CUET Mathematics 2026 31st May Shift 2 PYQs

For any non-zero matrix $A = [a_{ij}]_{3\times3}$ and $|A| \neq 0$, then Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | $\vert adj\,A \vert$ | I. | $\dfrac{1}{\vert A \vert}(adj\,A)$ | | B. | $(adj\,A)A$ | II. | $\vert A \vert^2$ | | C. | $A^{-1}$ | III. | $\dfrac{1}{\vert A \vert}$ | | D. | $\vert A^{-1} \vert$ | IV. | $\vert A \vert I$ | Choose the correct answer from the options given below:

$\displaystyle\int_0^2 x\sqrt{2-x}\,dx$ is equal to :

Solution of differential equation $x\,dy - y\,dx = 0$ represents:

The area enclosed between $y^2 = 4x$, $x = 1$ and $x = 4$ in first quadrant is :

If $A$ and $B$ are invertible matrices of order 3. If $|A| = 2$ and $|(AB)^{-1}| = \dfrac{-1}{6}$, then the value of $|B|$ is :

If $A = \begin{bmatrix} 1 & -2 & 3 \\ -4 & 2 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & -2 \\ 3 & -4 \\ 2 & 4 \end{bmatrix}$, then $AB$ is :

The feasible region for a LPP is shown in the given figure. The maximum value of $z = 2x + 5y$ is : <img src="https://balti.afterboards.in/2VFikhAtkrZoa4p" width="500px"/>

Let $f(x)$ be a function defined on an interval $[a,b]$ such that $f(x)$ is differentiable on $(a,b)$. Then Match the LIST-I with LIST-II | | LIST-I<br>Where $I$ is subset of $[a,b]$ | | LIST-II | |---|---|---|---| | A. | function $f(x)$ is increasing on interval $I$ | I. | $f'(x) < 0\ \ \forall x \in I$ | | B. | function $f(x)$ has local maxima at $x = a$ | II. | $f'(a) = 0\ \&\ f''(a) > 0$ | | C. | function $f(x)$ has local minima at $x = a$ | III. | $f'(x) > 0\ \ \forall x \in I$ | | D. | function $f(x)$ is decreasing on interval $I$ | IV. | $f'(a) = 0\ \&\ f''(a) < 0$ | Choose the correct answer from the options given below:

$\displaystyle\int \dfrac{x^3}{x+2}dx$ is equal to: (where $C$ is an arbitrary constant and $\log_e x = \log x$)

If $m$ and $n$ are respectively order and degree of the differential equation $\left(\dfrac{d^2y}{dx^2}\right)^5 + 6\cdot\dfrac{\left(\dfrac{d^2y}{dx^2}\right)^3}{\dfrac{d^3y}{dx^3}} + \dfrac{d^3y}{dx^3} = x^2+5$ then :

General solution of the differential equation $\dfrac{dy}{dx} = e^{ax+by}$ is: (where C is an arbitrary constant)

A die is rolled. If the outcome is an odd number, then the probability that the number is prime, is:

The function $f(x) = 2x^3 - 3x^2 - 36x + 7$ is : A. Increasing in $(-\infty,-2)$ B. Decreasing in $(-2,3)$ C. Neither increasing nor decreasing in $(-2,3)$ D. Increasing in $(3,\infty)$ Choose the correct answer from the options given below:

Let $A = [a_{ij}]_{3\times3}$ be a matrix such that $a_{ij} = \dfrac{i-j}{i+j}$, then which of the following statements is/are TRUE? A. A is a symmetric matrix B. A is a skew symmetric matrix C. $|A| = 0$ D. $|A| \neq 0$ Choose the correct answer from the options given below:

If the function $f(x) = x^4 - 62x^2 + ax + 9$ has a critical point at $x = 1$, then $a$ is equal to:

Area of the region bounded by the curve $y = \cos x$ and $x-axis$ between $x = 0$ and $x = \pi$ is:

The ordinate of the point on the curve $y^2 = 8x$ for which abscissa and ordinate change at the same rate is:

A relation $R$ on set of real numbers $(\mathbb{R})$ is defined as $R = \{(a,b): a \le b, a,b \in \mathbb{R}\}$. The relation is :

If $x = a\left(t - \dfrac{1}{t}\right)$, $y = b\left(t + \dfrac{1}{t}\right)$, then $\dfrac{dy}{dx} =$

If $A$ and $B$ are two events such that $P(\overline{A} \cup \overline{B}) = \dfrac{2}{3}$ and $P(A \cup B) = \dfrac{5}{9}$, then which of the following are TRUE? A. $P(A \cap B) = \dfrac{1}{3}$ B. $P(A \cup B) + P(A \cap B) = \dfrac{7}{9}$ C. $P(A) + P(B) = \dfrac{2}{9}$ D. $P(\overline{A}) + P(\overline{B}) = \dfrac{10}{9}$ Choose the correct answer from the options given below:

A LPP $max\,Z = 3x + 8y$ subjected to the constraints $2x + y \le 10$, $x + 3y \le 15$, $x,y \ge 0$, then $max\,Z$ is

The area of the region bounded by the curves $x = at^2$ and $y = 2at$ between the lines parallel to $y-axis$ corresponding to $t = 1$ and $t = 2$ is equal to :

Match the LIST-I with LIST-II (where $[x]$ denotes greatest integer function) | | LIST-I<br>Integral | | LIST-II<br>Values | |---|---|---|---| | A. | $\displaystyle\int_{0}^{2} [x]\, dx$ | I. | $0$ | | B. | $\displaystyle\int_{0}^{1.5} [x^2]\, dx$ | II. | $1$ | | C. | $\displaystyle\int_{-\pi/4}^{\pi/4} \sin x \, dx$ | III. | $\sqrt{2}$ | | D. | $\displaystyle\int_{-\pi/4}^{\pi/4} \cos x \, dx$ | IV. | $2-\sqrt{2}$ | Choose the correct answer from the options given below:

In a factory of fans, machine A, B and C manufacture respectively 20%, 40% and 40% of total fans. Out of their output 2, 3 and 5 percent are defective fans respectively. A fan is drawn at random from the products then the probability that the drawn fan is defective is:

If the lines $x = ay+b$, $z = cy+d$ and $x = py+q$, $z = ry+s$ are perpendicular, then $ap + cr$ is equal to

If $y = \left[\dfrac{2}{1+x^{b-a}+x^{c-a}} + \dfrac{2}{1+x^{c-b}+x^{a-b}} + \dfrac{2}{1+x^{a-c}+x^{b-c}}\right]^x$, then $\dfrac{dy}{dx}$ is equal to :

The function $f: R \to [0,1]$ defined by $f(x) = \dfrac{x^2}{x^2+1}$ is: (Where $R$ is set of real numbers) A. One-one B. one-one and onto C. onto D. Not one-one Choose the correct answer from the options given below:

If the function $f(x) = \dfrac{(4^x-1)^3}{\sin\dfrac{x}{4}\cdot\log\left(1+\dfrac{x^2}{3}\right)}$ is continuous at $x = 0$, then the value of $f(0)$ is: (Take $\log_e x = \log x$)

If $|\vec{a}| = 3$ and $|\vec{b}| = 4$, then a value of $\lambda$ for which $\vec{a} + \lambda\vec{b}$ and $\vec{a} - \lambda\vec{b}$ are perpendiculars is.

A LPP $max\,z = ax+by$ having bounded feasible region with vertices on $(2,1), (3,2), (5,6)$ and $(1,7)$. Then which of following are TRUE? A. $max\,z$ occurs at $(1,7)$ and $(5,6)$ if $b = 4a$ B. $max\,z$ occurs at $(1,7)$ and $(5,6)$ if $b = -4a$ C. $max\,z$ does not exist D. if $max\,z$ occurs at $(1,7)$ and $(5,6)$, then $max\,z$ occurs for infinite number of value of $x$ and $y$ Choose the correct answer from the options given below:

$\displaystyle\int \dfrac{1+\cos\theta}{1-\cos\theta}\,d\theta =$

If $\begin{vmatrix} 1 & -2 & 5 \\ 2 & \lambda & -1 \\ 0 & 4 & 2\lambda \end{vmatrix} = 86$, the sum of the values of $\lambda$ is:

The number of all possible matrices of order $2 \times 2$ with each entry 0 or 1 having their determinants as positive value is :

If $\vec{a} = 2\hat{i} + \hat{j}$ and $\vec{b} = \hat{j} - \hat{k}$, then Match List-I with List-II | LIST-I | LIST-II | |---|---| | A. Unit vector along $\vec{a}+\vec{b}$ | I. $\dfrac{1}{3}\left(-\hat{i}+2\hat{j}+2\hat{k}\right)$ | | B. Unit vector perpendicular to both $\vec{a}$ and $\vec{b}$ | II. $1$ | | C. $\left\vert \vec{a}+\vec{b} \right\vert$ | III. $\dfrac{1}{3}\left(2\hat{i}+2\hat{j}-\hat{k}\right)$ | | D. $\vec{a}\cdot\vec{b}$ | IV. $3$ | Choose the correct answer from the options given below:

If $|\vec{a}| = \sqrt{26}, |\vec{b}| = 7, |\vec{a}\times\vec{b}| = 35$ and $\theta$ be the angle between $\vec{a}$ and $\vec{b}$ then Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | $\sin\theta$ | I. | $61$ | | B. | $\cos\theta$ | II. | $5/\sqrt{26}$ | | C. | $\vec{a} \cdot \vec{b}$ | III. | $1/\sqrt{26}$ | | D. | $\vert \vec{a} - \vec{b} \vert^2$ | IV. | $7$ | Choose the correct answer from the options given below:

The rate of change in area of a triangle having sides 10cm and 12cm when the variable angle between them at an angle $60°$, is:

The value of $\displaystyle\int_{\pi/6}^{\pi/3} \dfrac{\sin x+\cos x}{\sqrt{\sin 2x}}\,dx$ is:

Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | If $A$ and $B$ are mutually exclusive events then $P(A \cup B) =$ | I. | $\dfrac{P(A \cap B)}{P(B)}, P(B) \neq 0$ | | B. | If $A$ and $B$ are independent events then $P(A \cap B) =$ | II. | $\dfrac{P(A \cap B)}{P(A)}, P(A) \neq 0$ | | C. | If $A$ and $B$ are two events of a sample space of an experiment, then $P(A/B) =$ | III. | $P(A) \cdot P(B)$ | | D. | If $A$ and $B$ are two events of a sample space of an experiment, then $P(B/A) =$ | IV. | $P(A) + P(B)$ | Choose the correct answer from the options given below:

If $A = \begin{bmatrix} 2 & -3 & -5 \\ -1 & 4 & 5 \\ 1 & -3 & -4 \end{bmatrix}$, then $A^2$ is equal to :

A line is perpendicular to two lines having direction ratios $1,-2,-2$ and $0,2,1$ then the direction cosines of the line are:

The distance between the two lines $L_1$ and $L_2$ given by $L_1: \dfrac{x-1}{2} = \dfrac{y-2}{3} = \dfrac{-z-4}{-6}$ and $L_2: \dfrac{x-3}{2} = \dfrac{y-3}{3} = \dfrac{z+5}{6}$ is

The function $f(x) = 24x^4 - 32x^3 - 96x^2 + 7$ on the interval $\left[-\dfrac{3}{2}, 4\right]$ is : A. increasing in $(-1,0)$ B. decreasing in $(0,4)$ C. increasing in $(2,4)$ D. decreasing in $\left(-\dfrac{3}{2},-1\right)$ Choose the correct answer from the options given below:

If $\begin{bmatrix} 0 & x \\ 2 & 1 \end{bmatrix} + 2\begin{bmatrix} 3 & 1 \\ y & 0 \end{bmatrix} = \begin{bmatrix} 6 & 5 \\ 8 & 1 \end{bmatrix}$, then the value of $2x+3y$ is :

If $a, b$ and $c$ are non-zero real number such that $\begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix} = 0$, then value of $\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}$ is

Let $A = \begin{bmatrix} 1 & -2 & 3 \\ 1 & 2 & 1 \\ \lambda & 2 & -3 \end{bmatrix}$. If $A^{-1}$ does not exist, then $\lambda =$

The general solution of the differential equation $x^2\dfrac{dy}{dx} + y^2 = xy$ is: (take $\log_e x = \log x$)

Match the LIST-I with LIST-II | | LIST-I<br>Differential equation | | LIST-II<br>Integrating factor | |---|---|---|---| | A. | $\dfrac{dy}{dx} + 3y = e^{-2x}$ | I. | $\dfrac{1}{x}$ | | B. | $x\dfrac{dy}{dx} + y = 3x^2$ | II. | $e^{-x}$ | | C. | $x\dfrac{dy}{dx} - y = 3x^2$ | III. | $x$ | | D. | $\dfrac{dy}{dx} - y = x$ | IV. | $e^{3x}$ | Choose the correct answer from the options given below:

In $\triangle ABC$, Which of the following are True? <img src="https://balti.afterboards.in/l7bZkkmbWl3YkhX" width="400px"/> A. $\overline{AB}+\overline{BC}+\overline{CA}=\vec{0}$ B. $\overline{AB}+\overline{BC}-\overline{AC}=\vec{0}$ C. $\overline{AB}+\overline{BC}-\overline{CA}=\vec{0}$ D. $\overline{AB}-\overline{CB}+\overline{CA}=\vec{0}$ Choose the correct answer from the options given below:

A letter is known to have come either from LONDON or CLIFTON. On the envelop just two consecutive letter 'ON' are visible. The probability that the letter has come from LONDON is:

The value of $\cos^{-1}\left\{\dfrac{\sin x+\cos x}{\sqrt{2}}\right\}, \dfrac{5\pi}{4} < x < \dfrac{9\pi}{4}$ is :

The Periodic payment of ₹ R, in a sinking fund required to accumulate a sum of ₹ A over $n$ periods with interest charged at a rate $i$ per period per rupee is

Let $A = \begin{bmatrix} 2 & 4 \\ -2 & 8 \end{bmatrix}$. If $A^{-1} = \alpha I + \beta A$, $\alpha,\beta \in R$ (Where R is set of real numbers) and I is a $2\times2$ identity matrix, than the value of $4(\alpha-2\beta)$ is equal to:

If the mean and variance of a binomial distribution are 4 and 3 respectively, then the probability of getting exactly 5 successes in the distribution is:

A random variable X has the following probability distribution: | X | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | |---|---|---|---|---|---|---|---|---| | P(X) | 0 | k | 2k | 2k | 3k | $k^2$ | $2k^2$ | $7k^2+k$ | Then, which of the following are correct ? A. $k = 0.1$ B. $P(X<3) = 0.3$ C. $P(0<X<3) = 0.8$ D. $P(X>6) = 0.17$ Choose the correct answer from the options given below:

In what ratio must a grocer mix two varieties of sugar A and B worth ₹ 40 per kg and ₹ 50 per kg respectively, so that by selling that mixture at ₹ 46.20 per kg, he may gain 10%?

