CUET Mathematics 2025 26 May Shift 2 PYQs

If the objective function z = 4x + 3y has maximum value on a line joining points (3, a) and (b, 2) where a > 0, b > 0 such that a - b = 2, then the maximum value of z is:

In the following differential equation $\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^2 = 2x^2 \log\left(\frac{d^2y}{dx^2}\right)$ order and degree is:

If P and Q are non-singular square matrices of the same order, then $(PQ^{-1})^{-1}$ equals

$\frac{d}{dx}\left(e^{2\log_e x^3}\right)$ equals

If the random variable X has the following probability distribution: | X | 0 | 1 | 2 | otherwise | |---|---|---|---|---| | P(X) | k | 3k | 5k | 0 | Match List-I with List-II | List-I | List-II | |---|---| | (A) k | (I) $\frac{13}{9}$ | | (B) E (X) | (II) $\frac{4}{9}$ | | (C) P (X ≤ 1) | (III) $\frac{8}{9}$ | | (D) P (1 ≤ X ≤ 2) | (IV) $\frac{1}{9}$ | Choose the correct answer from the options given below: 1. (A) - (II), (B) - (I), (C) - (IV), (D) - (III) 2. (A) - (IV), (B) - (I), (C) - (II), (D) - (III) 3. (A) - (IV), (B) - (II), (C) - (I), (D) - (III) 4. (A) - (III), (B) - (II), (C) - (I), (D) - (IV)

With respect to the following shaded feasible region (ABCDEFA), the maximum value of the objective function z = 3x + 4y – 2 is at point(s): <img src="https://balti.afterboards.in/gUAK5hc16W6wryv" width="300px"/>

The area of the region bounded by the curve $y = x + 1$, $x = axis$ and the lines $x = 2$ and $x = 3$ is

$\int_{1}^{2} \frac{1}{x(x+1)} dx, x > 0$ equals

If $A = \begin{bmatrix} 1 & 0 \\ 0 & 0 \end{bmatrix}, B = \begin{bmatrix} 0 & 0 \\ 3 & 0 \end{bmatrix}$ then

The function $f(x) = x^3 + 3x^2 + 4x + 4$, $x \in \mathbb{R}$ (set of real numbers) :

If $A = \begin{bmatrix} x+z & 2 & -3 \\ x & 0 & 4 \\ 3 & x-y & 0 \end{bmatrix}$ is a skew-symmetric matrix, then which of the following are true? (A) $y > z > x$ (B) $x > y$ (C) $x + y + z > 0$ (D) $z > x$ Choose the correct answer from the options given below:

The solution of the differential equation $xdy - ydx = 0$ represents

The maximum value of the function $f(x) = x^2(60 - x)$ in [20, 80] is:

$\int \frac{(x-1)e^x}{x^2} dx, x > 0$ equals (where C is an arbitrary constant)

If $\begin{bmatrix} 1 & 0 & 0 \\ 0 & y+1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} 2x & \\ -2 & \\ z-3 & \end{bmatrix} = \begin{bmatrix} 6 \\ 4 \\ 1 \end{bmatrix}$ then $x + y + z$ is

The particular solution of the differential equation $\frac{dy}{dx} = e^{x^2/2} + xy$, when $x = 0$, $y = 1$, is

If the points (-1, -1, 2), (2, m, 5) and (3, 11, 6) are collinear, then m equals

Let $A = [a_{ij}]_{3 \times 3}$ be a matrix, defined by $a_{ij} = \begin{cases} 2i+3j & , i < j \\6 &, i=j\\ 3i-2j & , i > j \end{cases}$. The number of elements in A which are greater than 6, is

Derivative of $x^x$ with respect to $x\log x$ is

If $x = a\sec^3 \theta$, $y = a \tan^3 \theta$, then $\frac{dy}{dx}$ at $ \theta = \frac{\pi}{3}$ is

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

If $|\vec{a}| = a$, then the value of $|\vec{a} \times \hat{i}|^2 + |\vec{a} \times \hat{j}|^2 + |\vec{a} \times \hat{k}|^2$ is

If the events A and B are independent, then which of the following statements are true? (A) P(A'B) = [1-P(A)] P(B) (B) A and B are mutually exclusive (C) P(A) = P(B) (D) P(A'B') = [1-P(A)] [1-P(B)] Choose the correct answer from the options given below:

Which of the following statements are true? (A) The vector equation of the line through the point (5, 2, -4) and parallel to the vector $3\hat{i} + 2\hat{j} - 8\hat{k}$ is $\vec{r} = (5\hat{i} + 2\hat{j} - 4\hat{k}) + \lambda(3\hat{i} + 2\hat{j} - 8\hat{k})$ (B) Vector form of the equation of line $\frac{x-5}{3} = \frac{y+4}{7} = \frac{z-6}{2}$ is $\vec{r} = (5\hat{i} - 4\hat{j} + 6\hat{k}) + \lambda(3\hat{i} + 7\hat{j} + 2\hat{k})$ (C) The direction cosines of z-axis are (1, 1,0). (D) If a line has direction ratios 2, -1, -2, then its direction cosines are -2/3, -1/3, -2/3. Choose the correct answer from the options given below:

The edge of a cube is increasing at a rate of 7 cm/s. The rate of change of area of the cube when its side is 3 cm is:

$\int e^x \left(\frac{1-x}{1+x^2}\right)^2 dx$ is equal to

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined as $f(x) = [x]$, where [x] denotes the greatest integer less than or equal to x. Then which of the following statements are correct? (A) f is one-one but not onto (B) f is not onto (C) f is not one-one (D) f is one-one and onto Choose the correct answer from the options given below:

If $\vec{a}$, $\vec{b}$ and $\sqrt{3}\vec{a} + \vec{b}$ are unit vectors, then the angle between $\vec{a}$ and $\vec{b}$ is:

The function $f(x) = \begin{cases} \frac{(\sin 2x)}{x} + \cos x & , if \ x \neq 0 \\ K & , if \ x = 0 \end{cases}$ is continuous at $x = 0$, then the value of K is:

The corner points of a bounded feasible region determined by the following system of linear inequalities $x + 3y \leq 60, x + y \geq 10$, $x \leq y$, $x \geq 0$, $y \geq 0$ are (0,10), (5,5), (15, 15) and (0, 20). Let $z = 2px + qy$, $p, q > 0$. If maximum of z occurs at both (15, 15) and (0, 20), then the relation between p and q is

If $e^x + e^y = e^{x+y}$, then $\frac{dy}{dx}$ equals

Area (in sq. units) of the region bounded by the curves $y = -1$, $y = 2$, $x = y^3$ and $x = 0$ is

The value of p so that the lines $\frac{x-1}{-3} = \frac{2y-2}{2p} = \frac{z-3}{2}$ and $\frac{x-1}{-3p} = \frac{y-1}{4} = \frac{6-z}{5}$ are at right angles is

If it is given that at $x = 1$, the function $f(x) = x^4 - 62x^2 + 2ax + b$ attains its maximum value on the interval [0, 2], then the value of a is:

Arrange the principal values of the following functions in ascending order (A) $\cosec^{-1}(2)$ (B) $\tan^{-1}(-\sqrt{3})$ (C) $\tan^{-1}(1)$ (D) $\tan^{-1}\left(\cos\frac{3\pi}{7}\right)$ Choose the correct answer from the options given below:

If A and B are two distinct events such that P(A|B) = P(B|A), then which of the following is /are possible? (A) A= B (B) P (A) = P(B) (C) A ⊂ B but A ≠ B (D) A∩ B = ɸ Choose the correct answer from the options given below:

If $|\vec{a}| = 10$, $|\vec{b}| = 2$ and $\vec{a} \cdot \vec{b} = 12$, then value of $|\vec{a} \times \vec{b}|$ is :

If $f(x)$ and $g(x)$ are continuous functions in [0, a] such that $f(x) = f(a - x)$ and $g(x) + g(a - x) = a$ then $\int_{0}^{a} f(x)g(x)dx =$

A and B throw a die alternatively till one of them gets 3 or 6 and wins the game. If B starts the game, then the probability of winning the game by A is

Let A = {1, 2, 3}. The number of equivalence relations containing (1, 3) is

If $A = \begin{bmatrix} 2 & -1 & 0 \\ 1 & 1 & 2 \\ -1 & 0 & 1 \end{bmatrix}$, then which of the following statement(s) is/are correct? (A) A is singular matrix (B) |3A| = 135 (C) |adj A| = 125 (D) $|A^{-1}| = \frac{1}{5}$ Choose the correct answer from the options given below:

The area (in sq. units) of the region bounded by the curve $x^2 = 250y$, $y = 0$ and $x = 50$ is

The value of $\int_{0}^{\pi/2} \frac{\tan^7 x}{\cot^7 x + \tan^7 x} dx$ is

Match List-I with List-II | List-I | List-II | |---|---| | Differential Equations | Order and degree | | (A) $ydx + x\log(y/x)dy - 2xdy = 0$ | (I) Order : 2, degree:1 | | (B) $\left(\frac{d^3y}{dx^3}\right)^2 + 3\frac{d^2y}{dx^2} + 2\left(\frac{dy}{dx}\right)^4 = y^2$ | (II) Order :1, degree:1 | | (C) $\frac{dy}{dx} + \log\left(\frac{dy}{dx}\right) + x = y$ | (III) Order : 3, degree:2 | | (D) $\left(\frac{ds}{dt}\right)^4 + 2s\frac{d^2s}{dt^2} = 0$ | (IV) Order : 1, degree: Not defined | Choose the correct answer from the options given below:

The corner points of the bounded feasible region of the LPP: Maximize $z = x + y$ subject to constraints $2x + 5y \leq 100$, $8x + 5y \leq 200$, $x \geq 0$, $y \geq 0$ are

Let A, B, C be three events. If the probability of occurring exactly one out of A and B is $\frac{3}{5}$, exactly one of B and C is $\frac{1}{5}$, exactly one of C and A is $\frac{3}{5}$ and that of occurring of three events is $\frac{4}{25}$, then the probability of occurring at least one of them is

The value of $\begin{vmatrix} 2^x & 1 & 6^x \\ 4^x & 1 & 3^x \\ 2^x & 1 & 6^x \end{vmatrix}$, where $x \neq 0$ is:

For the matrix $A = \begin{bmatrix} 2 & -1 & -1 \\ 0 & 2 & 3 \\ 1 & -2 & 1 \end{bmatrix}$, which of the following statements are correct? (A) The order of the matrix is 3 × 3 (B) |A| = 21 (C) $|adj\ A| = 225$ (D) A is skew symmetric matrix Choose the correct answer from the options given below:

A line passes through the point with position vector $2\hat{i} - \hat{j} + 4\hat{k}$ and is in the direction of the vector $\hat{i} + \hat{j} - 2\hat{k}$. The equation of the line in Cartesian form is:

For two matrices $A = \begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 & 1 \end{bmatrix}$ and $B^T = \begin{bmatrix} -1 & 2 & 1 \\ 1 & 2 & 3 \end{bmatrix}$, A - B equals