List of top Questions asked in CUET (UG)- 2026

If \( A = \begin{bmatrix} \cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha \end{bmatrix} \) then \( A^2 - (2 \cos \alpha) A \) is equal to: (Where I is identity matrix of order 2)

A line passes through (2, 1, 3) and (1, 2, -1), then
(A) Equation is \( \frac{x-2}{1} = \frac{y-1}{1} = \frac{z-3}{4} \)
(B) Equation is \( \frac{x+2}{-1} = \frac{y+1}{1} = \frac{z+3}{4} \)
(C) Equation is \( \vec{r} = 2\vec{i} + \vec{j} + 3\vec{k} + \lambda(\vec{i} - \vec{j} + 4\vec{k}) \)
(D) Equation is \( \frac{x-1}{1} = \frac{y-2}{-1} = \frac{z+1}{4} \)
Choose the correct answer:

If a machine is correctly set up, it produces 80% acceptable items. If it is incorrectly set up, it produces only 30% acceptable items. From the past experience it was known that 90% of the setups are correctly done. If after a certain setup, the machine produces 2 acceptable items then the probability that the machine was correctly set up, is:

The integral of \( \int_{-2}^{2} x^4 \, dx \) denominator \( (1+5x^2) \) is:

The solution set of the inequation \( 2x + 3y > 12 \) is

The area bounded by the lines \( y = 1 + |x + 1| \), \( x = -3 \), \( x = 3 \) and \( y = 0 \) is

If \( A = \begin{bmatrix} 1 & 2 & -1 \\ -1 & 1 & 2 \\ 2 & -1 & 1 \end{bmatrix} \) then \( |adj(adj A)| \) is equal to

If A and B are two independent events and P(A) = 1/2, P(B) = 1/3, then Match List-I with List-II

Solution of \( \frac{x^2 - 4x + 7}{x^2 - 7x + 12} \le \frac{2}{3} \) is/are:
Choose the correct answer:

The maximum value of the linear programming problem, max. \( z = 3x + 4y \) subject to the constraints: \( x - y \le -1 \), \( x \ge y \), \( x, y \ge 0 \) is

If A, B and C are square matrices of order n x n, then which of the following are TRUE? [Where $A^T$ is transpose of matrix A]
(A) \( (A + B)^T = A^T + B^T \)
(B) \( (AB)^T = A^T B^T \)
(C) \( (ABC)^T = C^T B^T A^T \)
(D) \( (BA)^T = A^T B^T \)
Choose the correct answer:

The integral \( \int \frac{\cos 5x + \cos 4x}{1 - 2\cos 3x} \, dx \) is equal to (where C is an arbitrary constant):

General solution of the differential equation \( (x + 2y^3) dy = y dx \) is (Where C is an arbitrary constant)

If \( \int \frac{1 + \cos\theta}{\tan 2\theta - \cot 2\theta} d\theta = \lambda \cos\theta + c \), then \( \lambda \) is equal to (where c is constant of integration)

Let $\mathbb{N}, \mathbb{Z}$ and $\mathbb{R}$ be the set of natural numbers, integers and real numbers respectively, $[\cdot]$ denotes the greatest integer function. Match List-I with List-II:}

If $A_1, A_2, A_3$ are independent events such that $P(A_i)=\frac{1}{i+1}$, then probability that none occur is:}

If \( \vec{a} \) and \( \vec{b} \) are two vectors such that \( |\vec{a}| = 2 \), \( |\vec{b}| = 1 \) and \( \vec{a} \cdot \vec{b} = \sqrt{3} \) then the angle between \( 2\vec{b} \) and \( -\vec{a} \) is:

Let $R = \{(1,1),(2,2),(3,3),(1,2)\}$ be a relation on $\{1,2,3\}$. The minimum number of elements to be added so that $R$ is an equivalence relation is:}

Let $\vec{a}$ and $\vec{b}$ be two unit vectors such that $\vec{a}+\vec{b}$ is also a unit vector. Then which of the following are TRUE?} (A) $|\vec{a}-\vec{b}|=0$
(B) $|\vec{a}-\vec{b}|=\sqrt{3}$
(C) Angle between $\vec{a}$ and $\vec{b}=\frac{2\pi}{3}$
(D) Angle between $\vec{a}$ and $\vec{b}=\frac{\pi}{3}$

The determinant \( \begin{vmatrix} \lambda & \sin\theta & \cos\theta \\ -\sin\theta & -\lambda & 1 \cos\theta & 1 & \lambda \end{vmatrix} \) is equal to:

If $\vec{a}=\hat{i}+\hat{j}-\hat{k}$ and $\vec{b}=\hat{i}-2\hat{j}+\hat{k}$ then Match List-I with List-II:}

If $A=\begin{bmatrix} a & b \\ b & a \end{bmatrix}$ and $A^{2}=\begin{bmatrix} \alpha & \beta \\ \beta & a \end{bmatrix}$, then $(a-b)$ is:

Area bounded by the curve $y=x^{3}$ and line $y=4x$ is:

If vertices A and C of a $\Delta ABC$ lie along a line and the line segment AC has length 3, then the area of $\Delta ABC$ is:

If the lines $x=ay+b, z=cy+d$ and $x=a'y+b', z=c'y+d'$ are perpendicular, then: