List of top Mathematics Questions asked in CUET (UG)

The solution of initial value problem: \(\frac{dy}{dx}=e^{3x+4y};\ y(0)=-\frac{1}{4}\) is

Match the LIST-I with LIST-II

	LIST-I Inequality		LIST-II Solution Space
A.	\(2x+3y \geq 6\)	I.	half plane contains the origin, also points on the line \(2x+3y=6\)
B.	\(2x+3y \leq 6\)	II.	half plane contains the origin but not points on the line \(2x+3y=6\)
C.	\(2x+3y > 6\)	III.	half plane not contains the origin but contains points on the line \(2x+3y=6\)
D.	\(2x+3y < 6\)	IV.	half plane neither contains the origin nor contains points on the line \(2x+3y=6\)

Choose the correct answer from the options given below:

Area of the region bounded by the lines \(|x|+|y|=1,\ x\geq 0,\ y\geq 0\) is

The solution of the differential equation \(\frac{dy}{dx}=\frac{x}{y}\) represents a family of

The order and degree of the differential equation \(\sqrt{1+\left(\frac{dy}{dx}\right)^{2}}=\left(\frac{d^{2}y}{dx^{2}}\right)^{\frac{1}{3}}\) are

If \(2f(x)+f\left(\frac{1}{x}\right)=\frac{1}{x}-5,\ x\neq 0\), then \(\displaystyle\int_{1}^{2}f(x)dx\) is equal to:
(consider \(\log_e x = \log x\))

The function \(f(x) = \dfrac{x}{\log x}\) is increasing in the interval
(consider \(\log_e x = \log x\))

If \(A\) is a square matrix of order \(3 \times 3\), and \(|\text{adj } A| = 25\), then the value of \(|2A|\) is

The minimum value of \(e^x + e^{-x}\) is

\(\displaystyle\int e^{x}\left(\log x+\frac{1}{x^{2}}\right)dx\) is equal to
(consider \(\log_e x = \log x\))

If \(y = \sqrt{\dfrac{1-x}{1+x}}\), then the value of \((1 - x^2)\dfrac{dy}{dx} + y\) is

If \(AB = A\) and \(BA = B\), where \(A\) and \(B\) are square matrices of same order, then

If \(\Delta = \begin{vmatrix} 1 & x & x^2 \\ x^2 & 1 & x \\ x & x^2 & 1 \end{vmatrix} = (1 + ax^3)^b\), then which of the following statements are TRUE?
A. \(a = -1\) and \(b = 2\)
B. \(x = 1\) is a multiple root of \(\Delta = 0\)
C. \(x = 1\) is a simple root of \(\Delta = 0\)
D. \(x = 3\) is a simple root of \(\Delta = 0\)
Choose the correct answer from the options given below:

\(A\) is any matrix, defined by \(A = [a_{ij}]_{3\times 3}\), where \(a_{ij} = |i - j|\), then which of the following statements are true ?
A. \(A\) is symmetric matrix.
B. \(A\) is skew-symmetric matrix.
C. \(A\) is diagonal matrix.
D. \(A\) is non singular matrix.
Choose the correct answer from the options given below:

Let $A$ be a $3 \times 3$ matrix such that $A^2 = I$. If $\det(A) = -1$ and the sum of eigenvalues is $1$, find the set of eigenvalues of $A$.

Find the total number of distinct binary relations that can be defined over a set \( A \) containing exactly 3 elements.

The function \[ f(x)=\sum_{k=1}^{7}(x-k)^2 \] has a minimum value at \(x=a\). Then, \(a\) is equal to:

Evaluate the principal value of the inverse trigonometric expression: \( \sin^{-1}\left(\sin\frac{2\pi}{3}\right) \)

Determine the exact expression for the Integrating Factor (I.F.) of the following first-order linear differential equation: \( \frac{dy}{dx} - y\tan x = e^x \)

Let \(A\) be a non-singular \(3\times3\) matrix satisfying \[ A^3-6A^2+11A-6I=O. \] If \[ B=A^2-5A+7I, \] then find \(\det(B)\) given that \(\det(A)=6\).

If \[ \sin^{-1}x+\cos^{-1}x=\theta \] find \(\theta\).

If \( A=\begin{bmatrix}2 & 3 \\ 5 & -2\end{bmatrix} \), then:

Find the total area of the region bounded between the curve \( y = x^3 \), the x-axis, and the vertical lines \( x = -1 \) and \( x = 1 \).