List of top Mathematics Questions asked in CUET (UG)

Find the angle \( \theta \) between the line \( \frac{x-1}{1} = \frac{y+2}{-2} = \frac{z-3}{2} \) and the plane \( 2x - y + 2z = 7 \).
Find the general solution of the following homogeneous differential equation: \[ \frac{dy}{dx} = \frac{x^2 + y^2}{xy} \]
Two independent events \( A \) and \( B \) have individual probabilities of occurring given by \( P(A) = 0.4 \) and \( P(B) = 0.5 \). Find the probability that at least one of these two events occurs.
If \( A \) is a skew-symmetric matrix of order \( 5 \times 5 \), what is the value of its determinant \( |A| \)?
Evaluate the definite integral using standard definite integral properties: \[ \int_{0}^{\frac{\pi}{2}} \frac{\sin^5 x}{\sin^5 x + \cos^5 x} \, dx \]

Calculate the mean (expected value) of a random variable \( X \) given its probability distribution setup below: 

\( X \)123
\( P(X) \)\( 0.2 \)\( 0.5 \)\( 0.3 \)
Simplify the following expression using inverse trigonometric properties: \( \tan\left(\sin^{-1}x + \cos^{-1}x\right) \) where \( |x| \le 1 \).
Find the interval where the function \( f(x) = x^2 - 4x + 6 \) is strictly decreasing.
If a square matrix \( A \) satisfies the condition \( A^T = -A \), then the matrix \( A \) is classified as a:
Evaluate the principal value of the inverse trigonometric expression: \( \sin^{-1}\left(\sin\frac{2\pi}{3}\right) \)
If two vectors \( \vec{a} = 2\hat{i} + \lambda\hat{j} + \hat{k} \) and \( \vec{b} = 4\hat{i} - 2\hat{j} - 2\hat{k} \) are perpendicular to each other, determine the value of the scalar constant \( \lambda \).

A random variable \( X \) has the following probability distribution table: 

\( X \)012
\( P(X) \)\( k \)\( 2k \)\( 3k \)

Find the exact value of the unknown parameter \( k \).

Find the slope of the normal to the curve \( y = 2x^2 + 3\sin x \) at the coordinate point where \( x = 0 \).
If the function \( f(x) \) defined below is continuous at \( x = 2 \), find the value of the constant \( k \): \[ f(x) = \begin{cases} kx^2 & \text{if } x \le 2 3x - 2 & \text{if } x > 2 \end{cases} \]
Find the particular solution of the differential equation \( \frac{dy}{dx} = \frac{y}{x} \) given the initial boundary condition that \( y = 2 \) when \( x = 1 \).
Find the integrating factor (I.F.) for the linear differential equation: \[ \frac{dy}{dx} - y\tan x = e^x \]
In a Linear Programming Problem (LPP), if the objective function to maximize is \( Z = 3x + 4y \) and the corner points of the feasible bounded region are \( (0,0), (4,0), (2,3), \) and \( (0,4) \), find the maximum value of \( Z \).
Let \( A \) be a square matrix of order 3 such that \( |A| = 5 \). Find the value of the determinant of its adjoint matrix, \( |\text{adj}(A)| \).
Find the general solution of the separable differential equation: \[ \frac{dy}{dx} = e^{x-y} + x^2e^{-y} \]
If \( A \) is a square matrix of order 3 such that its determinant value is \( |A| = -2 \), find the value of the scalar-scaled determinant \( |4A| \).
Evaluate the indefinite integral using pattern-based substitution: \[ \int \frac{\ln x - 1}{(\ln x)^2}\,dx \]
Find the area of the region enclosed by the ellipse given parametrically by the coordinates \( x = 2\sin\theta \) and \( y = 3\cos\theta \) where \( 0 \le \theta \le 2\pi \).
Determine the sum of the order and the degree of the following differential equation: \[ \left[1 + \left(\frac{dy}{dx}\right)^2\right]^{frac{3}{2}} = k \frac{d^2y}{dx^2} \]
Find the integrating factor (I.F.) for the linear differential equation: \[ \frac{dy}{dx} + \frac{2x}{1+x^2}y = \frac{1}{(1+x^2)^2} \]
Find the adjoint of \[ A= \begin{pmatrix} 1& 2\\ 3& 4 \end{pmatrix} \]