CUET Mathematics 2026 14th May Shift 2 PYQs

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