List of top Mathematics Questions asked in CUET (UG)

For the differential equation $(x \log x) \, dy = (\log x - y) \, dx$:
(A) Degree of the given differential equation is 1.
(B) It is a homogeneous differential equation.
(C) Solution is $2y \log x + A = (\log x)^2$, where $A$ is an arbitrary constant.
(D) Solution is \(2y \log x + A = \llog(\ln x)\), where $A$ is an arbitrary constant.

The direction cosines of the line which is perpendicular to the lines with direction ratios 1,-2,-2 and 0, 2, 1 are:

$\text{ If } f(x) = \sin x + \frac{1}{2} \cos 2x \text{ in } \left[ 0, \frac{\pi}{2} \right], \text{ then:}$
(A) $f'(x) = \cos x - \sin 2x$
(B)The critical points of the function are $x = \frac{\pi}{6}$ and $x = \frac{\pi}{2}$
(C) The minimum value of the function is 2
(D) The maximum value of the function is $\frac{3}{4}$

$\text{ If } \Delta = \begin{vmatrix} 1 & \cos x & 1 \\ -\cos x & 1 & \cos x \\ -1 & -\cos x & 1 \\ \end{vmatrix} , \text{ then:}$
$(A)\space \Delta = 2(1 - \cos^2 x)$
$(B)\space \Delta = 2(2 - \sin^2 x)$
(C) Minimum value of ∆ is 2
(D) Maximum value of $\Delta$ is 4

$\text{The matrix }$ $\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{bmatrix} \text{ is a:}$
(A) Scalar matrix
(B) Diagonal matrix
(C) Skew-symmetric matrix
(D) Symmetric matrix

For a square matrix } A_{n \times n}:
(A) $|\text{adj } A| = |A|^{n-1}$ 
(B) $|A| = |\text{adj } A|^{n-1}$ 
(C) $A (\text{adj } A) = |A|$ 
(D) $|A^{-1}| = \frac{1}{|A|}$ 
$\text{Choose the \textbf{correct} answer from the options given below:}$

If the random variable X has the following distribution:

X	0	1	2	otherwise
P(X)	k	2k	3k	0

Match List-I with List-II:

Choose the correct answer from the options given below:

$\text{ If the function } f : \mathbb{N} \to \mathbb{N} \text{ is defined as } f(n) = \begin{cases} n - 1, & \text{if } n \text{ is even} \\ n + 1, & \text{if } n \text{ is odd} \end{cases} \text{, then:}$
(A) f is injective
(B) f is into
(C) f is surjective
(D) f is invertible
Choose the correct answer from the options given below:

Match List-I with List-II:

If $\vec{a}, \vec{b}$ and $\vec{c}$ are three vectors such that $\vec{a} + \vec{b} + \vec{c} = 0$, where $\vec{a}$ and $\vec{b}$ are unit vectors and $|\vec{c}| = 2$, then the angle between the vectors $\vec{b}$ and $\vec{c}$ is:

The value of the integral $\int_{\ln 2}^{\ln 3} \frac{e^{2x} - 1}{e^{2x} + 1} \, dx$ is:

If $A$ is a square matrix and $I$ is an identity matrix such that $A^2 = A$, then $A(I - 2A)^3 + 2A^3$ is equal to:

The area of the region bounded by the lines $\frac{x}{7\sqrt{3a}} + \frac{y}{b} = 4$, $x = 0$, and $y = 0$ is:

The rate of change (in cm2/s) of the total surface area of a hemisphere with respect to the radius r at r = 3.