List of top Mathematics Questions asked in CUET (UG)

If a square matrix \( A \) satisfies the condition \( A^T = -A \), then the matrix \( A \) is classified as a:

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 \( \lambda \).

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 \[ A= \begin{pmatrix} 1& 2\\ 3& 4 \end{pmatrix} \]

Find the derivative of \[ f(x)=e^{x^2} \]

Is \[ f(x)=|x-2| \] differentiable at \(x=2\)?

Consider a \(3\times3\) matrix \(A\). If \[ \operatorname{adj}(A)= \begin{pmatrix} 2& 0& 0\\ 0& 2& 0\\ 0& 0& 2 \end{pmatrix} \] find \(\det(A)\).

Find the shortest distance between the lines \[ \vec r= \hat i+2\hat j+\hat k+\lambda(\hat i-\hat j+\hat k) \] and \[ \vec r= 2\hat i-\hat j-\hat k+\mu(2\hat i+\hat j+2\hat k) \]

Find the local maximum of \[ f(x)=x^3-3x+2 \]

Find the domain of \[ f(x)=\sin^{-1}(2x-1) \]

Probability that the second ball is red, given the first was blue (3 red and 5 blue balls, without replacement).

Identify the order and degree of the differential equation: \[ \left(\frac{d^3y}{dx^3}\right)^2 + 4\left(\frac{dy}{dx}\right)^4 + y = \sin(x) \]

Maximize \[ Z=3x+4y \] subject to \[ x+y\le10,\qquad x,y\ge0 \]