CUET Mathematics 2026 12th May Shift 2 PYQs

The area of region bounded by the curves $4y = x^3, y = 0$ and $x = 4$ in the first quadrant is :

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

If $x$ is real, then the minimum value of $x^2 - 8x + 25$ is

If $y = \dfrac{\log_e x}{x}$, then $\dfrac{d^2y}{dx^2}$ is :

If $A$ is a $3\times 3$ matrix with $|A|=4$, then $|4A|$ is equal to :

If $A$ is a non-singular matrix of order $n$, then $adj(adj\ A)$ is equal to :

If the matrix $\begin{bmatrix} 0 & -1 & 3x \\ 1 & y & -5 \\ -6 & 5 & 0 \end{bmatrix}$ is skew symmetric, then the value of $x+y$ is

If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}$, then $A^2 - 5A$ is equal to : (where $I_2$ is identity matrix of order 2)

A die is thrown once then, Match **List-I** with **List-II** | List-I | List-II | |---|---| | (A) Probability of getting odd number | (I) $\dfrac{1}{3}$ | | (B) Probability of getting number more than 4 | (II) $\dfrac{2}{3}$ | | (C) Probability of getting number less than or equal to 4 | (III) $\dfrac{1}{2}$ | | (D) Probability of getting number 2 | (IV) $\dfrac{1}{6}$ | Choose the **correct** answer from the options given below:

The function $f(x) = x^3 + 2x^2 - 1$ is (A) increasing in $\left(\dfrac{-4}{3}, 0\right)$ (B) decreasing in $\left(\dfrac{-4}{3}, 0\right)$ (C) increasing in $\left(-\infty, \dfrac{-4}{3}\right)$ (D) increasing in $(0, \infty)$ Choose the **correct** answer from the options given below:

The solution of the differential equation $\dfrac{dy}{dx} = x^2y^2$ with $y = 1$ at $x = 0$ is

The general solution of the differential equation $\dfrac{dy}{dx} = 1+x+y+xy$ is: (where $C$ is an arbitrary constant) (A) $1+y = x+\dfrac{x^2}{2}+C$ (B) $\log_e|1+y|^2 = x^2+2x+C$ (C) $\log_e|1-y| = x-\dfrac{x^2}{2}+C$ (D) $\log_e|1+y| = x+\dfrac{x^2}{2}+C$ Choose the **correct** answer from the options given below:

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

If $\displaystyle\int_0^{40} \dfrac{dx}{2x+1} = \log_e k$, then the value of $k$ is :

In the linear programming problem maximize $Z = 4x+3y$ subject to the constraints $x+y \ge 8$, $3x+5y \le 15$, $x\ge0, y\ge0$, the feasible region has

A cylinder with height 'h' and radius of base is 'r' which is open at the top having a given outer surface area, then volume of the cylinder is maximum if

The system of equations in 3 variables $x, y$ and $z$ as $x+y=5$, $y+az=3$, $x+by=8$ has a unique solution if the value of $a$ and $b$ are (A) $a=1, b=1$ (B) $a=0, b=1$ (C) $a \in (-\infty,0)$ and $b\neq1$ (D) $a\neq0$ and $b\in(3,4)$ Choose the **correct** answer from the options given below:

The general solution of the differential equation $ydx + (x-y^3)dy = 0$ is :

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

If $\vec{a}.\vec{b} = \vec{a}.\vec{c}$ and $\vec{a}\times\vec{b} = \vec{a}\times\vec{c}$, $\vec{a}\neq\vec{0}$, then

Let $A$ be set of all real numbers and $R$ be a relation on $A$ defined by $R=\{(a,b): 1+ab>0\}$, then relation $R$ is

A bag contains 4 balls. Let E be an event in which two balls are drawn at random and found to be white, then Match **List-I** with **List-II** | List-I | List-II | |---|---| | (A) Probability that all balls are white | (I) $\dfrac{1}{6}$ | | (B) Probability of drawing 2 white ball at random given that there are 3 white ball | (II) $\dfrac{3}{5}$ | | (C) P(E) | (III) $\dfrac{1}{2}$ | | (D) Probability of drawing 2 white ball at random given that there is only 2 white ball | (IV) $\dfrac{5}{9}$ | Choose the **correct** answer from the options given below:

Let $\vec{a}=\hat{i}-\hat{j}$, $\vec{b}=3\hat{j}-\hat{k}$ and $\vec{c}=7\hat{i}-\hat{k}$. Then a vector $\vec{d}$ which is perpendicular to both $\vec{a}$ and $\vec{b}$ and $\vec{c}.\vec{d}=1$ is

Match **List-I** with **List-II** | List-I | List-II | |---|---| | **Indefinite integral** | **Solution (where 'c' is an arbitrary constant)** | | (A) $\displaystyle\int \sqrt{x^2-a^2} \, dx$ | (I) $\dfrac{1}{a}\tan^{-1}\dfrac{x}{a} + c$ | | (B) $\displaystyle\int \dfrac{1}{x^2-a^2} \, dx$ | (II) $\dfrac{x}{2}\sqrt{x^2+a^2} + \dfrac{a^2}{2}\log\left[x+\sqrt{x^2+a^2}\right] + c$ | | (C) $\displaystyle\int \dfrac{1}{x^2+a^2} \, dx$ | (III) $\dfrac{x}{2}\sqrt{x^2-a^2} - \dfrac{a^2}{2}\log\left[x+\sqrt{x^2-a^2}\right] + c$ | | (D) $\displaystyle\int \sqrt{x^2+a^2} \, dx$ | (IV) $\dfrac{1}{2a}\log\left\vert \dfrac{x-a}{x+a} \right\vert + C$ | Choose the **correct** answer from the options given below:

If the points $A(-1,3,2)$, $B(-4,2,-2)$ and $C(5,5,\lambda)$ are collinear, then value of $\lambda$ is :

Two vectors $\vec{a}$ and $\vec{b}$ are inclined at angle $\theta=60°$ such that $|\vec{a}|=1$, $|\vec{b}|=2$, then $\left|(\vec{a}+3\vec{b})\times(3\vec{a}-\vec{b})\right|^2$ is equal to

The feasible region for an LPP is shown in the given figure. Let $Z=3x+4y$ be the objective function. Then which of the following is/are TRUE? <img src="https://balti.afterboards.in/keY7zvrtj9K8Dlg" width="400px"/> (A) The minimum value of Z is 156 (B) The minimum value of Z is 152 (C) The maximum value of Z is 196 (D) Neither minimum nor maximum value of Z exists Choose the **correct** answer from the options given below:

If angle between the lines $\dfrac{x-1}{\propto} = \dfrac{y+2}{-5} = \dfrac{z+\frac{7}{3}}{\beta}$ and $x=z, y=0$ is $\dfrac{\pi}{4}$, then

The values of $x, y, z$ and $w$ such that $\begin{bmatrix} x-y & 2z+w \\ 2x-y & 2x+w \end{bmatrix} = \begin{bmatrix} 5 & 3 \\ 12 & 15 \end{bmatrix}$ are given by

Match **List-I** with **List-II** | List-I (Functions) | List-II (Range, principal value) | |---|---| | (A) $\sin^{-1}x$ | (I) $[0,\pi]-\left\{\dfrac{\pi}{2}\right\}$ | | (B) $\tan^{-1}x$ | (II) $\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right]-\{0\}$ | | (C) $cosec^{-1}x$ | (III) $\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right]$ | | (D) $\sec^{-1}x$ | (IV) $\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right)$ | Choose the **correct** answer from the options given below:

From a lot of 10 items containing 3 defectives, a sample of 4 items is drawn at random. Let X denotes the number of defective items in the sample. If the sample is drawn randomly, then Match **List-I** with **List-II** (P(X) denotes the probability of occurence of X) | List-I | List-II | |---|---| | (A) P (X = 0) | (I) $\dfrac{^3C_3\times{}^7C_1}{^{10}C_4}$ | | (B) P (X = 1) | (II) $\dfrac{^7C_4\times{}^3C_0}{^{10}C_4}$ | | (C) P (X = 2) | (III) $\dfrac{^3C_1\times{}^7C_3}{^{10}C_4}$ | | (D) P (X = 3) | (IV) $\dfrac{^3C_2\times{}^7C_2}{^{10}C_4}$ | Choose the **correct** answer from the options given below:

Let $A=R-\{2\}$ and $B=R-\{1\}$ and a function $f:A\to B$ defined by $f(x)=\dfrac{x-1}{x-2}\ \forall x\in A$, then the function $f(x)$ is :

If $x^2+y^2 = t+\dfrac{1}{t}$ and $x^4+y^4=t^2+\dfrac{1}{t^2}$, then $\dfrac{dy}{dx}$ is equal to

If $[2\ \ x\ \ 3]\begin{bmatrix}-1 & 0 & -1\\ -1 & 1 & 0\\ 0 & 1 & 1\end{bmatrix}\begin{bmatrix}x\\0\\-1\end{bmatrix}=[-4]$, then the value(/s) of $x$ is

For a given line L: $\dfrac{x}{2}=\dfrac{y+1}{3}=\dfrac{-z-3}{-5}$, which of the following is/are True ? (A) The direction ratio of line L is (2, 3, -5) (B) The perpendicular distance of the point (1, 1, 3) on the line L is $\sqrt{3}$ (C) The foot of perpendicular from the point (1, 1, 3) on line L is (2, 2, 1) (D) The image of point (1, 1, 3) with respect to line L is (3, 3, 1) Choose the **correct** answer from the options given below:

If $x=a(\theta+\sin\theta)$, $y=a(1-\cos\theta)$, then $\dfrac{d^2y}{dx^2}=$

The linear constraints for which the shaded region in the figure are: <img src="https://balti.afterboards.in/v0QsIyGIrwouZMF" width="500px"/>

The position vectors of the points A and B are $\vec{a}=2\hat{i}-3\hat{j}+2\hat{k}$ and $\vec{b}=2\hat{i}+3\hat{j}+\hat{k}$ respectively, then area of triangle OAB is:

The maximum value of $f(x)=\dfrac{1}{3(x^2-x+1)}$ is :

The area of region $\{(x,y): 9x^2+16y^2\le144, x\ge0, y\ge0\}$ is-

If $A=[a_{ij}]_{3\times3}$ and $a_{ij}=2i-j$, then Match **List-I** with **List-II** | List-I | List-II | |---|---| | (A) $a_{21}+a_{32}$ | (I) 0 | | (B) $\lvert A\rvert$ | (II) 19 | | (C) Number of the elements in A | (III) 7 | | (D) $a_{22}.a_{31}+a_{21}.a_{33}$ | (IV) 9 | Choose the **correct** answer from the options given below:

For the function $f(x)=ax^3-9ax^2+9x+3, x\in R$, then which of the following statements are True? (A) $f'(x)=3[ax^2-6ax+3]$ (B) It is increasing for $a\in\left[0,\dfrac{1}{3}\right]\ \forall x\in R$ (C) It is increasing for $a\in(-\infty,0)\ \forall x\in R$ (D) It is increasing for $\forall a\in R$ Choose the **correct** answer from the options given below:

Suppose that A and B are independent events with $P(A)=\dfrac{1}{7}$ and $P(B)=\dfrac{3}{7}$, then $P(A\cap B)$ is

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

If $\begin{vmatrix}1 & 1 & 1\\ c & b-x & a\\ b & a & c-x\end{vmatrix}=0$, then $x$ is equal to

Function $f(x)=[x]$, greatest integer function is (A) Continuous at $x=2.5$ (B) Continuous at $x=1$ (C) Differentiable at $x=2$ (D) Differentiable at $x=-1.2$ Choose the **correct** answer from the options given below:

If $\begin{vmatrix}3 & x\\ x & 1\end{vmatrix}=\begin{vmatrix}3 & 2\\ 4 & 1\end{vmatrix}$, then value of $x$ is/are (A) $x=2$ (B) $x=-2$ (C) $x=2\sqrt2$ (D) $x=-2\sqrt2$ Choose the **correct** answer from the options given below:

If $\displaystyle\int\dfrac{x^3\,dx}{\sqrt{1+x^2}} = a(1+x^2)^{3/2}+b\sqrt{1+x^2}+c$, where 'C' is an arbitrary constant, then the value of $a$ and $b$ are

Given that the events A and B are mutually exclusive such that $P(A)=\dfrac{1}{2}$, $P(A\cup B)=\dfrac{2}{3}$ and $P(B)=p$, then the value of $p$ is:

The value of $\displaystyle\int_{-1}^{1}|x^4-x|\,dx$ is equal to: