CUET Mathematics 2026 PYQs22 May Shift 2. Free, no login required.

The area (in sq. units) of the region in the first quadrant enclosed between the line $x + y = 2$, parabola $y^2 = x$ and the x-axis, is

If $f(x) = \begin{vmatrix} 0 & x+a & x+b \\ x-a & 0 & x+c \\ x-b & x-c & 0 \end{vmatrix}$ then the value of $f(0)$ is equal to:

Match List-I with List-II | List-I | List-II | |---|---| | (A) $\int_{-1}^{1} \lvert x \rvert dx =$ | (I) 3 | | (B) $\int_{-\pi}^{\pi} \cos x \, dx =$ | (II) 1 | | (C) $\int_{-1}^{1} (\lvert x \rvert-1) dx =$ | (III) 0 | | (D) $\int_{-1}^{1} (\lvert x \rvert+1) dx =$ | (IV) -1 | Choose the correct answer from the options given below:

For the function $f(x) = (x+1)^2(x-2)^2$, which of the following statements are TRUE? (A) $f(x)$ is decreasing on $(-\infty,-1)$ (B) $f(x)$ is increasing on $\left(-1,\frac{1}{2}\right)$ (C) $f(x)$ is decreasing on $\left(\frac{1}{2},2\right)$ (D) $f(x)$ is increasing on $(2,\infty)$ Choose the correct answer from the options given below:

A bag contains 8 red and 7 black balls. Two balls are drawn at random. The probability that both the balls are of the same colour is:

The number of diagonal matrices of order 3 with elements either 1 or 2, is:

For a given differential equation $e^{dy/dx} = x + 1; x \in (-1,\infty)$, then which of the following statements are TRUE? (A) Its general solution is $y = x\log_e(x+1) - x + \log_e(x+1) + C$; C is an arbitrary constant. (B) Its particular solution is $y = (x+1)\log_e(x+1) - x + 5; y(0) = 5$ (C) Its general solution is $y = (x-1)\log(x+1) - x + C$; C is an arbitrary constant (D) Its particular solution is $y = (x-1)\log(x+1) - x + 5; y(0) = 5$ Choose the correct answer from the options given below:

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

If $y^2 = ax + b, a,b \in \mathbb{R}$ where $\mathbb{R}$ is the set of real numbers, then $y\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^2$ is equal to:

The general solution of the differential equation $\frac{dy}{dx} = \frac{3e^{2x}+3e^{4x}}{e^x+e^{-x}}$ is

If the function $f(x)$ defined by $f(x) = x^3 - 3x + 100, (x \in \mathbb{R})$, (Where $\mathbb{R}$ is set of real numbers), then $f(x)$ has

$\int \left\{\frac{1}{\log x} - \frac{1}{(\log x)^2}\right\} dx$ is equal to:(where C is an arbitrary constant)

The product of the order and degree of the differential equation $\left(\frac{d^3y}{dx^3}\right)^2 - 3\frac{d^2y}{dx^2} + 2\left(\frac{dy}{dx}\right)^4 = y^4$ is

The feasible region represented by the constraints $2x+y \le 12, x+2y \le 12, 4x+5y \ge 20, x,y \ge 0$ of LPP is <img src="https://balti.afterboards.in/F6Aeuqyz9ztpZ7K" width="400px"/>

Match List-I with List-II | List-I | List-II | |---|---| | (A) If $A = [a_{ij}]_{n \times n}$, where $a_{ij} = \begin{cases}0, & i \ne j \\ k, & i=j, k\ne 0\end{cases}$ then A is ___ | (I) Symmetric matrix | | (B) If $A = [a_{ij}]_{2\times 2}$, where $a_{ij} = \begin{cases}1, & i \ne j \\ 0, & i=j\end{cases}$, then $A^2$ is ___ | (II) Skew-Symmetric matrix | | (C) If A and B are matrices of the same order, then $(AB^T - BA^T)$ is ___ | (III) Identity matrix | | (D) If A and B are symmetric matrices of the same order, then $(AB+BA)$ is ___ | (IV) Scalar matrix | Choose the correct answer from the options given below:

$\cos[\tan^{-1}\{\sin(\cot^{-1}x)\}]$ is equal to

If $\int \frac{(\sqrt{x})^5}{(\sqrt{x})^7+x^6} dx = a\log\left|\frac{x^k}{1+x^k}\right| + C$; Where C is an arbitrary constant, then the value of $a.k$ is:

The points on the line $\frac{x+2}{3} = \frac{y+1}{2} = \frac{z-3}{2}$ at a distance of $\sqrt{17}$ from the point (-2, -1, 3) are:

A vector of magnitude 9, which is perpendicular to both the vectors $4\hat{i}-\hat{j}+3\hat{k}$ and $-2\hat{i}+\hat{j}-2\hat{k}$ is:

Two numbers are selected at random from the integers 1 through 19. If the sum is even, then the probability that both are odd numbers is:

Urn A contains 1 white, 2 black and 3 red balls, Urn B contains 2 white, 1 black and 1 red ball and Urn C contains 4 white, 5 black and 3 red balls. One Urn is chosen at random and two balls are drawn. If it is found that there is one white and one red, Then the probability that they come from A is:

If A and B are two independent events such that $P(A) = \frac{4}{7}$ and $P(B) = \frac{2}{7}$ then $P(\overline{A} \cap \overline{B})$ equals

The corner points of the feasible region of a LPP are (0,2), (3,0), (6,0), (6,8) and (0,5). If the objective function is $z = 4x + 6y$, then the sum of maximum and minimum value of z is equal to:

Particular solution of the differential equation $dy = e^{2x+y}dx$, $y(0) = 0$ is:

Consider a function $f:\left[0,\frac{\pi}{2}\right] \to R$, given by $f(x)=\sin x$ and $g:\left[0,\frac{\pi}{2}\right] \to R$, given by $g(x)=\cos x$, Where R is a set of real numbers, Which of the following statements are correct? (A) f and g are one-one (B) f and g are not one-one (C) f+g is not one-one (D) f+g is one-one Choose the correct answer from the options given below:

For the function $f: \mathbb{R} \to \mathbb{R}$ given by $f(x) = \lvert x-3 \rvert + \lvert x+4 \rvert$, Where $\mathbb{R}$ is set of real numbers, which of the following statements are correct? (A) $f(x)$ is continuous as well as differentiable at $x=3$. (B) $f(x)$ is continuous but not differentiable at $x=3$ and $x=-4$ (C) $f(x)$ is neither continuous nor differentiable at $x=3$ (D) $f(x)$ is continuous on $\mathbb{R}$ Choose the correct answer from the options given below:

The relation R on the set A = {1, 2, 3} defined by R = {(1,1), (2,2), (3,3), (1,3), (2,3), (1,2)} is

If $A = \begin{bmatrix}0 & a & -3 \\ 2 & 0 & -1 \\ b & 1 & 0\end{bmatrix}$ is a skew-symmetric matrix, then

If $\begin{bmatrix}3 & 1\\2 & 1\end{bmatrix}P\begin{bmatrix}2 & 1\\3 & 2\end{bmatrix}=\begin{bmatrix}1 & -1\\0 & 1\end{bmatrix}$ then matrix P is

If $A=\begin{bmatrix}0 & b-a & c-a\\a-b & 0 & c-b\\a-c & b-c & 0\end{bmatrix}$ then the value of $\lvert A \rvert$ is

Match List-I with List-II | List-I | List-II | |---|---| | (A) The distance of a point $P(a,b,c)$ from x-axis | (I) $\sqrt{a^2+b^2+c^2}$ | | (B) The distance of a point $P(a,b,c)$ from y-axis | (II) $\sqrt{b^2+c^2}$ | | (C) The distance of a point $P(a,b,c)$ from Z-axis | (III) $\sqrt{a^2+c^2}$ | | (D) The distance of a point $P(a,b,c)$ from origin | (IV) $\sqrt{a^2+b^2}$ | Choose the correct answer from the options given below:

Let A be the area of the triangle with vertices (3, 8), (5, -1) and $(k, 2)$, $k \in \mathbb{Z}$ (set of integers). If $2A = 75$, then k is equal to:

If $A=\begin{bmatrix}k & 2\\2 & k\end{bmatrix}$ such that $\lvert A^3 \rvert = 125$ then which of the following statements are TRUE? (A) $\lvert k.adj(3A) \rvert = 405$ (B) $\lvert k.adj(3A) \rvert = 2025$ (C) $\lvert adj(3A) \rvert = 95$ (D) $\lvert adj(3A) \rvert = 45$ Choose the correct answer from the options given below:

The area (in sq. units) of the region bounded by the curve $x=at^2$, $y=2at$ between the ordinates corresponding to t = 1 and t = 2 is

If $y=\tan^{-1}(x+y)$, then $\frac{d^2y}{dx^2}$ is equal to:

$\int \frac{2\cos 2x \, dx}{(\sin x+\cos x)^2}$ is equal to:(where C is an arbitrary constant)

The area (in sq. units) of the region bounded by the line $2y=3x+6$, x-axis and the ordinates x=-3 and x=1 is:

The shortest distance (in units) between the lines $L_1:\frac{x-1}{2}=\frac{y-2}{3}=\frac{z+4}{6}$ and $L_2:\frac{x-3}{2}=\frac{3-y}{-3}=\frac{z+5}{6}$ is:

If $\vec{a},\vec{b}$ and $\vec{c}$ are three vectors such that $\lvert \vec{a} \rvert=\frac{1}{\sqrt{2}}$, $\lvert \vec{b} \rvert=\frac{1}{\sqrt{3}}$, $\lvert \vec{c} \rvert=\frac{1}{\sqrt{6}}$, $\lvert \vec{a}+\vec{b}+\vec{c} \rvert=1$ and $\vec{c}=\lambda(\vec{a}\times\vec{b})$. The angle between $\vec{a}$ and $\vec{b}$ is

If $A=\begin{bmatrix}5 & 0 & 0\\0 & 5 & 0\\0 & 0 & 5\end{bmatrix}$ such that $A^5=\lambda^2 A$, then the value of $\lambda$ is

Match List-I with List-II | List-I: Linear differential equation | List-II: Integrating factor | |---|---| | (A) $x\frac{dy}{dx}-y=2x^3$ | (I) $e^{-x}$ | | (B) $2x\frac{dy}{dx}+y=3x^2$ | (II) $e^x$ | | (C) $\frac{dy}{dx}+y=\cos x-\sin x$ | (III) $x^{1/2}$ | | (D) $\frac{dy}{dx}-y=e^x$ | (IV) $1/x$ | Choose the correct answer from the options given below:

The area (in sq. units) of the parallelogram whose diagonals are represented by the vectors $\vec{a}=2\hat{i}-\hat{j}+\hat{k}$ and $\vec{b}=3\hat{i}+4\hat{j}-\hat{k}$, is

Let the median of a variable equilateral triangle is increasing at the rate of $2\sqrt{3}$ cm/s. Then the rate at which its each side is increasing is:

If the function $f(x)=\begin{cases}\frac{e^{2\log_e x^2}-1}{x-1}, & x\ne 1\\ a, & x=1\end{cases}$ is continuous at x=1, then the value of a is:

$\int_0^{2\pi} \cos^5 x \, dx$ is equal to

Consider the LPP: Minimize $z=-50x+20y$ subject to $2x-y\ge -5, 3x+y\ge 3, 2x-3y\le 12, x\ge 0, y\ge 0$. Then which of the following statements are TRUE? (A) Corner points of the feasible region of the LPP are (0,5), (0,3), (1,0), (6,0). (B) The optimum value of the objective function is -300 (C) Optimum value does not exist (D) The optimum value of the objective function is 100 Choose the correct answer from the options given below:

A unit vector perpendicular to both the vectors $4\hat{i}-\hat{j}+3\hat{k}$ and $-2\hat{i}+\hat{j}-2\hat{k}$ is:

The interval in which $f(x)=\frac{x}{\log x}$ is increasing, is:

Two dice are thrown simultaneously. If X denotes the number of sixes appearing on two dice, then which of the following are correct? (A) $P(X=0)=\frac{1}{36}$ (B) $P(X=1)=\frac{10}{36}$ (C) $P(X=1)+P(X=0)=\frac{35}{36}$ (D) $P(X=1)+P(X=2)=\frac{11}{36}$ Choose the correct answer from the options given below:

If the local maximum value of the function $f(x)=x^3-2\lambda x^2+\lambda^2 x, \lambda>0$ is 108, Then the local minimum value of the function occurs at

If $A=\begin{bmatrix}x+4 & 3\\2 & 1\end{bmatrix}, B=\begin{bmatrix}5 & 2x-1\\2 & x\end{bmatrix}$ and $\lvert adj(AB) \rvert=32$, then the value of x is:

Match List-I with List-II | List-I | List-II | |---|---| | Matrix A | $\left\vert \text{adj } A \right\vert^2$ | | (A) $\begin{bmatrix} 3 & 7 \\ 2 & 8 \end{bmatrix}$ | (I) $121$ | | (B) $\begin{bmatrix} 5 & -1 \\ 2 & 4 \end{bmatrix}$ | (II) $144$ | | (C) $\begin{bmatrix} 3 & 6 \\ 5 & 14 \end{bmatrix}$ | (III) $484$ | | (D) $\begin{bmatrix} 7 & 5 \\ 2 & 3 \end{bmatrix}$ | (IV) $100$ | Choose the correct answer from the options given below:

Let y(x) be the solution curve of the differential equation $x(1+y^2)dx - y(1+x^2)dy = 0$ and it passes through the point (0, 1), then

Let $r_e$ denote the effective rate corresponding to the nominal rate r, compounded m times in a year. Let P be the principal and rate per conversion period is $i=\frac{r}{m}$, then effective rate of interest is:

If $A=\begin{bmatrix}1 & 2 & 2\\2 & 1 & -2\\\alpha & 2 & \beta\end{bmatrix}$ and $AA^T=9I$, where I is the identity matrix of order 3, then $(\beta-\alpha)$ equals:

Which of the following statements are true? (A) A matrix which is both symmetric as well as skew-symmetric is a null matrix. (B) All positive integral powers of a symmetric matrix are symmetric. (C) If A is a square matrix, then $A+A^T$ is a symmetric matrix. (D) All positive even integral powers of a skew-symmetric matrix are skew-symmetric. Choose the correct answer from the options given below:

A cistern can be filled by two pipes filling separately in 8 and 10 minutes respectively. Both the pipes are opened together but being clogged for a certain time, only $\frac{7}{10}$ of the full quantity of water flows through the former and only $\frac{3}{8}$ through the later pipe. The obstructions, however, being suddenly removed, the cistern is filled in 2 minutes from that moment. How long was it before the full flow began?

The cost function of a product is given by $C(x)=\frac{1}{3}x^3-45x^2-900x+36$, where x is the number of units produced. In order to minimize the marginal cost, how many units of the product must be produced?

The function $f(x)=x^2-x\sqrt{2}$ is strictly decreasing in the interval :

Mohan wishes to purchase a house for ₹10,000,000 with a down payment of ₹20,00,00.00. If he pays the balance amount in 25 years by equal monthly instalment at 9% compounded monthly, then the total interest paid by Mohan is: [Use $(1.0075)^{300} = 9.4084$]

The sampling distribution of the sample mean approaches a normal distribution as the sample size gets larger, no matter what is the shape of the population distribution. The above statement is:

For the LPP, $Z=20x+10y$ Subject to $x+2y\le 40$ $3x+y\ge 30$ $4x+3y\ge 60$ $x,y\ge 0$ Match List-I with List-II | List-I | List-II | |---|---| | (A) $Max.Z$ | (I) 180 | | (B) $Min.Z$ | (II) 320 | | (C) $Max.Z - 2\,Min.Z$ | (III) 240 | | (D) If $Min.Z$ is attained at $(\alpha,\beta)$, then $\alpha^2+\beta^2$ is | (IV) 800 | Choose the correct answer from the options given below:

Which of the following are true about sinking fund? (A) Sinking fund is a fixed term account. (B) A fixed amount is deposited at pre defined regular intervals. (C) Sinking fund can be used in any emergency. (D) It is setup for a particular upcoming expense. Choose the correct answer from the options given below:

A motor boat can travel 5 km/hr in still water. It travelled 9 km downstream in river and then returned back taking altogether 10 hours. The rate of flow of water in the river is:

The least non-negative remainder when $3^{2026}$ is divided by 13 is:

Five bad apples are mixed with 15 good apples accidently. Let the random variable X be the number of bad apples in a draw of two apples, then mean of X is

A fire in a factory delaying production for some time is:

At what rate of interest will the present value of a perpetuity of ₹10000 payable at the end of every six months be ₹200,000?

$\int_{1/3}^{1} \frac{(x-x^3)^{1/3}}{x^4} dx$ equals

If the heights of 300 students are normally distributed with mean 68 inches and standard deviation 3 inches. If Z is the standard normal variate such that $P(0\le Z\le 1.33)=0.4082, P(Z\ge 1.33)=0.0918$ and $P(0\le Z\le 1)=0.3413$, then which of the following statements are correct? (A) There are 27 students whose height is greater than 72 inches. (B) The number of students having heights less than or equal to 64 inches is 27. (C) 210 students have their heights between 65 and 71 inches. (D) There are 35 students whose height is greater then 72 inches. Choose the correct answer from the options given below:

Let $f(x)=\int \frac{3x-2}{(x+1)^2(x+3)}dx = \alpha\log\left|\frac{x+1}{x+3}\right|+\beta\left(\frac{1}{x+1}\right)+\gamma$, where $\gamma$ is the constant of integration. If $f(0)=\frac{11}{4}\log\left(\frac{1}{3}\right)+4$, then which of the following are correct? (A) $4\alpha+2\beta+6\gamma=22$ (B) $f(1)=\alpha[1-\log 2]$ (C) $\alpha+\beta+\gamma=\frac{27}{4}$ (D) $\gamma=-\frac{5}{2}$ Choose the correct answer from the options given below:

The probability that a man aged 35 years will die before reaching the age of 40 years may be taken as 0.018. Out of a group of 100 men, now aged 35 years, what is the approximate probability that one man will die within next five years? (Given: $e^{-1.8}=0.1653$)

A person invested ₹2,00,000 in a mutual fund in year 2012. The value of the mutual fund increased to ₹3,00,000 in year 2017. The percentage of compound annual growth rate on the investment is: (Given: $(1.5)^{1/5} = 1.084$)

At a game of billiards, A can give B 15 points in 60 and A can give C 20 points in 60. How many points can B give C in a game of 180?

For the given five values 15, 24, 18, 33, 45, which of the following is not the three years moving average?

At x = 1, the function $f(x)=x^4-48x^2+\alpha x+120$ attains its maximum value in the interval [0, 2], then the value of $\alpha$ is:

A washing machine costing ₹40000 has an estimated useful life of 4 years and a scrap value of ₹5000. The depreciation rate percentage is:

A company has been producing steel tubes of mean inner diameter of 3 cm. A sample of 17 tubes gives an inner diameter of 3.01 cm and a standard deviation of 0.064. Then the value of the t-test statistic is:

In reference to linear programming problem (LPP), which of the following statement is NOT correct?

A bottle is full of antiseptic liquid. One third of it is taken out and then an equal amount of water is poured into the bottle to fill it. This process is repeated three times. If the final ratio of antiseptic liquid and water is $\frac{p}{q}$, where $\gcd(p,q)=1$, then $(p+q)$ is

For the function $y(x)=\sqrt{x+1}-\sqrt{x-1}$, which of the following are true? (A) $\left(\frac{dy}{dx}\right)_{at\,x=2}=\frac{1-\sqrt{3}}{2\sqrt{3}}$ (B) $(x^2-1)\frac{d^2y}{dx^2}-\frac{dy}{dx}+4y=0$ (C) $(x^2-1)\left(\frac{dy}{dx}\right)^2-4y^2=0$ (D) If $P(x)\frac{d^2y}{dx^2}+Q(x)\frac{dy}{dx}+\alpha y=0$, then $P(x)-xQ(x)-4\alpha=0$ Choose the correct answer from the options given below:

Match List-I with List-II | List-I | List-II | |---|---| | (A) If $A=\begin{bmatrix}2 & -5\\3 & 4\end{bmatrix}$, then adj A = | (I) $\begin{bmatrix}4 & -5\\-2 & -3\end{bmatrix}$ | | (B) If $A=\begin{bmatrix}2 & 3\\5 & -2\end{bmatrix}$, then $A^{-1}=$ | (II) $\begin{bmatrix}\frac{1}{17} & \frac{-5}{17}\\\frac{3}{17} & \frac{2}{17}\end{bmatrix}$ | | (C) If $A=\begin{bmatrix}-3 & 5\\2 & 4\end{bmatrix}$, then adj A = | (III) $\begin{bmatrix}4 & 5\\-3 & 2\end{bmatrix}$ | | (D) If $A=\begin{bmatrix}2 & 5\\-3 & 1\end{bmatrix}$, then $A^{-1}=$ | (IV) $\begin{bmatrix}\frac{2}{19} & \frac{3}{19}\\\frac{5}{19} & \frac{-2}{19}\end{bmatrix}$ | Choose the correct answer from the options given below:

A random variable X has the following probability distribution: | $X=x_i$ | 1 | 2 | 3 | 4 | |---|---|---|---|---| | $P(X=x_i)$ | k | 2k | 3k | 4k | The value of $P(X\ge 3)$ is

A sample of 100 LED TVs is taken at random. Out of 100 we found 35 TVs are of Sony, 50 are of LG and 15 are of Samsung. The point estimate of population proportion of LG is

Match List-I with List-II | List-I: Inequation | List-II: Solution set | |---|---| | (A) $2(2x+3)-10<6(x-2)$ | (I) $x\in(-\infty,3.9)$ | | (B) $\frac{2x-1}{12}-\frac{x-1}{3}<\frac{3x+1}{4}$ | (II) $x\in\left(-\infty,\frac{-1}{2}\right)\cup\left[\frac{1}{2},\infty\right)$ | | (C) $\frac{x}{2x+1}\ge \frac{1}{4}$ | (III) $x\in(0,\infty)$ | | (D) $\frac{2x-3}{4}+6>2+\frac{4x}{3}$ | (IV) $x\in(4,\infty)$ | Choose the correct answer from the options given below: