CUET Mathematics 2026 PYQs14 May Shift 2. Free, no login required.

$\int \frac{x^8}{(x^3+1)^{1/3}} dx$ is equal to

The solution of the differential equation $\frac{dy}{dx} = x^2 + x + \frac{1}{x}$ is

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

If A (a, a − b), B (a + b, − b) and C (b, a) are three collinear points, where a, b, c, $\in \mathbb{R}$, then :

If $y=\frac{\log x}{x}$, then $\frac{d^2y}{dx^2}$ is equal to(Consider $\log_e x = \log x$):

The feasible region for a linear programming problem is shown in the figure. Let $Z = 3x - 4y$ be the objective function, then minimum of Z occurs at the point <img src="https://balti.afterboards.in/1HJxDfPzgbvge0L" width="400px"/>

If $(AB)^T = C$, where $A = \begin{bmatrix} x & -1 \\ 2 & 3 \end{bmatrix}$, $B = \begin{bmatrix} 4 & 5 \\ 1 & -2 \end{bmatrix}$ and $C = \begin{bmatrix} 3 & 11 \\ 7 & y \end{bmatrix}$, then $x+y$ is :

Area of the region bounded by the curves $y = x^2$, $x=0$, $x=2$ and $x-axis$ is

The minimum value of $f(x) = e^x + e^{-x}$ is

A pair of coins thrown then Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | Probability of occurance of head on both coins is | I. | $\dfrac{3}{4}$ | | B. | Probability of occurance of at least one tail is | II. | $\dfrac{1}{2}$ | | C. | Probability of occurance of one tail only is | III. | $1$ | | D. | Probability of a tail appears on one coin given that only one coin shows head. | IV. | $\dfrac{1}{4}$ | Choose the correct answer from the options given below:

Particular solution of the differential equation $dy + 2xy^2 dx = 0$, given that $y=1$, when $x=0$, is

If $\int_0^1 \frac{1-x}{1+x} dx = A\log 2 + B$, then the value of A and B are

If $a,b,c$ are the roots of $x^3+px+q=0$, then the value of $\begin{vmatrix} a & b & c \\ b & c & a \\ c & a & b \end{vmatrix}$ is equal to

If $A = \begin{bmatrix} 0 & x & x \\ 2y & y & -y \\ z & -z & z \end{bmatrix}$ such that $AA^T=2I$ (where I is an identity matrix of order 3), then which of the following are True? A. $x^2=1, 3y^2=2$ B. $6y^2=4, 2z^2=3$ C. $9z^2=6, x^2=1$ D. $x^2:y^2:z^2 = 3:1:2$ Choose the correct answer from the options given below:

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

If $\vec a, \vec b, \vec c$ are mutually perpendicular vectors of equal magnitude, the angle between $\vec a+\vec b+\vec c$ and $\vec a$ is

If A is a 3x3 matrix then: Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | $\vert adj A\vert$ | I. | $\vert A\vert^{-1}$ | | B. | $\vert A.adj A\vert$ | II. | $\vert A\vert$ | | C. | $\vert A^{-1}\vert$ | III. | $\vert A\vert^2$ | | D. | $\vert A^{-1}.adj A\vert$ | IV. | $\vert A\vert^3$ | Choose the correct answer from the options given below:

Four cards are drawn successively without replacement from a deck of 52 playing cards. The probability that all the four cards are king is:

If $x\sqrt{1+y}+y\sqrt{1+x}=0, x\neq y$, then $\frac{dy}{dx}$ is equal to

A bag contains 5 white, 4 black and 3 red balls. Which of the following statements are True? A. The probability of drawing three red balls one by one without replacement is $\frac{1}{220}$ B. One by one three balls drawn without replacement then probability that third ball is red is $\frac{1}{4}$ C. The probability of drawing 2 white balls one by one without replacement is $\frac{3}{4}$ D. One by one 3 balls are drawn without replacement then probability that third ball is red is $\frac{3}{4}$ Choose the correct answer from the options given below:

If $\vec a=\hat i+\hat j+2\hat k$ and $\vec b=2\hat i+\hat j+2\hat k$, then the unit vector in the direction of $2\vec a-\vec b$ is equal to :

$\int \frac{\sqrt{1+x^2}}{x^4} dx$ is equal to :

Match the LIST-I with LIST-II | LIST-I | | LIST-II | | |---|---|---|---| | A. | The degree of the differential equation $\left(\frac{d^3y}{dx^3}\right)^4+\left(\frac{d^2y}{dx^2}\right)^5+\left(\frac{dy}{dx}\right)+y=0$ | I. | 0 | | B. | The order of the differential equation $\left(\frac{d^3y}{dx^3}\right)^4+\left(\frac{d^2y}{dx^2}\right)^5+\left(\frac{dy}{dx}\right)+y^2=0$ | II. | 4 | | C. | The number of arbitrary constants in the general solution of a differential equation of second order is | III. | 3 | | D. | The number of arbitrary constants in a particular solution of a differential equation of third order is | IV. | 2 | Choose the correct answer from the options given below:

If $f(x)=\begin{cases}\frac{\sin(a-b)x}{x}, & x<0\\ 2a+b, & x=0\\ \frac{-\tan 12x}{bx}, & x>0\end{cases}$, $(b>0)$ is continuous at $x=0$, then

Consider a determinant $\Delta=\begin{vmatrix}3a & -a+b & -a+c\\ -b+a & 3b & -b+c\\ -c+a & -c+b & 3c\end{vmatrix}$, then Match the LIST-I with LIST-II | | LIST-I (Value of $a, b, c$) | | LIST-II (Value of $\Delta$) | |---|---|---|---| | A. | $a = 0, b = 0, c = 1$ | I. | $27$ | | B. | $a = 0, b = 1, c = 1$ | II. | $0$ | | C. | $a = 0, b = 2, c = -1$ | III. | $6$ | | D. | $a = 1, b = 1, c = 1$ | IV. | $-6$ | Choose the correct answer from the options given below:

Match the LIST-I with LIST-II | | LIST-I (Definite integrals) | | LIST-II (Value) | |---|---|---|---| | A. | $\displaystyle\int_{-6}^{6} \vert x \vert \, dx$ | I. | $1$ | | B. | $\displaystyle\int_{-\pi/2}^{\pi/2} \sin^{2017} x \, dx$ | II. | $36$ | | C. | $\displaystyle\int_{0}^{\pi/4} \cos x \, dx$ | III. | $0$ | | D. | $\displaystyle\int_{0}^{2} \dfrac{\sqrt{x}}{\sqrt{x}+\sqrt{2-x}} \, dx$ | IV. | $\dfrac{1}{\sqrt{2}}$ | Choose the correct answer from the options given below:

If $\vec a=2\hat i-3\hat j+\hat k, \vec b=-\hat i+\hat k, \vec c=2\hat j-\hat k$ are three vectors, then area of the parallelogram having diagonals $(\vec a+\vec b)$ and $(\vec b+\vec c)$ is

If $A=\begin{bmatrix}a & 1 & c\\ b & 2 & 1\\ 2 & 1 & c\end{bmatrix}$ is a singular matrix, then

The probability of drawing a one-hundred rupee currency from two boxes one of which contain 3 fifty-rupee currency and 2 one-hundred rupee and other box contain 2 fifty-rupee currency and 3 one-hundred rupee currency notes is-

A pair of unbaised dice is thrown together and sum of the numbers appearing is observed. The probability that the sum of numbers on the dice was 10, given that the observed sum was at least 9, is:

The shortest distance between the lines whose vector equations are $\vec r=(\hat i+2\hat j+3\hat k)+\lambda(2\hat i+3\hat j+4\hat k)$ and $\vec r=(2\hat i+4\hat j+5\hat k)+\mu(4\hat i+6\hat j+8\hat k)$ is:

In a sphere the rate of change of volume with respect to(w.r.t) time is

If the coordinates of the points A, B, C, D be (1, 2, 3), (4, 5, 7), (−4, 3, −6) and (2, 9, 2) respectively, then the angle between the lines AB and CD is

The maximum value of the function $f(x)=\sin x(1+\cos x)$ in the internal $[0,\pi]$ is

If $A=\begin{bmatrix}a & 0\\0 & 0\end{bmatrix}$ and $B=\begin{bmatrix}0 & 0\\0 & b\end{bmatrix}$ then the matrix $A^3B^3$ is:

For a linear programming problem, the maximum value of the objective function $z=2x+3y$ subject to constraints: $x-y\le-1, -x+y\le0, x,y\ge0$ is

If C is an arbitrary constant, then Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | $\displaystyle\int a^x \, dx$ | I. | $\sin^{-1}\dfrac{x}{a} + C$ | | B. | $\displaystyle\int \dfrac{dx}{\sqrt{a^2 - x^2}}$ | II. | $\log_e \vert x + \sqrt{x^2 - a^2} \vert + C$ | | C. | $\displaystyle\int \dfrac{dx}{\sqrt{a^2 + x^2}}$ | III. | $\dfrac{a^x}{\log_e a} + C$ | | D. | $\displaystyle\int \dfrac{dx}{\sqrt{x^2 - a^2}}$ | IV. | $\log_e \vert x + \sqrt{a^2 + x^2} \vert + C$ | Choose the correct answer from the options given below:

For the function $f(x)=x^4-2x^2+5, x\in R$, then which of the following statements are True? A. $f(x)$ is increasing on $(-\infty,-1)$ B. $f(x)$ is decreasing on $(-\infty,-1)$ C. $f(x)$ is increasing on $(-1,0)\cup(1,\infty)$ D. $f(x)$ is decreasing on $(1,\infty)$ Choose the correct answer from the options given below:

The general solution of the differintial equation : $x\frac{dy}{dx}-ay=1(a\neq0)$ is

If $\vec a\times\vec b=\vec a\times\vec c$ and $\vec a\neq\vec 0$, then which of the following is/are TRUE? A. $\vec b=\vec c$ B. $\vec b+\vec c=\vec 0$ C. $\vec b=\vec c+\lambda\vec a$ for some scalar λ D. $\vec b+\vec c=\lambda\vec a$ for some scalar λ Choose the correct answer from the options given below:

Match the LIST-I with LIST-II | | LIST-I (Functions) | | LIST-II (Principal Values) | |---|---|---|---| | A. | $\sin^{-1}\left(-\dfrac{1}{2}\right) + \cos^{-1}\left(-\dfrac{1}{2}\right)$ | I. | $-\dfrac{\pi}{3}$ | | B. | $\cos^{-1}\left(\dfrac{1}{2}\right) + 2\sin^{-1}\left(\dfrac{1}{2}\right)$ | II. | $\dfrac{3\pi}{4}$ | | C. | $\tan^{-1}\sqrt{3} - \sec^{-1}(-2)$ | III. | $\dfrac{\pi}{2}$ | | D. | $\cos^{-1}\left(-\dfrac{1}{\sqrt{2}}\right)$ | IV. | $\dfrac{2\pi}{3}$ | Choose the correct answer from the options given below:

The area bounded by the line $y=x$, the $x-axis$ and the ordinates $x=-1$ and $x=2$ is

The image of the point (1, 6, 3) with respect to the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ is

In a linear programming problem, the corner points of the feasible region, determined by the system of linear inequalities are (0, 0), (5, 0), (3, 4) and (0, 5). Let $z=5x+qy, q>0$ be the objective function. For what value of q the maximum value of z occurs at both (3, 4) and (0, 5)?

If $y=(\sqrt x)^\pi$ such that $\frac{dy}{dx}=\frac{\pi}{a}y^{\pi+b}$ where $a,b\in\mathbb R$ then:

Consider the system of equations $x+y+z=2, 2x+3y+2z=5, x+2y+\lambda z=\mu$ then which of the following statements are TRUE? A. The system of equations has unique solution if $\lambda=2$ and $\mu\in\mathbb R$ (set of real number) B. The system of equations is inconsistent if $\lambda=1$ and $\mu=1$ C. The system of equations is consistent if $\lambda=1$ and $\mu=1$ D. The system of equations is consistent if $\lambda=1$ and $\mu=3$ Choose the correct answer from the options given below:

Let N be the set of natural numbers and R be the set of all real numbers. If function $f:N\to R$ defined by $f(x)=4x^2+12x+15$, then $f:N\to range(f)$ is

The area of the region bounded by the curve $y=x^3, y=8$ and $x=0$ is equal to :

Given the relation $R=\{(1,2),(2,3)\}$ on a set $A=\{1,2,3\}$, then which of following statements are TRUE? A. Minimum number of ordered pairs are added to R so that enlarged relation is reflexive is 3 B. Minimum number of ordered pairs are added to R so that enlarged relation is symmetric is 2 C. Minimum number of ordered pairs are added to R so that enlarged relation is an equivalence relation is 7 D. Minimum number of ordered pair are added to R so that enlarged relation is an equivalence relation is 6. Choose the correct answer from the options given below:

Which of the following statement are true? A. The angle between the vectors $2\hat i+\hat j+3\hat k$ and $3\hat i-2\hat k$ is $\frac{\pi}{2}$ B. If $\vec a$ and $\vec b$ are two non-zero vectors, then projection of $\vec b$ on $\vec a$ is $\frac{\vec a\cdot\vec b}{|\vec a|}$ C. The unit vector normal to both vectors $\vec a=\hat i-\hat j-\hat k$ and $\vec b=\hat i+\hat j+\hat k$ is $\frac{1}{\sqrt2}(-\hat j+\hat k)$ D. The area of triangle formed by adjacent sides represented by vectors $\vec a=3\hat i+4\hat j$ and $\vec b=-5\hat i+7\hat j$ is 41 sq. units Choose the correct answer from the options given below:

If $R(x)$ is the total revenue received and $C(x)$ is the total cost incurred in the production of x units of a commodity, then the profit function $P(x)$

If X has a Poisson distribution such that $2P(X=1)=P(X=2)$, then which of the following are correct? A. The mean of X is 4 B. The mean of X is 2 C. $P(X=2)=\frac{8}{e^4}$ D. $P(X=3)=\frac{32}{e^4}$ Choose the correct answer from the options given below:

The second order derivative of the function $y=\log(4x^3+6)$ with respect to 'x' will be:

A man rows 8 km upstream in 4 hours and 16 km downstream in 4 hours . What is the speed of the current?

Match the LIST-I with LIST-II | | LIST-I (Differential equation) | | LIST-II (Degree) | |---|---|---|---| | A. | $\left(\dfrac{dy}{dx}\right)^2 + \dfrac{1}{\dfrac{dy}{dx}} = 5$ | I. | $2$ | | B. | $\dfrac{d^3y}{dx^3} = \left\{3 + \left(\dfrac{dy}{dx}\right)^2\right\}^{3/2}$ | II. | $4$ | | C. | $\dfrac{d^2y}{dx^2} = \left(\dfrac{dy}{dx}\right)^{5/4}$ | III. | $1$ | | D. | $y\dfrac{d^2x}{dy^2} = y^2 + 1$ | IV. | $3$ | Choose the correct answer from the options given below:

In a hypothesis test, the probability of making the wrong decision when the null hypothesis is true is called

At what rate converted semi-annually will the present value of perpetuity of ₹750/- payable at the end of each 6 months be ₹ 25000?(where p.a. denotes per annum)

Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | In a L.P.P the objective function is always | I. | Finite | | B. | Feasible region for an L.P.P is always a | II. | Convex set | | C. | In an L.P.P having bounded feasible region, the maximum value of the objective function $z = ax + by$ is always | III. | Linear | | D. | Feasible region is the set of points which satisfy | IV. | All the given constraints | Choose the correct answer from the options given below:

If A is a skew symmetric matrix, then $A^2$ is

Two pipes, A and B, can fill a cistern in 10 minutes and 12 minutes respectively. Pipe C can empty the cistern in 15 minutes. If all 3 pipes are opened together, how long will it take to fill the cistern completely?

In a random experiment, a collection of trials is called Bernoulli trials if A. The number of trials is infinite. B. The trials are independent of each other. C. Each trial has exactly two outcomes, defined as success and failure. D. The probability of success will vary in each trial. Choose the correct answer from the options given below:

If $A=\begin{bmatrix}0 & 1\\0 & 0\end{bmatrix}$, then $A^{1999}$ is equal to

If the objective function $z=10(x-7y+190)$ and the corner points of the bounded feasible region are A(0,4), B(0,5), C(3,5), D(5,3), E(5,0), F(4,0), then the minimum value of z will be:

Given that the mean of the normal variate X is 10 and the standard deviation is 2, then what will be the z-score of the data point 16 ?

The components of time-series are A. Seasonal component B. Reverse component C. Cyclic component D. Irregular component Choose the correct answer from the options given below:

The 3-year moving averages for the loan (in lakh ₹) issued by a finance company for startups in different cities of India based on the values given below will be: | Year | 2019 | 2020 | 2021 | 2022 | 2023 | 2024 | |---|---|---|---|---|---|---| | Loan amount | 25 | 20 | 18 | 13 | 23 | 12 |

In a kilometer race, A can beat B by 100 m. In a race of 400 m, B can beat C by 40 m. By how many meters will A beat C in a race of 500 m?

If today is Friday, then what will be the day after 129 days?

$\int_1^4 x^3\log x\, dx$ is equal to:

In what ratio must sugar at ₹12 per kg be mixed with sugar at ₹20 per kg so that the mixture is worth ₹15 per kg?

Amit made an investment of ₹27,000 in a no-fee fund for 3 years. At the end of the third year, the value of the investment increased to ₹64,000. The compound annual growth rate (CAGR) percentage of the investment is

A machine costing ₹16,00,000 is expected to have a useful life of 15 years and a final scrap value of ₹1,00,000. Which of the following statements are correct ? A. The annual depreciation is ₹50,000. B. The annual depreciation is ₹1,00,000. C. The book value at the end of the sixth year is ₹9,00,000. D. The book value at the end of the sixth year is ₹10,00,000. Choose the correct answer from the options given below:

The area of the region bounded by curves $y=x^2$ and line $y=4$ is:

A and B are square matrices of order 3 each such that $|A|=3, |B|=2$, then the value of $|4AB|$ will be?

The solution set of the given inequation $\frac{2x+3}{x-1}<4 (x\neq1)$ is:

The present value of an immediate perpetuity of ₹ R payable at the end of every year at the rate of i per period per rupee is given by:

Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | In a binomial distribution, if $n = 16$, $p = 0.75$, then the mean is | I. | $4$ | | B. | In a binomial distribution, if $n = 25$, $p = \dfrac{1}{5}$, then variance is | II. | $32$ | | C. | In a binomial distribution, the mean is 8 and the variance is 6, then the number of trials is | III. | $18$ | | D. | If the mean and variance of a binomial distribution are 6 and 4 respectively, then the number of trials is | IV. | $12$ | Choose the correct answer from the options given below:

The relation between 'marginal cost (MC)' and 'average cost (AC)' of producing 'x' units of a product is

The effective rate $r_e$ corresponding to the nominal rate r compounded continuously is

Five students are selected at random from a school and their weights are found to be 50, 51, 53, 54 and 62. The point estimation of the population mean is:

Harish takes a loan of ₹6,00,000 at an interest of 10% per annum compounded annually for a period of 5 years. His EMI using a flat rate method is:

If A is a non-singular square matrix of order n, then which of the following are TRUE ? A. $|adj A|=|A|^{n-1}$ B. $|adj A|=|A|^{n-2}$ C. $|adj (adj A)|=|A|^{(n-2)^2}$ D. $|adj (adj A)|=|A|^{(n-1)^2}$ Choose the correct answer from the options given below:

Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | A matrix which is both symmetric and skew symmetric | I. | symmetric matrix | | B. | All positive integral powers of a symmetric matrix | II. | unit matrix | | C. | Positive odd integral powers of a skew-symmetric matrix | III. | null matrix | | D. | A square matrix $A = [a_{ij}]_{n\times n}$ with $a_{ij} = \begin{cases}0, & \forall\, i \neq j \\ 1, & \forall\, i = j\end{cases}$ | IV. | skew-symmetric matrix | Choose the correct answer from the options given below:

Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | Simple random sampling | I. | to get a team of 7 students with AI knowledge, selecting one of the students who will bring 6 more students. | | B. | Stratified sampling | II. | Asking colleagues to complete a survey for research work | | C. | Convenience sampling | III. | Selection of 100 employees from a company with 500 employees keeping gender balance in mind | | D. | Snowball sampling | IV. | Selection of 50 guests randomly from a party | Choose the correct answer from the options given below:

For the function $f(x)=2x^3-21x^2+36x-5$, which of the following statements are correct ? A. $x=2$ is a point of local maxima. B. $x=6$ is a point of local minima. C. The local maximum value is 12. D. The local maximum value is –94. Choose the correct answer from the options given below: