List of top Mathematics Questions asked in CUET (UG)

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

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

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)

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

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 $\vec{b}=\frac{\pi}{3}$

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 $\mathbb{N}, \mathbb{Z}$ 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 \( \vec{a} \) 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:

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:}

In a sphere, the rate of change of volume is:

Match List-I (Inverse Trigonometric function Principal values) with List-II:

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:}

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

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

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:

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:

Match List-I (Matrix expressions) with List-II (Properties).

If $x=t^{2}, y=t^{3}$, then $\frac{d^{2}y}{dx^{2}}$ is:

If $\int_{0}^{a}\sqrt{x}dx = \frac{4a}{3}$, then $\int_{a}^{a+1}x\,dx$ is:

If $a_{ij}=\begin{cases} 0,& i\ne j\\ 2i-j,& i=j \end{cases}$ then matrix A is:

If a unit vector makes equal acute angles with the coordinate axes, then the projection of this vector on $-5\mathbf{i}+7\mathbf{j}-\mathbf{k}$ is:

Area of the region bounded by the curves $x=y^{2},\; y=-1,\; y=2$ and y-axis is: