \frac{3}{4}x^2 - 5x + 21$, then the marginal cost when $x = 10$ is

The annual depreciation of a car is ₹ 40,000. If the scrap value of the car after 15 years is ₹ 50,000, then the original cost of the car using linear method is

A random sample of 100 individuals provides 25 positive responses. Then the point estimate of the population proportion with "positive" responses is:

Which of the following statement('s) is/are TRUE? (A) Skew symmetric matrix of even order is always symmetric (B) Skew symmetric matrix of odd order is non-singular (C) Skew symmetric matrix of odd order is singular (D) Skew symmetric matrix is always square matrix Choose the correct answer from the options given below:

Ram wishes to purchase a house for ₹ 15,00,000 and made a down payment of ₹ 5,00,000. If he can amortize the balance at 9% per annum compounded monthly for 25 years, then his EMI is: [Given $(1.0075)^{300} ≈ 9.41$]

The cost of a property appreciates by 10% of the previous month every month. If in end march 2024 it was ₹ 13.31 lakh, when was it ₹ 10 lakh?

The function $f: R \rightarrow R$ (where $R$ is set of real numbers) defined as $f(x) = x^2 + 2x$ is

The corner points of the bounded feasible region for an LPP are (0,4), (4,4), (6,6), (0,12). If the objective function is $Z = px + qy, p > 0, q > 0$, then the condition on p and q so that maximum of Z occurs at (6,6) and (0,12) is

$\int (x^4 + x^2 + 1)d(x^2)$ is equal to: (where c is an integration constant)

In a 200 m race, Rohan completes the race in 8 seconds and Vivan completes the race in 10 seconds. By how much distance Rohan beats Vivan?

A random variable X has the following probability distribution: | X | 0 | 1 | 2 | 3 | |---|---|---|---|---| | P(X) | 0.2 | 0.1 | 0.3 | 0.4 | The variance of X will be

In what ratio must rice at ₹ 60 per kg is mixed with rice at ₹ 90 per kg so that the mixture be worth ₹ 80 per kg?

A company is shut down due to unavailability of electricity due to non payment of electricity Bill because of some unavoidable circumstances. Under which component of time series does this situation fall?