CUET Mathematics 2026 PYQs21 May Shift 2. Free, no login required.

Consider the function $f(x) = -2x^3 + 3x^2 + 36x - 15$, then which of the following are TRUE? A. $f(x)$ increases on $(-2, 3)$ B. $f(x)$ decreases on $(-\infty, -2) \cup (3, \infty)$ C. $f(x)$ increases on $(-\infty, -2) \cup (3, \infty)$ D. $f(x)$ neither increases nor decreases on $(-2, 3)$ Choose the correct answer from the options given below:

For the function $f(x) = |x + 1| + |x - 1| + |x - 2|$ which of the following are TRUE? A. $f(x)$ is continous on $\mathbb{R}$ B. $f(x)$ is not differentiable at $x = 1$ C. $f(x)$ is differentiable on $\mathbb{R}$ D. $f(x)$ has no local maxima Choose the correct answer from the options given below:

The area (in sq. units) of the bounded region $\{(x, y): x^2 \le y \le x\}$ is

The number of all possible matrices of order $3 \times 3$ with each entry $-1, 0$ or $1$ is

Consider a LPP with objective function $z = ax + by$. If its feasible region R is bounded, then $z$

Match the LIST-I with LIST-II | LIST-I (Differential Equation) | | LIST-II (Degree of Differential Equation) | |---|---|---| | A. $\dfrac{d^3y}{dx^3} + \left(\dfrac{d^2y}{dx^2}\right)^2 - \dfrac{dy}{dx} + y = 0$ | | I. 2 | | B. $\dfrac{dy}{dx} + \left(\dfrac{d^2y}{dx^2}\right)^4 + 2\left(\dfrac{d^3y}{dx^3}\right)^3 = 0$ | | II. 4 | | C. $\left(\dfrac{d^3y}{dx^3}\right)^2 + \left(\dfrac{d^2y}{dx^2}\right)^4 - y = 0$ | | III. 1 | | D. $\left(\dfrac{d^2y}{dx^2}\right)^4 + \left(\dfrac{dy}{dx}\right)^3 + y = 0$ | | IV. 3 | Choose the correct answer from the options given below:

Let $y = f(x)$ be the solution curve of the differential equation $\dfrac{dy}{dx} + 2y^2 = 0$ if $f(1) = 1$, then $f(2)$ is equal to

If $y = ax^{n+1} + bx^{-n}$, then $x^2 \dfrac{d^2y}{dx^2}$ is equal to

$\displaystyle\int \dfrac{x + \dfrac{a}{x}}{x^2 + \dfrac{a^2}{x^2}}\,dx, a > 0$ is equal to (where C is an arbitrary constant)

Which of the following differential equations has $y = x$ as one of its particular solution?

If A and B are two events such that $P(A) = \dfrac{3}{10}, P(B) = \dfrac{2}{5}$ and $P(A \cup B) = \dfrac{3}{5}$, then $P(B|A) + P(A|B)$ is:

Let A be a square matrix of order 3 and $|A| = -3$, then $|adj(3A)|$ is equal to:

Let A, B, C be square matrices of equal orders and I be the identity matrix of same order, Then which of the following are TRUE? A. $(AB)C = A(BC)$ B. $AB = BA$ C. $A(B+C) = AB + AC$ D. $AI = IA = A$ Choose the correct answer from the options given below:

Let $I = \begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}$ and $A = \begin{bmatrix}1 & -2\\2 & 4\end{bmatrix}$ be two matrices such that $8A^{-1} = kI - A, k \in \mathbb{R}$, then the value of $k$ is:

Match the LIST-I with LIST-II | LIST-I (Definite integral) | | LIST-II (Value of definite integral) | |---|---|---| | A. $\displaystyle\int_4^9 \dfrac{1}{\sqrt{x}}\,dx$ | | I. $\dfrac{2}{3}$ | | B. $\displaystyle\int_{-1}^1 x^3\,dx$ | | II. 1 | | C. $\displaystyle\int_{-1}^1 x^2\,dx$ | | III. 0 | | D. $\displaystyle\int_1^2 [x]\,dx$, where $[\cdot]$ denotes greatest integer function | | IV. 2 | Choose the correct answer from the options given below:

Consider a LPP with objective function $Z = px + qy$ subjected to certain constraints with a bounded feasible region such that maximum $Z = 80$ and minimum $Z = 52$, which occur at the corner points $(0, 8)$ and $(2, 4)$ respectively, Then the value of $p+q$ is:

The area of region $R = \{(x,y): x^2 + y^2 \le 16, y \le \sqrt{3}x, x \ge 0, y \ge 0\}$ is: (in Sq. units)

If $\vec{a}, \vec{b}, \vec{c}$ are three vectors such that $|\vec{a}| = 2, |\vec{b}| = 5, |\vec{c}| = 3$ and $\vec{a} + 2\vec{b} - 3\vec{c} = \vec{0}$, then angle between $\vec{b}$ and $\vec{c}$ is equal to:

Let $\vec{a}$ and $\vec{b}$ be any two vectors such that $\vec{a} = 2\hat{i} + \hat{j} + 3\hat{k}$ and $\vec{b} = 3\hat{i} + 5\hat{j} - 2\hat{k}$ then Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | $\vert \vec{a} \vert$ | I. | $5$ | | B. | $\vert \vec{b} \vert$ | II. | $\sqrt{507}$ | | C. | $\vert \vec{a}.\vec{b} \vert$ | III. | $\sqrt{38}$ | | D. | $\vert \vec{a} \times \vec{b} \vert$ | IV. | $\sqrt{14}$ | Choose the correct answer from the options given below:

If $y = x\log_e\left(\dfrac{x}{2+x}\right)$, then $x^3\dfrac{d^2y}{dx^2}$ is equal to:

If the system of equation $\lambda x + 3y - z = 4$ $x + 2y + z = 20$ $-\lambda x + y + 2z = -5$ does not possess a unique solution, then

Let $\vec{a} = 2\hat{i} + 3\hat{j} + \hat{k}$ and $\vec{b} = 2\hat{i} - \hat{j} + 2\hat{k}$ be two vectors. Then which of the following are TRUE? A. $\vec{a}$ and $\vec{b}$ are perpendicular B. Projection of $\vec{a}$ on $\vec{b}$ is 1 C. $|\vec{a} \times \vec{b}| = 3\sqrt{13}$ D. $\vec{a} - \vec{b}$ is a unit vector Choose the correct answer from the options given below:

Let ABCD be a parallelogram with vertices $A(2,2,a), B(1,0,0), C(1,3,a)$ and D, where $a > 0$. If the area of parallelogram is 5 square units, then the value of $a$ is:

If A is a matrix of order $3 \times 3$ such that $|A| = 4$ and $|k \cdot adj\, A| = 32|A|, k \in \mathbb{R}$; then the value of k is:

Let A and B be two events such that $P(A \cap B) = 0$ then $P(A|(A \cup B))$ is equal to:

Match the LIST-I with LIST-II | LIST-I (Line) | | LIST-II (Direction cosiness) | |---|---|---| | A. $\vec{r} = (2\hat{i} - \hat{j} + \hat{k}) + \lambda(3\hat{i} + 2\hat{k})$ | | I. $\left\langle \dfrac{2}{\sqrt{5}}, \dfrac{1}{\sqrt{5}}, 0 \right\rangle$ | | B. $\dfrac{x-1}{2} = \dfrac{3-y}{1} = \dfrac{2z-1}{4}$ | | II. $\left\langle -\dfrac{1}{3}, \dfrac{2}{3}, -\dfrac{2}{3} \right\rangle$ | | C. $\dfrac{x+1}{1} = \dfrac{2y+1}{1}, z = -1$ | | III. $\left\langle \dfrac{3}{\sqrt{13}}, 0, \dfrac{2}{\sqrt{13}} \right\rangle$ | | D. $\dfrac{1-x}{1} = \dfrac{y}{2} = \dfrac{1-z}{2}$ | | IV. $\left\langle \dfrac{2}{3}, -\dfrac{1}{3}, \dfrac{2}{3} \right\rangle$ | Choose the correct answer from the options given below:

If a function $f: R \to T$, defined by $f(x) = \sqrt{3}\sin x + \cos x$ is an onto function, then the interval of $T$ is

The area (in square units) of the region bounded by the curve $y^2 = 4ax\ (a > 0)$ and the lines $y = 2a, x = 0$ is equal to:

Which of the following functions are strictly decreasing on $\left(0, \dfrac{\pi}{2}\right)$? A. $\cos x$ B. $-\cot x$ C. $\cos 2x$ D. $\sin x$ Choose the correct answer from the options given below:

For the function $f(x) = \min\{|x|, |x-2|\}$ which of the following are TRUE? A. Function $f(x)$ is continous on $\mathbb{R}$ B. Function $f(x)$ is differentible on $\mathbb{R}$ C. Function $f(x)$ is differentible on $\mathbb{R} \sim \{0,1,2\}$ D. Function is continous on $\mathbb{R}$ but not differentiable at $x = \dfrac{1}{2}$ Choose the correct answer from the options given below:

Match the LIST-I with LIST-II | LIST-I (Function) | | LIST-II (Range of the principal value branch) | |---|---|---| | A. $\cos^{-1}x$ | | I. $\left(-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right)$ | | B. $\text{cosec}^{-1}x$ | | II. $(0, \pi)$ | | C. $\tan^{-1}x$ | | III. $[0, \pi]$ | | D. $\cot^{-1}x$ | | IV. $\left[-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right] - \{0\}$ | Choose the correct answer from the options given below:

The point on curve $y^2 = 4x$ which is nearest to the point $(2, -8)$ is

The difference of absoulte maximum (largest) and absoulte minimum (smallest) values of the function $f(x) = 12x^{4/3} - 6x^{1/3}, x \in [-1, 1]$ is

The general solution of the differential equation $(y-x)dy + (x+y)dx = 0$ is: (where C is arbitrary constant)

A company has two plants $P_1$ and $P_2$ which produces 60% and 40% of pens respectively. At plant $P_1$ 80% of pens are rated of grade A and at plant $P_2$ 90% of pens are rated of grade A. A pen is picked up at random and is found to be of grade A. The probability that it has manufactured from plant $P_1$ is:

Bag I contains 4 red and 3 black balls and bag II contains 6 red and 5 black balls. One ball is drawn at random from one of the bags, the probability that it is a red ball, is

Two cards are drawn simultaneously from a well shuffled pack of 52 cards. If X denotes the number of Spades in two draws, then Match the LIST-I with LIST-II | LIST-I | | LIST-II | |---|---|---| | A. $P(X=0)$ | | I. 1 | | B. $P(X=1)$ | | II. $\dfrac{19}{34}$ | | C. $P(X=2)$ | | III. $\dfrac{13}{34}$ | | D. $P(X<3)$ | | IV. $\dfrac{1}{17}$ | Choose the correct answer from the options given below:

The relation R on the set N of natural numbers defined as $R = \{(x,y): y = x+3 \text{ and } x \le 5\}$ is

If a function $f(x) = \begin{cases}\lambda(x^2-2x), & x \le 0\\4x+1, & x>0\end{cases}$ then

Which one of the following set of constraints depicted the shaded region given below? <img src="https://balti.afterboards.in/WvAvPh4ykDeTidu" width="400px"/>

The matrix $A = \begin{bmatrix}-3 & 0 & 0\\0 & -3 & 0\\0 & 0 & -3\end{bmatrix}$ is a A. Symmetric matrix B. Scalar matrix C. Diagonal matrix D. Skew-symmetric matrix Choose the correct answer from the options given below:

$\displaystyle\int e^x(\sec x + \log_e(\sec x + \tan x))dx$ is equal to: (where C is an arbitrary constant)

The value of $\begin{vmatrix}2 & 3 & 4\\5 & 6 & 8\\6x & 9x & 12x\end{vmatrix}$ is

Let the square of the shortest distance between the lines $L_1: \vec{r} = (\hat{i}+2\hat{j}-4\hat{k}) + \lambda(2\hat{i}+3\hat{j}+6\hat{k})$ and $L_2: \vec{r} = (3\hat{i}+3\hat{j}-5\hat{k}) + \mu(2\hat{i}+3\hat{j}+6\hat{k})$ is $\dfrac{m}{n}$, where $\gcd(m,n)=1$. Then $m+n$ is equal to:

If $A = \begin{bmatrix}1 & 2\\3 & 4\end{bmatrix}$ such that $A^2 + \beta A + \gamma I = 0$ then $\beta + \gamma$ is equal to: (where $I$ is an identity matrix of order 2)

Let $[t]$ denotes the greatest integer $\le t$, then the value of $\left[\displaystyle\int_{\pi}^{3\pi/2} x|\sin x|\,dx\right]$ is:

Match the LIST-I with LIST-II | | LIST-I<br>Definite Integrals | | LIST-II<br>Values | |---|---|---|---| | A. | $\displaystyle\int_{-1}^{1} \vert x \vert \, dx$ | I. | $2$ | | B. | $\displaystyle\int_{-1}^{1} \sin^3 x \cos^4 x \, dx$ | II. | $1$ | | C. | $\displaystyle\int_{-1}^{1} 3\vert x \vert^2 \, dx$ | III. | $0$ | | D. | $\displaystyle\int_{0}^{4} \vert x-1 \vert \, dx$ | IV. | $5$ | Choose the correct answer from the options given below:

If $A = \begin{bmatrix}-2 & 2 & 0\\3 & 1 & 4\end{bmatrix}$ and $B = \begin{bmatrix}2 & 0 & -2\\7 & 1 & 6\end{bmatrix}$ are two matrices such that $-3A + 5B + 2C = 0$ then matrix C is equal to:

Let $L_1$ and $L_2$ be any two lines given by $L_1: 3\hat{i}+2\hat{j}-4\hat{k} + \lambda(\hat{i}+2\hat{j}+2\hat{k})$ $L_2: 5\hat{i}-2\hat{j} + \mu(3\hat{i}+2\hat{j}+6\hat{k})$ Where $\lambda$ and $\mu$ are parameters then which of the following statements are TRUE? A. Equation of a line passing through the point $(1,2,3)$ which is parallel to line $L_1$ is $\dfrac{x-1}{1} = \dfrac{y-2}{2} = \dfrac{z-3}{2}$ B. Direction cosines of line $L_2$ are $\dfrac{3}{7}, \dfrac{2}{7}, \dfrac{6}{7}$ C. Line $L_1$ is parallel to the line $L_2$ D. The angle between the two lines $L_1$ and $L_2$ is $\cos^{-1}\left(\dfrac{19}{21}\right)$ Choose the correct answer from the options given below:

consider the differential equation $\dfrac{dx}{dy} + Px = Q$, where $P$ and $Q$ are function of $y$. Then A. Its integrating factor (I.F.) is $e^{\int Pdy}$ B. Its integrating factor (I.F.) is $e^{\int Pdx}$ C. Its solution is given by $x(I.F.) = \int Q(I.F.)dy + C$ D. Its solution is given by $y(I.F.) = \int Q(I.F.)dx + C$ Choose the correct answer from the options given below:

Mr. Bean wishes to purchase a house for ₹90,00,000 with a down payment of ₹10,00,000 and balance in EMI for 25 years on reducing balance payment basis. If bank charges 6% per annum compounded monthly, then his EMI is; (Use $(1.005)^{300} = 4.4650$)

If $\begin{vmatrix}x-2 & 2x-3 & 3x-4\\x-4 & 2x-9 & 3x-16\\x-8 & 2x-27 & 3x-64\end{vmatrix} = 0$ then the value of x is:

If A is a square matrix of order 3 with $|A| = 4$, then the value of $|2\,adj\,A|$ is:

Renu takes a loan of ₹12,00,000 with 12% annual interest for 10 years on flat rate basis.. Match the LIST-I with LIST-II | LIST-I | | LIST-II | |---|---|---| | A. Principal of the loan | | I. ₹14,40,000 | | B. Total interest on the principal | | II. ₹26,40,000 | | C. EMI | | III. ₹12,00,000 | | D. Total amount paid in 10 years | | IV. ₹22,000 | Choose the correct answer from the options given below:

A shopkeeper has 180 kg of cumin seeds, a part of which he sells at 12% profit. The remaining quantity of cumin seeds is of low quality and that is why he sold it at 6% loss. Overall, he made a profit of 8%. The quantity of cumin seeds sold at 6% loss is:

The two positive numbers whose sum is 40 and the product of the cube of one number and the other number is maximum, are

In a 200 meter race, Taniya beats Geetansh by 40 meters or by 10 seconds. The time taken by Taniya to complete the race will be:

The demand function for a commodity is $p = 45 + x - x^2$, then the consumer's surplus at equilibrium price $p_0 = 25$ will be:

The value of $I = \displaystyle\int (x^3-1)^{1/3}x^5\,dx$ is

Taniya purchased a car costing ₹21,00,000 which has a useful life of 15 years. The estimated scrap value of the car is ₹3,00,000. The annual depreciation using straight line method is:

Given that the total cost function for x units of a commodity is $C(x) = \dfrac{x^3}{4} + 4x^2 - 8x + 20$. Then the marginal cost when $x=4$ is:

A random variable X follows Poisson distribution. The variance of X is 2. The value of $P(X=3)$ is

If $A = \begin{bmatrix}1 & -1\\2 & -1\end{bmatrix}, B = \begin{bmatrix}x & 1\\y & -1\end{bmatrix}$ and $(A+B)^2 = A^2 + B^2$, then which of the following are correct? A. $x=1$ B. $x=4$ C. $y=1$ D. $y=4$ Choose the correct answer from the options given below:

The present value of a perpetuity of ₹5,000 payable at the beginning of each year, if the money is worth 8% effective is

If a random variable X follows binomial distribution with mean $\dfrac{4}{3}$ and variance $\dfrac{8}{9}$. Which of the following are correct? A. Probability of success is $\dfrac{1}{3}$. B. Probability of failure is $\dfrac{2}{3}$. C. Number of trials is 4. D. $P(X \ge 1) = \dfrac{35}{81}$ Choose the correct answer from the options given below:

Geetansh invested ₹27,000 and it grows to ₹81,000 in 2 years. The CAGR % will be:

The corner points of the bounded feasible region for an LPP are $(0,5), (6,6), (9,9)$ and $(0,12)$. If the objective function is $Z = px + qy; p,q>0$, then the condition on $p$ and $q$ so that the maximum of $Z$ occurs at $(9,9)$ and $(0,12)$ is

In a single throw of a die, if X denotes the number on its upper face, then the mean of X is,

Which of the following pointers are the characteristics of sinking fund? A. It is a long term account which can be closed any time. B. It is set up for a particular upcoming expense. C. It can be used in any emergency. D. It can be used only for the purpose it was created. Choose the correct answer from the options given below:

If matrix $A = \begin{bmatrix}12 & 7 & 9\\6 & 3 & 2\\5 & 1 & 8\end{bmatrix}$, then Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | $\vert A \vert$ | I. | $38$ | | B. | Cofactor of $a_{31}$ | II. | $-23$ | | C. | Minor of $a_{23}$ | III. | $-83$ | | D. | Cofactor of $a_{12}$ | IV. | $-13$ | Choose the correct answer from the options given below:

Match the differential equation (List-I) with its order and degree (List-II) | LIST-I | | LIST-II | |---|---|---| | A. $\dfrac{d^3y}{dx^3} + x^2\left(\dfrac{d^2y}{dx^2}\right) = 0$ | | I. order =3; degree is not defined | | B. $\dfrac{d^3y}{dx^3} + y^2 + e^{\frac{dy}{dx}} = 0$ | | II. order =3; degree=1 | | C. $1 - \left(\dfrac{dy}{dx}\right)^2 = \left(a\dfrac{d^2y}{dx^2}\right)^{1/3}$ | | III. order =2; degree=1 | | D. $y = x\left(\dfrac{dy}{dx}\right)^3 + \left(\dfrac{d^2y}{dx^2}\right)^4$ | | IV. order =2; degree=4 | Choose the correct answer from the options given below:

Statistical inference is a process through which inference about the population are made based on informations obtained from the:

The random variable X has a probability distribution $P(X)$ of the following form, where $k$ is some real number. $P(X=x) = \begin{cases}k, & \text{if } x=0\\\dfrac{k}{2}, & \text{if } x=1 \text{ or } 2\\0, & \text{otherwise}\end{cases}$ On the basis of the above information, match List-I with List-II | LIST-I | | LIST-II | |---|---|---| | A. Value of $k$ | | I. $\dfrac{1}{4}$ | | B. $P(X<2)$ | | II. 0 | | C. $P(X>1)$ | | III. $\dfrac{1}{2}$ | | D. $P(X>2)$ | | IV. $\dfrac{3}{4}$ | Choose the correct answer from the options given below:

For the given five values, 13, 17, 21, 25, 35, the three years moving averages are:

The solution set for the inequality $|5x-3| \le \dfrac{1}{5}$ is:

Match the LIST-I with LIST-II | LIST-I (Term) | | LIST-II (Definition) | |---|---|---| | A. Confidence level | | I. In a confidence interval, the range of values, above and below the sample statistic. | | B. Margin of error | | II. It is the probability of making Type-I error, when null hypothesis is true as an equality. | | C. Level of significance | | III. It involves the use of sample data to calculate a single value of an unknown population parameter. | | D. Point estimation | | IV. It describes the uncertainty of a sampling method. | Choose the correct answer from the options given below:

In a survey question for a sample of 250 individuals, 100 students gave response 'good', 60 gave response 'average' and 90 students gave response as 'extra ordinary'. The point estimate of the proportion in the population who respond 'extra ordinary' is:

Consider an LPP: Maximise $Z = 15x + 10y$ Subject to $2x + y \le 40$ $2x + 3y \le 80$ $x, y \ge 0$ Which of the following are correct? A. The feasible region is bounded. B. The corner points of the feasible region are $(0,0), (40,0), (10,20)$ and $(0,40)$. C. The corner points of the feasible region are $(0,0), (20,0), (10,20)$ and $\left(0, \dfrac{80}{3}\right)$. D. The maximum value of Z is 350. Choose the correct answer from the options given below:

If $y = \sqrt{12^x(3x^2+2)}$, then $\dfrac{dy}{dx}$ will be (consider $\log_e x = \log x$)

The interval in which the function $f(x) = x^2 - 3x + 7$ is increasing, is

Irregular variations in a time series are caused by: A. Floods B. Natural calamities C. Labour strike D. Climate changes Choose the correct answer from the options given below:

A pipe can fill a tank with petrol in 3 hours. Due to leakage, it took $4\dfrac{2}{3}$ hours to fill the tank. How much time will it take for the leakage to drain all the petrol of the full tank?

The units digit in $12^{108}$ is:

If $A = \begin{bmatrix}1 & 2 & 3\\4 & 5 & 6\end{bmatrix}$ and $B = \begin{bmatrix}1 & 2\\3 & 4\\5 & 6\end{bmatrix}$, then $A + B$ is equal to

The ratio of the speed of a motorboat and that of the current of water is 14 : 8. The boat goes a certain distance along with the current in 3 hours 12 minutes. How much time does it take to come back?