CUET Mathematics 2026 PYQs19 May Shift 1. Free, no login required.

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

Match List-I with List-II | List-I (Definite Integral) | List-II (Value) | |---|---| | (A) $\int_{1}^{2} e^x\,dx$ | (I) $\frac{e^2(e^2-1)}{2}$ | | (B) $\int_{0}^{1} e^x\,dx$ | (II) $\frac{(e^2-1)}{2}$ | | (C) $\int_{1}^{2} e^{2x}\,dx$ | (III) $e-1$ | | (D) $\int_{0}^{1} e^{2x}\,dx$ | (IV) $e(e-1)$ | Choose the correct answer from the options given below:

If the sum of the lengths of hypotenuse and a side of a right angled triangle is given, then the area of the triangle is maximum when angle between them is:

The supply function for a commodity is $p = x^2 + x + 3$. The producer's surplus when $x = 3$ is,

The random variable X has the following probability distribution: | X | 1 | 2 | 3 | 4 | 5 | |---|---|---|---|---|---| | P(X) | $\frac{1}{10}$ | $\frac{1}{10}$ | $\frac{1}{3}$ | k | $\frac{1}{3}$ | The correct value of k is:

The monthly expectation of a two-wheeler accident at a particular railway crossing is 0.02. What is the probability that in a specific month, no accident occurred? (given $e^{-0.02} = 0.9802$)

Match List-I with List-II | List-I (Differential equation) | List-II (The sum of degree and order of the differential equation) | |---|---| | (A) $x\frac{d^2y}{dx^2} = \left(1+\left(\frac{dy}{dx}\right)^2\right)^{\frac{1}{3}}$ | (I) 2 | | (B) $x\frac{d^2y}{dx^2} = \left(2-\frac{dy}{dx}\right)^{\frac{1}{7}}$ | (II) 9 | | (C) $3+\frac{dy}{dx} = y+\frac{d^3y}{dx^3}$ | (III) 4 | | (D) $\frac{dy}{dx} = x+3$ | (IV) 5 | Choose the correct answer from the options given below:

The number that satisfies the inequality $\frac{29}{4} < \frac{x+20}{4} < 8$ is

Which of the following are TRUE? (A) The inverse of $\begin{bmatrix} 3 & -3 \\ 2 & 7 \end{bmatrix}$ is $\frac{1}{27}\begin{bmatrix} 7 & 3 \\ -2 & 3 \end{bmatrix}$. (B) The determinant of $\begin{bmatrix} 3 & -3 \\ 2 & 7 \end{bmatrix}$ is 29. (C) The inverse of $\begin{bmatrix} 3 & -3 \\ 2 & 7 \end{bmatrix}$ is $\frac{1}{29}\begin{bmatrix} 7 & 3 \\ -2 & 3 \end{bmatrix}$. (D) The adjoint of $\begin{bmatrix} 3 & -3 \\ 2 & 7 \end{bmatrix}$ is $\begin{bmatrix} 7 & 3 \\ -2 & 3 \end{bmatrix}$. Choose the correct answer from the options given below:

If $A = \begin{bmatrix} 1 & 2 & -3 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 3 \\ 7 & -8 \\ 1 & 2 \end{bmatrix}$, then which of the following are true? (A) AB is a $2 \times 3$ matrix (B) $B^2$ is a $3 \times 3$ matrix (C) BA is not possible (D) $A^3$ is not possible Choose the correct answer from the options given below:

Three taps A, B and C can fill a tank in 12 minutes, 15 minutes and 20 minutes respectively. If tap A is opened all the time while tap B and C are opened for 1 minute each alternately such that tap B opened first, then the time taken to fill the tank is :

Match List-I with List-II | List-I | List-II | |---|---| | (A) It describes the accuracy of a sampling method. | (I) Confidence interval | | (B) It describes the uncertainity of a sampling method. | (II) Hypothesis | | (C) It is used to express the precision and uncertainity of a sampling process. | (III) Margin of error | | (D) An educated guess which needs to be tested. | (IV) Confidence level | Choose the correct answer from the options given below:

Given a matrix $A = \begin{bmatrix} 0 & 3 & -8 \\ -3 & 0 & 13 \\ 8 & -13 & 0 \end{bmatrix}$. Which of the following statements is/are TRUE? (A) The matrix A is a skew-symmetric matrix. (B) The matrix A is a symmetric matrix. (C) The matrix A is a singular matrix. (D) The matrix A is a non-singular matrix. Choose the correct answer from the options given below:

If X is normally distributed with mean 30 and standard deviation 5, the value of $P(26 \le X \le 34)$ is: (Where $P(0 \le Z \le 0.8) = 0.2881$)

While solving an LPP, the corner points of a bounded feasible region were found to be (0,0), (1, 9), (3, 7), (4, 5.5) and (10, 0). The objective function $Z = 4x + y$ will maximise at:

A person has set up a sinking fund in order to have ₹ 20,000 in 10 years for his children's education. The amount to set aside each quarter into an account paying 6% per annum compounded quarterly is: [use $(1.015)^{40} = 1.8140$]

A container contains 100 litres of acid. From the container, 10 litres acid was taken out and replaced by equal amount of water. This process was repeated further twice, then the amount of acid left in the container is:

Jemina invested ₹ 50,000 in a mutual fund in 2019. The value of the mutual fund increased to ₹ 80,000 in 2024. The percentage of CAGR (Compound Annual Growth Rate) of her investment is: [Use $(1.6)^{1/5} = 1.098$]

The possible value (s) of x such that $28 \equiv x(mod\ 6)$ are :- (A) -2 (B) 4 (C) 6 (D) 10 Choose the correct answer from the options given below:

Usain Bolt runs a 100 m race and defeats his rival by 1 m. If Usain's speed was 9 m/s, the speed of the rival was :

The absolute maximum value of the function $f(x) = 2x^3 - 15x^2 + 36x + 7$ on the interval [1,5] is

If $A^T = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$ and $A^{-1} = \begin{bmatrix} p & q \\ r & s \end{bmatrix}$, then

The present value of a perpetuity of ₹x at the end of every 6 months is ₹4,00,000. If money is worth 6% per annum compounded semi-annually, what is value of x ?

Mrs. Soma takes a loan of ₹ 5,00,000 with 10% annual interest rate for 5 years. What will be her EMI under flat rate system?

Match List-I with List-II | List-I | List-II | |---|---| | (A) It is the amount the bond issuer pays at maturity. | (I) Coupon rate | | (B) It is the rate at which a bond yield interest. | (II) Face value | | (C) It is the annual interest rate paid by the bond issuer to the bond holder. | (III) Nominal rate of interest | | (D) The price at which the bond is sold to buyers at the time of issue. | (IV) Redemption price | Choose the correct answer from the options given below:

Tamanna was researching on problem of under-age workers at factories. She met a suitable child and interviewed him. He put her in contact with three another workers. Those three workers brought her in contact with ten other underage workers. This process of sampling is known as:

Match List-I with List-II | List-I | List-II | |---|---| | (A) $\begin{bmatrix} 5 & 3 \\ -7 & 1 \end{bmatrix} + \begin{bmatrix} 7 & 3 \\ 7 & 2 \end{bmatrix}$ | (I) Identity matrix | | (B) $\begin{bmatrix} 5 & 3 \\ -7 & 1 \end{bmatrix} + \begin{bmatrix} -4 & -3 \\ -6 & 0 \end{bmatrix}$ | (II) Upper Triangular Matrix | | (C) $\begin{bmatrix} 5 & -3 \\ -2 & -1 \end{bmatrix} + \begin{bmatrix} -5 & 3 \\ 2 & 1 \end{bmatrix}$ | (III) Zero Matrix | | (D) $\begin{bmatrix} 5 & 13 \\ -2 & 6 \end{bmatrix} + \begin{bmatrix} -4 & -13 \\ 2 & -5 \end{bmatrix}$ | (IV) Lower Triangular Matrix | Choose the correct answer from the options given below:

Irregular variations in a time series is :

The value of $\int_{0}^{3} \frac{\sqrt{x}}{\sqrt{3-x}+\sqrt{x}}\,dx$ is

For a certain data $(x_i, y_i)$, $i = 1,2,...,7$: $\sum_{i=1}^{7} y_i = 246$ and $\sum_{i=1}^{7} u_iy_i = 29$, $\sum_{i=1}^{7} u_i^2 = 28$ where $u_i = x_i - 2004$, then straight line trend by the method of least square is :

The value of an item costing ₹ x depreciates in such a way that after 6 years the value is just a quarter of original value. The annual depreciation is:

Two cards are drawn successively with replacement from a well shuffled pack of 52 playing cards. Which of the following is correct probability distribution of number of Queens(X) as $\binom{X}{P(X)}$?

The shaded unbounded area of an LPP is the result of constraints: <img src="https://balti.afterboards.in/y0blO5vsYu6Kium" width="400px"/>

The interval in which the function $f(x) = \log_e(2+x) - \frac{2x}{2+x}$ is increasing is

A random sample of 17 values from a normal population has a mean of 105 cm and the sample standard deviation is 8.489. If normal population mean is 110 cm, then the upper limit of confidence at 5% level of significance is : (Given $t_{16}(0.05) = 2.12$)

A man rows a boat downstream 30 km and upstream 20 km. It takes him 5 hours to cover each distance. Which of the following are TRUE? (A) The speed of the boat in still water is 10 km/hr. (B) The speed of the boat in still water is 5 km/hr. (C) The speed of the current is 1 km/hr. (D) The speed of the current is 6 km/hr. Choose the correct answer from the options given below: