CUET Mathematics 2026 26th May Shift 2 PYQs

Match the LIST-I with LIST-II | | LIST-I<br>Differential equation | | LIST-II<br>Order and Degree | |---|---|---|---| | A. | $\left(\dfrac{dy}{dx}\right)^2 + 3y\left(\dfrac{d^2y}{dx^2}\right) = 0$ | I. | $1,1$ | | B. | $\sqrt{1-\left(\dfrac{dy}{dx}\right)^2} = a\left(\dfrac{d^2y}{dx^2}\right)^{1/3}$ | II. | $1,2$ | | C. | $y = \dfrac{dy}{dx} + \dfrac{5}{(dy/dx)}$ | III. | $2,1$ | | D. | $\sqrt{1-y^2}\,dx + \sqrt{1-x^2}\,dy = 0$ | IV. | $2,2$ | Choose the correct answer from the options given below:

The area of the region bounded by the line $3x - y + 2 = 0$, the $x-axis$ and the ordinates $x = -1$ and $x = 1$ is:

The value of $\displaystyle\int_0^1 xe^{x^2}\,dx$ is equal to :

$\displaystyle\int x\sqrt{x^2-1}\,dx$ is equal to : ( where C is an arbitrary constant )

For the function $f(x) = 3x^4 + 4x^3 - 12x^2 + 12$, then Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | $x = 0$ | I. | Local minimum value of $f(x)$ | | B. | $x = -2$ | II. | Local maximum of value of $f(x)$ | | C. | $f(0)$ | III. | Point of local minima | | D. | $f(1)$ | IV. | Point of local maxima | Choose the correct answer from the options given below:

The solution of the differential equation $\dfrac{dy}{dx} = \dfrac{x+2}{3-y}, (y \neq 3), y(0) = 0$ represents

If A and B are symmetric matrices of the same order then which of the following statements are correct? A. AB is symmetric matrix B. AB - BA is skew symmetric matrix C. $B^TAB$ is symmetric matrix D. $A - A^T$ is skew symmetric matrix Choose the correct answer from the options given below:

If $e^y(x+1)=1$, then

A green and a yellow dice are rolled in order, then the probability that a sum greater than 9 is

General solution of the differential equation $x(xdy - ydx) = y\,dx$ is :(where c is an arbitrary constant)

If $xy\log_e(x+y) = 1$, then $\dfrac{dy}{dx} =$

If the feasible region (shaded portion)of a LPP is as shown in the graph, then max $z = 50x + 15y$ is: <img src="https://balti.afterboards.in/otjxKl9u8ocOuNi" width="400px"/>

If $A = \dfrac{1}{9}\begin{bmatrix} -8 & 1 & 4 \\ 4 & 4 & 7 \\ 1 & -8 & 4 \end{bmatrix}$, then (Where $A^{-1}$ and $A^T$ represent inverse and transpose of matrix $A$ respectively)

If a matrix $A = \begin{bmatrix} x+3 & 3 \\ 2x+1 & 5 \end{bmatrix}$ is singular , then the value of $x$ will be

If $[2x \quad 4]\begin{bmatrix} x \\ -8 \end{bmatrix} = [0]$, then the value of $x$ is/are A. $-4$ B. $4$ C. $16$ D. $-16$ Choose the correct answer from the options given below:

The area of the region $\{(x,y): x^2 \le y \le x\}$ is:

Given that the two numbers appearing on throwing 2 dice are different, the probability of the event " sum of number on the dice is 4 " is

If $y = (\log_e x)^{\log_e x}$, then $\dfrac{dy}{dx}$ is equal to:

Value of $\displaystyle\int_{-1}^{1} \dfrac{x^5+|x|+1}{x^2+2|x|+1}\,dx$ is equal to :

If the points $P(3,\mu,6), Q(-1,-1,2)$ and $R(2,8,5)$ are collinear, then the value of '$\mu$' is

Match the LIST-I with LIST-II | | LIST-I<br>Equation of line | | LIST-II<br>Point on the line, direction ratios of the line | |---|---|---|---| | A. | $\dfrac{x-5}{3} = \dfrac{y-2}{2} = \dfrac{z+4}{-8}$ | I. | $(-3, -2, 8), \langle 5, 2, -4 \rangle$ | | B. | $\dfrac{x+5}{3} = \dfrac{y+2}{2} = \dfrac{z-4}{-8}$ | II. | $(3, 2, -8), \langle 5, 2, -4 \rangle$ | | C. | $\dfrac{x-3}{5} = \dfrac{y-2}{2} = \dfrac{z+8}{-4}$ | III. | $(-5, -2, 4), \langle 3, 2, -8 \rangle$ | | D. | $\dfrac{x+3}{5} = \dfrac{y+2}{2} = \dfrac{z-8}{-4}$ | IV. | $(5, 2, -4), \langle 3, 2, -8 \rangle$ | Choose the correct answer from the options given below:

Let $A = \{ 1,2,3 \}$, then Match List-I with List-II | LIST-I | LIST-II | |---|---| | A. $R_1 = \{(1,1), (2,2), (3,3), (1,2)\}$ | I. Symmetric but neither reflexive nor transitive | | B. $R_2 = \{(1,1), (3,3), (1,3), (3,1)\}$ | II. Reflexive and transitive but not symmetric | | C. $R_3 = \{(1,1), (2,2), (3,3), (1,2), (2,1), (2,3), (3,2)\}$ | III. Symmetric and transitive but not reflexive | | D. $R_4 = \{(2,2), (3,3), (1,2), (2,1)\}$ | IV. Reflexive and symmetric but not transitive | Choose the correct answer from the options given below:

If $\hat{i}, \hat{j}, \hat{k}$ represents unit vectors along x, y, z axes respectively, then Match List-I with List-II | LIST-I | | LIST-II | |---|---|---| | A. | $\hat{i}.\hat{i}$ | I. 0 | | B. | $\hat{i}.\hat{j}$ | II. $\vec{0}$ | | C. | $\hat{i} \times \hat{j}$ | III. 1 | | D. | $\hat{i} \times \hat{i}$ | IV. $\hat{k}$ | Choose the correct answer from the options given below:

Which one of the region I, II, III, IV is represented by the constraints $x + 3y \le 60, x + y \ge 10, x \le y, x \ge 0, y \ge 0$ <img src="https://balti.afterboards.in/7RrSxYZnoQ28sxW" width="400px"/>

$\displaystyle\int \dfrac{1-\sin x}{\cos^2 x}\,dx$ is equal to: (where $c$ is an arbitrary constant)

If the order and degree of the differential equation $y + \dfrac{dy}{dx} = \int y\,dx$ are m and n respectively, then (m - n) is equal to

Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | The range of $\sin^{-1} x$ | I. | $[-1, 1]$ | | B. | Domain of $\cos^{-1} x$ | II. | $(-\infty, \infty)$ | | C. | The range of $\tan^{-1} x$ | III. | $\left[-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right]$ | | D. | Domain of $\tan^{-1} x$ | IV. | $\left(-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right)$ | Choose the correct answer from the options given below:

If A is a square matrix of order 4 and $|adj\,A| = 8$, then $|A| =$

General solution of the differential equation $(1+x^2)dy + 2xy\,dx = \cot x\,dx$ is: (where $C$ is an arbitrary constant)

Which of the following statements are correct ? A. If the product of 2 non-zero square matrices is a zero matrix, then either A is singular or B is singular B. If A is a non singular matrix , then $|A^{-1}| = \dfrac{1}{|A|}$ C. If A is an invertible square matrix then $adj\,A^T = \dfrac{1}{adj\,A}$ D. If A and B are invertible matrices then $(AB)^{-1} = B^{-1}A^{-1}$ Choose the correct answer from the options given below:

$\displaystyle\int \dfrac{1}{e^x-1}\,dx$ is equal to: (where C is an arbitrary constant)

The value/s of '$\lambda$' for which the system of equations $\lambda x + 3y - z = 1$ $x + 2y + z = 2$ $-\lambda x + y + 2z = -1$ has unique solution is/are: (where $R$ is set of real numbers)

The value of $\lambda$ so that the lines $\dfrac{1-x}{3} = \dfrac{7y-14}{2\lambda} = \dfrac{z-3}{2}$ and $\dfrac{7-7x}{3\lambda} = \dfrac{y-5}{1} = \dfrac{6-z}{5}$ are at right angles is:

Bag I contains 3 red and 4 black balls while Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be red. then the probability that it was drawn from Bag I is

If shortest distance between the lines $\vec{r} = \hat{i} - \hat{j} + \lambda(2\hat{i}+\hat{k})$ and $\vec{r} = 2\hat{i} - \hat{j} + \mu(\hat{i}-\hat{j}-\hat{k})$ is $\dfrac{\sqrt{14}}{14}m$ units, the value of $m$ is

Let $\vec{a},\vec{b},\vec{c}$ are three vectors such that $|\vec{a}|=3, |\vec{b}|=2, |\vec{c}|=1$. If the projection of $\vec{b}$ along $\vec{c}$ is equal to the projection of $\vec{a}$ along $\vec{c}$ and $\vec{b} \perp \vec{a}$ , then the value of $|2\vec{a}-2\vec{b}+3\vec{c}|$ is equal to

If $f\left(x+\dfrac{1}{x}\right) = x^2 + \dfrac{1}{x^2}$ then $f(x) =$

The matrix $\begin{bmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{bmatrix}$ is

Let $f(x) = |3-x| + (3+x)$ be a function, then which of the following statements are TRUE? A. $f(x)$ is continuous at $x=3$ B. $f(x)$ is continuous at $x=-3$ C. $f(x)$ is differentiable at $x=3$ D. $f(x)$ is differentiable at $x=-3$ Choose the correct answer from the options given below:

For any linear programming problem the feasible region is shaded region as given below, then constraints are: <img src="https://balti.afterboards.in/eDjlSn0UZGoOxjt" width="400px"/>

Area (in sq. units) of the triangle with vertices A (1,1,1) B (1,2,3) and C (2,3,1) is:

If $\begin{vmatrix} 1 & x & x^2 \\ x^2 & 1 & x \\ x & x^2 & 1 \end{vmatrix} = (x^{\lambda}-1)^{\mu}$ then the value of $\lambda$ and $\mu$ are given by

For the function $f(x) = |\sin 4x + 3|$, then which of the following statements are correct ? A. Minimum value of $f(x)$ is 2 B. There is no minimum value C. Maximum value of $f(x)$ is 4 D. Maximum value of $f(x)$ is 3 Choose the correct answer from the options given below:

If $\vec{a} = 5\hat{i} - \hat{j} - 3\hat{k}$ and $\vec{b} = \hat{i} - 3\hat{j} - 5\hat{k}$ then $(\vec{a}+\vec{b}).(\vec{a}-\vec{b})$ is equal to:

If the area(in square units) bounded by the curves $y^2 = 4x$ and $y = x$ is $\dfrac{k^3}{3}$, then the value of $k$ is:

A committee of 4 students is selected at random from a group consisting of 8 girls and 4 boys. Given that there is at least one boy in the committee, the probability that there are exactly 2 boys in the committee is

For a biased die, the probabilities of outcomes are given as under. $P(1)=P(2)=\dfrac{2}{10}, P(3)=P(5)=P(6)=\dfrac{1}{10}, P(4)=\dfrac{3}{10}$. The die is thrown two times. Let A and B be events defined as A is getting same number each time and B is getting a total of 10 or more on die , then which one of the following is TRUE?

Consider the function $f(x) = x^4 - 2x^2$, then which of the following are TRUE? A. $f(x)$ is increasing on $(-1,0)$ B. $f(x)$ is decreasing on $(0,1)$ C. $f(x)$ is increasing on $(-\infty,-1)$ D. $f(x)$ is decreasing on $(1,\infty)$ Choose the correct answer from the options given below:

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

The volume of a cube is increasing at the rate 9 $cm^3/s$. How fast is the surface area increasing when the length of an edge is 10 cm ?

If A is a square matrix of order 3 such that $|A| = 3$, then the value of $|adj\,A| + |adj\,(adj\,A)|$ is

The least non-negative remainder when $5^{48}$ is divided by 7 is

A random variable $X$ has the following probability distribution: | X | 0 | 1 | 2 | 3 | 4 | |---|---|---|---|---|---| | P(X) | 0 | $\dfrac{k}{2}$ | $\dfrac{3k}{2}$ | $\dfrac{k}{3}$ | $2k$ | Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | Value of $k$ | I. | $\dfrac{7}{13}$ | | B. | Value of $P(X \leq 3)$ | II. | $\dfrac{3}{26}$ | | C. | Value of $P(X > 1)$ | III. | $\dfrac{23}{26}$ | | D. | Value of $P(X < 2)$ | IV. | $\dfrac{3}{13}$ | Choose the correct answer from the options given below:

If the supply curve is $p = \sqrt{9+x}$ and the quantity sold in market is 7 units, then the producer's surplus will be

If $\dfrac{dy}{dx} = e^{x-y} + x^2e^{-y}$, then the solution of the differential equation will be:-

A traffic police officer records the number of motorcycle riders that use a particular lane on a highway. He records that an average of 2.5 motorcycle riders use the lane every hour. Given that the number of motorcycles that use the particular lane follows a Poisson distribution. The probability that less than 2 motorcycle riders will use the lane within an hour will be:- (Use $e^{2.5} = 12.2$)

Factors affecting the calculation of the annual depreciation of an asset are A. Body shape of the asset B. Original cost of the asset C. Scrap value of the asset D. Useful life of the asset Choose the correct answer from the options given below:

If $A = \begin{bmatrix} 9 & 7 & 5 \\ 6 & 4 & 2 \\ 1 & 3 & 8 \end{bmatrix}$, then (cofactor of $a_{13}$ - cofactor of $a_{32}$ )will be equal to :

Two pipes A and B fill a tank in 12 minutes and 15 minutes respectively. If both the pipes are opened simultaneously and pipe A is closed after 3 minutes, then how much more time will it take to fill the tank with pipe B?

In what ratio must a grocer mix two varieties of cumin seeds worth ₹ 60 per kg and ₹ 65 per kg respectively, so that by selling the mixture at ₹ 68.20 per kg, he may gain 10%?

In a random experiment, a collection of trials is called Bernoulli trials then which of the following statements are TRUE? A. The number of trials is infinite. B. Each trial has exactly two outcomes defined as success and failure. C. The trials are dependent by nature. D. The probability of success remains the same in each trial. Choose the correct answer from the options given below:

$\displaystyle\int \dfrac{x^0}{x-\sqrt{x^2-1}}\,dx$ is equal to :

Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | Column matrix | I. | $\begin{bmatrix}1 & 2 & 3\end{bmatrix}$ | | B. | Row matrix | II. | $\begin{bmatrix}1 & 0 & 0\\ 0 & 2 & 0\\ 0 & 0 & 3\end{bmatrix}$ | | C. | Diagonal matrix | III. | $\begin{bmatrix}1\\ 2\\ 3\end{bmatrix}$ | | D. | Scalar matrix | IV. | $\begin{bmatrix}2 & 0 & 0\\ 0 & 2 & 0\\ 0 & 0 & 2\end{bmatrix}$ | Choose the correct answer from the options given below:

Consider the following data: | Year($x_i$) | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | |---|---|---|---|---|---|---|---| | Profit (₹ 000)($y_i$) | 26 | 26 | 44 | 42 | 108 | 120 | 166 | Using method of least squares, the trend value for year 2004 will be

Ravi row to a place 45km distant and back in 20 hours. He finds that he can row 12km with stream in the same time as 4km against the stream ,then the speed of the stream is:

The normal distribution is called as standard normal distribution when

If $A = \begin{bmatrix} 1 & 0 \\ -1 & 7 \end{bmatrix}$ is a matrix such that $A^2 = 8A + KI$,where $I$ is an identity matrix of order 2 then value of $K$ is :

Consider an LPP: Maximize $Z = 5x + y$ Subject to $x + 3y \le 12$ $3x + y \le 12$ and $x,y \ge 0$ then which of the following statements are TRUE ? A. The corner points of the bounded feasible region are (0,0), (4,0), (3,3) and (0,4). B. Maximum value of $z$ occurs at (3,3). C. Maximum value of $z$ occurs at (4,0). D. The maximum value of $z$ is 20. Choose the correct answer from the options given below:

If A is a skew-symmetric matrix then, the matrix $B^TAB$ is:-

If a manufacturer's total cost 'C' is given by $C = \dfrac{x^2}{25} + 3x$, then the marginal cost when 7 units are produced will be:-

Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | Book value of an asset at a given date | I. | Original value of the asset - scrap value of the asset | | B. | Useful life of an asset | II. | The value of a depreciable asset at the end of its useful life. | | C. | Total depreciation | III. | An accounting estimate of the number of years an asset is likely to remain in service for the purpose of cost-effective revenue generation. | | D. | Residual value | IV. | Original value of the asset - accumulated depreciation at that time | Choose the correct answer from the options given below:

If the sample size is 45, then the degree of freedom is equal to

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

Harish invested ₹ 40,000 in a no-fee fund. After one year, the value of the fund rose to ₹ 60,000 then the nominal rate of return on the investment is

Which of the following statement(s) mentioned below do/does not specify the concept of time series analysis:- A. Time series analysis comprises methods for analysing time series data in order to extract meaningful statistics and other characteristics of the data. B. Time series analysis provides good forecasts or predictions of further values of the time series. C. The time series analysis does not derive conclusions after arranging the time series in a systematic manner. D. The measurement analysis and study of components of time series is called time series analysis. Choose the correct answer from the options given below:

Match the terms mentioned List I with the definitions mentioned in List II. | LIST-I | LIST-II | |---|---| | A. Confidence interval | I. In a hypothesis test, the probability of making wrong decision when the null hypothesis is true. | | B. Margin of error | II. The number of independent pieces of information on which an approximation is based. | | C. Significance level | III. A range of values, derived from sample statistic which is likely to contain the value of an unknown population parameter. | | D. Degree of freedom | IV. In a confidence interval, the range of values, above and below the sample statistic. | Choose the correct answer from the options given below:

Let us denotes R=Periodic payment,i=interest per period per rupee ,n=number of payment,P=pricipal payment Match the terms in List I with their respective formula in List II. | LIST-I | LIST-II | |---|---| | A. The amount in a sinking fund after $n$ period with payment at end | I. $\dfrac{Pi(1+i)^n}{(1+i)^n - 1}$ | | B. EMI by using flat rate method | II. $P\left(i + \dfrac{1}{n}\right)$ | | C. The amount in a sinking fund after $n$ period with payment at beginning | III. $R\left\{\dfrac{(1+i)^n - 1}{i}\right\}$ | | D. EMI by using reducing balance payment rate method | IV. $R(1+i)\left[\dfrac{(1+i)^n - 1}{i}\right]$ | Choose the correct answer from the options given below:

From a drum filled with 48 litres of soya milk, 12 litres of soya milk was taken out and replaced by an equal amount of cow milk. The process was further repeated twice. How much soya milk is left in the drum now?

If the objective function for an LPP is $Z = 2x + 5y$ and the corner points of the bounded feasible region are (0, 0), (5, 0) , $\left(\dfrac{8}{5},\dfrac{6}{5}\right)$ and (0, 2) then the maximum value of $z$ occurs at

$\displaystyle\int \sqrt[3]{x}(x^3+4x^2+7)\,dx$ is equal to-

Which of the following are the true? A. The cost of Rs.7200 , 8% stock at Rs.90 is Rs.6480. B. The cost of Rs.4500 , 8.5% stock at 4% premium is Rs.4680. C. The cost of Rs.6400 , 10% stock at 15% discount is Rs.5440. D. The cost of Rs.7200 , 8% stock at Rs.90 is Rs.5961.60. Choose the correct answer from the options given below:

If $y = x^3\log(3x^2+6)$, then $\dfrac{dy}{dx} =$

For the following data from the simple random sample: 4, 7, 9, 8, 11, 15, the point estimate of the population mean will be

In a 10 km race, A, B and C each running at uniform speed get the gold, silver and bronze medals respectively. If A beats B by 1 km and B beats C by 1 km, then by how many meters does A beat C?

Chintan has borrowed ₹ 5,00,000 from a bank to purchase a car and decided to repay the loan in equal monthly installments in 10 years. If bank charges interest at 6% per annum compounded monthly, the EMI on reducing balance method will be : (Given $(1.005)^{120} = 1.82$)