CUET Mathematics 2026 19th May Shift 1 PYQs

The general solution of the given differential equation $\frac{dy}{dx} = \frac{3e^{2x}+3e^{4x}}{e^{x}+e^{-x}}$ (where C is an arbitrary constant)

Given that $Y_{3\times k}$, $W_{n\times 3}$ and $P_{p\times k}$ are matrices of specified order, then the condition for n, p, k so that $3PY + 2WY$ is well defined, is:

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

If $y = 500e^{7x} + 600e^{-7x}$, then $\frac{d^2y}{dx^2}$ equals :

The maximum area of a rectangle inscribed in a circle of radius $3\sqrt{2}$ cm, is:

$\int \frac{dx}{(a^2-x^2)^{3/2}}$ is equal to: (where C is an arbitrary constant)

The solution of the initial value problem $x\frac{dy}{dx} = 2, y(1) = 2$ is

Match List-I with List-II | List-I | List-II | |---|---| | (A) $y + \frac{dy}{dx} = \frac{1}{4}\int y\,dx$ | (I) Order 1, Degree 1 | | (B) $y = \frac{dy}{dx} + \frac{C}{dy/dx}$ | (II) Order 2, Degree 2 | | (C) $(xy^2+x)dx + (y-x^2)dy = 0$ | (III) Order 2, Degree 1 | | (D) $\left[\left\{1+\left(\frac{dy}{dx}\right)^2\right\}^{3/2}/\frac{d^2y}{dx^2}\right] = K$ | (IV) Order 1, Degree 2 | Choose the correct answer from the options given below:

If $A = \begin{bmatrix} a & b \\ c & \frac{1+bc}{a} \end{bmatrix}$, then $aA^{-1}$ is equal to which of the following? [I is the identity matrix of order 2]

If $A = \begin{bmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{bmatrix}$, then which of the following statements are TRUE? [where $A_{ij}$ is the cofactor of the (i, j)th element, $a_{ij}$ of matrix A, $1 \gt i, j \le 3$.] (A) $a_{11}A_{31} = -24$ (B) $a_{12}A_{32} = -66$ (C) $a_{13}A_{33} = -90$ (D) $a_{21}A_{21} = -24$ Choose the correct answer from the options given below:

For the function $f(x) = \frac{x^4}{4} - 2x^3 + \frac{11}{2}x^2 - 6x$, which of the following statements are TRUE? (A) Critical points of $f(x)$ are $x = 1, 2$ and $3$. (B) $f(x)$ is increasing over $(1,2)$. (C) $f(x)$ is decreasing over $(2,3)$. (D) $f(x)$ is increasing over $(3,\infty)$. Choose the correct answer from the options given below:

The maximum value of $z = 4x + 2y$, subjected to the constraints: $2x + 3y \le 18$, $x + y \ge 5$; $x, y \ge 0$, is

The value of integral $I = \int_{3}^{5} \frac{x^2}{(x-1)(x-2)}\,dx$ is

A die is thrown twice and the sum of the numbers appearing is observed to be 6. Then the probability that the number 4 has appeared at least once, is

The area of the region bounded by the line $3y = -2x + 7$, x-axis and the lines $x = 0$ and $x = 4$, is (in Sq. units)

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

A man is known to speak truth 8 out of 11 times. He takes out two balls from a bag containing 3 white, 2 black and 5 red balls. What is the probability that he reports both the balls to be white?

If $A = \begin{bmatrix} 1 & -3 \\ 2 & 0 \end{bmatrix}$, then which of the following statement(s) is/are TRUE? (A) Matrix A is non-singular (B) $|3A| = 54$ (C) $|adjA| = 36$ (D) $A^2 = \begin{bmatrix} -5 & -3 \\ 2 & -6 \end{bmatrix}$ Choose the correct answer from the options given below:

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

At $x = 2$, $f(x) = [x]$ is [where [.] is greatest integer function]

Let A (1, 3), B (0, 0) and C (k, 0) be three points such that area of $\Delta(ABC) = 3$ sq. units, then the value of k is:

If $\theta$ is the angle between the lines $L_1$ and $L_2$, whose direction cosines are $l_1, m_1, n_1$ and $l_2, m_2, n_2$ respectively, then Match List-I with List-II | List-I | List-II | |---|---| | (A) $\cos\theta$ | (I) $l_1l_2+m_1m_2+n_1n_2$ | | (B) $\sin\theta$ | (II) $l_1l_2+m_1m_2+n_1n_2=0$ | | (C) $L_1$ and $L_2$ are perpendicular | (III) $\frac{l_1}{l_2}=\frac{m_1}{m_2}=\frac{n_1}{n_2}$ | | (D) $L_1$ and $L_2$ are parallel | (IV) $\sqrt{\sum(m_1n_2-m_2n_1)^2}$ | Choose the correct answer from the options given below:

If A is a 3-rowed square matrix and $|A| = 5$, then $|adjA|$ is equal to

The value of $\int_{0}^{1} \frac{e^x}{1+e^{2x}}\,dx$ is

For the functions $f(x) = x^2$ and $g(x) = x^3$, which of the following statements are TRUE? [where N is the set of natural numbers and Z is the set of integers] (A) $f: N \to N$ is one-one but not onto. (B) $f: Z \to Z$ is neither one-one nor onto. (C) $g: N \to N$ is one-one but not onto. (D) $g: Z \to Z$ is one-one but not onto. Choose the correct answer from the options given below:

The corner points O, A, B, C, D and E of the bounded feasible region determined by the system of linear constraints are shown in the given figure. If $z = 3x - 4y$ be the objective function, then the minimum of z, is: <img src="https://balti.afterboards.in/vJkqCBUToInGq31" width="400px"/>

Match List-I with List-II | List-I | List-II | |---|---| | (A) $f(x) = \begin{cases} x^{10}-1 & , x \leq 1 \\ x^2 & , x > 1 \end{cases}$ | (I) is continuous at all points of domain | | (B) $g(x) = [x]$, $[x]$ denotes the greatest integer function | (II) is continuous at $x = 0$ | | (C) $h(x) = \begin{cases} \dfrac{\sin x}{x} & , x < 0 \\ x+1 & , x \geq 0 \end{cases}$ | (III) is discontinuous at $x = -2$ | | (D) $p(x) = \begin{cases} \dfrac{x}{\left\vert x \right\vert} & , x < 0 \\ -1 & , x \geq 0 \end{cases}$ | (IV) is discontinuous at $x = 1$ | Choose the correct answer from the options given below:

Match List-I with List-II [c is an arbitrary constant] | List-I | List-II | |---|---| | (A) $\int \frac{\sin^2 x - \cos^2 x}{\sin^2 x \cos^2 x}\,dx$ | (I) $\tan x - x + c$ | | (B) $\int \frac{\sec^2 x}{\text{cosec}^2 x}\,dx$ | (II) $2\tan x - 3\sec x + c$ | | (C) $\int \sec x(\sec x + \tan x)\,dx$ | (III) $\tan x + \cot x + c$ | | (D) $\int \frac{2-3\sin x}{\cos^2 x}\,dx$ | (IV) $\tan x + \sec x + c$ | Choose the correct answer from the options given below:

Let $A = \{0, 1, 2, 3\}$ and R be a relation on set A defined as $R = \{(0,0), (0,1), (0,3), (1,0), (1,1), (2,2), (3,0), (3,3)\}$, then the relation R is

If $\vec{a}$ and $\vec{b}$ are two collinear vectors, then which of the following statements is/are incorrect? (A) $\vec{b} = \lambda\vec{a}$, for some scalar $\lambda$. (B) Always $\vec{a} = \pm\vec{b}$. (C) the respective components of $\vec{a}$ and $\vec{b}$ are proportional. (D) both vectors $\vec{a}$ and $\vec{b}$ always have same direction. Choose the correct answer from the options given below:

If $y = \cot^{-1}\left(\frac{1-x}{1+x}\right)$ then $\frac{dy}{dx}$ equals

Let $\vec{a} = (\hat{i}+4\hat{j}+2\hat{k})$, $\vec{b} = (3\hat{i}-2\hat{j}+7\hat{k})$, $\vec{c} = (2\hat{i}-\hat{j}+4\hat{k})$. A vector $\vec{d}$, which is perpendicular to both $\vec{a}$ and $\vec{b}$, such that $\vec{c}.\vec{d} = 18$, is

The height of a closed cylinder of given surface area and maximum volume is equal to the

The function $f(x) = 3x + \cos 3x$ is (where R is set of real numbers)

$\int \frac{x^9}{(4x^2+1)^6}\,dx$ is equal to: [where c is an arbitrary constant]

Match List-I with List-II | List-I | List-II | |---|---| | (A) $P(A \cap B) = P(A).P(B)$ | (I) $\frac{P(B \cap A)}{P(A)}, P(A) \ne 0$ | | (B) $\frac{P(S \cap B)}{P(B)}$, S = Sample space | (II) A, B are independent events | | (C) $P(B/A) =$ | (III) $P(\bar{A} \cap \bar{B})$ | | (D) $P(\overline{A \cup B})$ | (IV) 1 | Choose the correct answer from the options given below:

The shortest distance between the lines whose vector equations are $\vec{r} = (6\hat{i}+2\hat{j}+2\hat{k}) + \lambda(\hat{i}-2\hat{j}+2\hat{k})$ and $\vec{r} = (-4\hat{i}-\hat{k}) + \mu(3\hat{i}-2\hat{j}-2\hat{k})$

The matrix X such that it satisfies the equation: $X\begin{bmatrix} 3 & 2 \\ 1 & -1 \end{bmatrix} = \begin{bmatrix} 4 & 1 \\ 2 & 3 \end{bmatrix}$ is

For $f(x) = x^3 - 6x^2 + 9x + 15$, which of the following statements are TRUE? (A) $f'(x) = 3x^2 - 12x + 15$. (B) The critical points are 3 and 1. (C) $x = 1$ is a point of local maxima. (D) Local minimum value is 19. Choose the correct answer from the options given below:

A man speaks the truth 8 out of 10 times. A die is tossed. He reports that it was 5. What is the probability that it was actually 5?

The general solution of the differential equation $\frac{dy}{dx} + y\cot x = 2\cos x$ is (Where C is an arbitrary constant)

Match List-I with List-II | List-I | List-II | |---|---| | (A) $(\vec{a}-\vec{b}) \times (\vec{a}+\vec{b})$ equals | (I) $\vec{0}$ | | (B) $\vec{a} = (3\hat{i}+\hat{j}-4\hat{k}), \vec{b} = (6\hat{i}+5\hat{j}-2\hat{k})$, then $\left\vert \vec{a}\times\vec{b} \right\vert$ equals | (II) $5$ | | (C) $\vec{a}\times(\vec{b}+\vec{c}) + \vec{b}\times(\vec{c}+\vec{a}) + \vec{c}\times(\vec{a}+\vec{b}) =$ | (III) $2(\vec{a}\times\vec{b})$ | | (D) Projection of vector $(\hat{i}+3\hat{j}+7\hat{k})$ on vector $(2\hat{i}-3\hat{j}+6\hat{k})$ is | (IV) $27$ | Choose the correct answer from the options given below:

Which of the following statements is/are TRUE? (A) The angle between the lines whose direction ratios are proportional to (4, -3, 5) and (3, 4, 5) is 60°. (B) If A(1,2,3) and B(2, 0, 5) are two points on a line, then its direction ratios are proportional to 1, -2, 2. (C) The direction cosines of z-axis are 0, 0, 1. (D) The vector equation of a line which passes through the point with position vector $3\hat{i}-\hat{j}+\hat{k}$ and is in the direction of $2\hat{i}+3\hat{j}+\hat{k}$ is $\vec{r} = (2\hat{i}+3\hat{j}+\hat{k}) + \lambda(3\hat{i}-\hat{j}+\hat{k})$, where $\lambda$ is a parameter. Choose the correct answer from the options given below:

Two thirds of the students in a class are boys and the rest are girls. It is known that the probability of a girl getting a first class is 0.25 and that of a boy getting a first class is 0.28, then the probability that a student chosen at random will get first class marks in the subject is

If $z = px + qy$, where $p, q > 0$, is the objective function. Then the condition on p and q so that the maximum value of z occurs at A(4, 10) and B(6, 8), is:

The value of the integral $\int_{-6}^{0} |x+3|\,dx$ is

The area bounded by the curve $y^2 = 2x$ and the lines $y = 2, y = 4$ and y-axis, is

If $P = \begin{bmatrix} 1 & 2 \\ -1 & 3 \end{bmatrix}$, $Q = \begin{bmatrix} 4 & 0 \\ 1 & 5 \end{bmatrix}$ and $R = \begin{bmatrix} 2 & 0 \\ 1 & -2 \end{bmatrix}$, then which of the following are TRUE? (A) $(P^T)^T = P^T$ (B) $(P-Q)R = PR - QR$ (C) $(P-Q)^T = Q^T - P^T$ (D) $(PQ)^T = Q^TP^T$ Choose the correct answer from the options given below:

Let A be the matrix $\begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix}$. If A is expressed as the sum of P and Q, where P is a symmetric and Q is a skew symmetric matrix, then which of the following options define P and Q correctly?

The position vector of a point R which divides the line joining the points A(-2, 1, 3) and B(3, 5, -2) internally in the ratio 2:1, is