Let $f(x)$ be a function defined by $f(x) = 2x^3 - 24x + 107$. If $\alpha$ and $\beta$ are the maximum and minimum values respectively in the interval $[1,3]$, then $\alpha-\beta$ is equal to:

Match the LIST-I with LIST-II [$a$ is an arbitrary constant] | | LIST-I<br>Differential Equation | | LIST-II<br>Family of curves | |---|---|---|---| | A. | $x\,dy - y\,dx = 0$ | I. | $x^2 + y^2 = a^2$ | | B. | $2y\,dx - x\,dy = 0$ | II. | $y = ax$ | | C. | $x\,dx + y\,dy = 0$ | III. | $y^2 = 16x + a$ | | D. | $y\,dy - 8\,dx = 0$ | IV. | $x^2 = ay$ | Choose the correct answer from the options given below:

Match the LIST-I with LIST-II | | LIST-I<br>Matrix A | | LIST-II<br>$\vert adj\,A \vert$ | |---|---|---|---| | A. | $\begin{bmatrix}1 & 2 & 3\\ 0 & 2 & 5\\ 0 & 0 & 1\end{bmatrix}$ | I. | $9$ | | B. | $\begin{bmatrix}3 & -1 & 4\\ 0 & 1 & 2\\ 0 & 0 & -1\end{bmatrix}$ | II. | $16$ | | C. | $\begin{bmatrix}4 & 2 & -3\\ 0 & -2 & 5\\ 0 & 0 & 1\end{bmatrix}$ | III. | $64$ | | D. | $\begin{bmatrix}2 & 5 & 3\\ 0 & 2 & 1\\ 0 & 0 & 1\end{bmatrix}$ | IV. | $4$ | Choose the correct answer from the options given below:

The price at which the bond is sold to the investors at the time of issue is known as:

Ankur takes a personal loan of ₹ 3,00,000 at the rate of 12% per annum for two years. His EMI using a flat rate method will be:

Consider the following hypothesis test : $H_0: \mu \le 35$ $H_a: \mu > 35$ A sample of 49 provided a sample mean of 38.2 The population standard deviation is 8. The value of test-statistic is,

Which of the following statements are true about the sinking fund ? A. In the sinking fund, a fixed amount at regular intervals is deposited. B. Sinking fund can be used in an emergency. C. In the sinking fund, any amount, anytime, can be deposited. D. Sinking fund can be used only for the purpose it was created. Choose the correct answer from the options given below:

If the corner points of the bounded feasible region for an LPP are $(5,0), (0,4), (0,2), (3,4)$, and $(0,7)$, then the minimum value of the objective function $z = 2x+5y$ occurs at :

Let X denote the number of hours a person watches television during a randomly selected day. The probability that X can take the value $x_i$, has the following form, where $k$ is some unknown constant. $P(X=x_i) = \begin{cases} 0.5 & \text{if } x_i=0 \\ kx_i & \text{if } x_i=1 \\ k(4-x_i) & \text{if } x_i=2 \text{ or } 3 \\ 0 & \text{otherwise} \end{cases}$ The probability that the person watches at most 2 hours of television on a selected day is :

The rate of change of $\sqrt{x^2-2}$ with respect to $\dfrac{x}{x+1}$ at $x=2$ is :

Match the LIST-I with LIST-II | LIST-I | | LIST-II | |---|---|---| | A. | Decrease in production due to fire in a factory | I. Seasonal trend | | B. | Woolen clothes sales are higher in winter. | II. Long term trend | | C. | Rise and fall of the share market. | III. Irregular trend | | D. | Continuous increase in population | IV. Cyclical trend | Choose the correct answer from the options given below:

The solution set $\{x: x \in R, 3x-2 < x+2 \le 2x+6\}$ (Where $R$ is set of real numbers) is :

Match the LIST-I with LIST-II | | LIST-I<br>Function $f(x)$ | | LIST-II<br>Second order derivative of $f(x)$ w.r.t $'x'$ | |---|---|---|---| | A. | $x^2 \log_e x$ | I. | $e^x(2 + 4x + x^2)$ | | B. | $e^x \log_e x$ | II. | $e^x\left(\log_e x + \dfrac{2}{x} - \dfrac{1}{x^2}\right)$ | | C. | $x^2 e^x$ | III. | $2\log_e x + 3$ | | D. | $x^{-2} e^x$ | IV. | $\dfrac{e^x}{x^2}\left(\dfrac{6}{x^2} - \dfrac{4}{x} + 1\right)$ | Choose the correct answer from the options given below:

In which of the following cases the value of the integral is more than 10? A. $\displaystyle\int_0^2 |x|\,dx$ B. $\displaystyle\int_0^2 (x+3)^2\,dx$ C. $\displaystyle\int_0^2 e^x\,dx$ D. $\displaystyle\int_0^2 (2x+5)\,dx$ Choose the correct answer from the options given below:

A random sample consists of five observations: 2,4,5,6,8. The point estimate of the population mean is :

The present value of a perpetuity of ₹ 900 payable at the end of each year, if money is worth 6 % per annum, is:

Consider a LPP given by: Maximize $z = 3x+4y$, Subject to: $x+y \le 40$, $x+2y \le 60$, $x,y \ge 0$. Then which of the following statements are correct ? A. The corner points of the feasible region are $(0,0), (0,30), (40,0), (20,20)$. B. The feasible region is unbounded. C. The feasible region is bounded. D. The maximum value of $z=3x+4y$ is obtained at $(60,40)$. Choose the correct answer from the options given below:

If A is a square matrix of order $n$ and $k$ is a scalar such that $|kA| = \alpha|A|$ then the value of $\alpha$ is:

A tap can fill a tank in 45 minutes whereas another tap can empty it in 1 hour 30 minutes. If both taps are opened at 9 A.M., then the time at which the tank will be filled is

The probability distribution table of a random variable X is given below. | $X_i$ | $P(X_i)$ | |---|---| | 0 | 1/8 | | 1 | a | | 2 | b | | 3 | 1/8 | If $E(X) = \dfrac{3}{2}$, then the values of a and b are:

If $\displaystyle\int_{-1}^{b} x^3\,dx = \dfrac{15}{4}$, then $b$ can take the value

If the matrix $\begin{bmatrix} 5 & x^2 \\ 3x-2 & x-1 \end{bmatrix}$ is symmetric, then values of $x$ are :

If the supply function for a commodity is $p = 3+x^3$. Then the producer's surplus, if 10 units of the goods are sold, is:

Which of the following facts are not true ?( Where $R$ is set of real numbers) A. $|x+y| \le |x|+|y|, x,y \in R$ B. $|x-y| \ge |x|+|y|, x,y \in R$ C. $|x+y| \ge |x|+|y|, x,y \in R$ D. $|x-y| \le |x|+|y|, x,y \in R$ Choose the correct answer from the options given below:

Match the LIST-I with LIST-II | LIST-I | | LIST-II | |---|---|---| | A. | The measurable characteristic of a population is called | I. Statistic | | B. | The measurable characteristic of a sample is called | II. Sample size | | C. | The number of objects in a sample is called | III. Null hypothesis | | D. | A tentative assumption about population | IV. Parameter | Choose the correct answer from the options given below:

Observe the following table: | Year | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | |---|---|---|---|---|---|---| | Annual Sale | 40 | 50 | 60 | 70 | 80 | 90 | If the three-year moving averages of the above observations are A, B, C, D respectively, then the largest value of the three-year moving averages is :

If matrix $A = \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}$, then $A^2+I$ is equal to: (Where I is an identity matrix of order 2)

The value of $m$ satisfying $m \equiv 12(mod\ 7)$ is:

In a kilometer race, A beats B by 100 meters and B beats C by 125 meters. Then A beats C by

In 2001, a vehicle was purchased for ₹ 2 Lakh. In 2011, the scrap value of the vehicle became ₹ 50,000. What was the annual depreciation?