List of top Mathematics Questions asked in CUET (UG)

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

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

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

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

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

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 \[ f(x)=x^3-3x+2 \]

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

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

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

The sum of order and degree of the differential equation \[ y=x\frac{dy}{dx}+2\sqrt{1+\left(\frac{dy}{dx}\right)^2} \] is:

Find the area of the region bounded by the curve \( y^2 = x \) and the line \( x = 4 \):

Find the interval in which the function \( f(x) = 2x^3 - 3x^2 - 36x + 7 \) is strictly increasing:

A bag contains \( 5 \) red and \( 4 \) black balls. Two balls are drawn at random one after the other without replacement. What is the conditional probability that the second ball drawn is red, given that the first ball drawn was black?

Find the general solution of the differential equation: \( \frac{dy}{dx} + \frac{y}{x} = x^2 \)

Find the value of the composite inverse trigonometric expression: \( \cot^{-1}\left[2\cos\left(2\sin^{-1}\frac{1}{2}\right)\right] \)

If \( A \) is a square matrix of order \( 3 \) such that \( |2(\text{adj}\,A)| = 288 \), then the possible value of the determinant \( |A| \) is:

Evaluate the indefinite integral: \( \int \frac{x^2+1}{x^4+1}\,dx \)

Let \( A \) be a non-singular \( 3 \times 3 \) matrix satisfying the equation \( A^3 - 6A^2 + 11A - 6I = O \). If \( B = A^2 - 5A + 7I \) and \( \det(A) = 6 \), then the value of \( \det(B) \) is equal to:

Let \(X\) denote the number of heads in a simultaneous toss of three coins, then \[ P(0<X<3) \] is:

The area of region bounded by the curve \[ y^2=4ax \] and the straight line \[ x=2a,\qquad a>0 \] in the first quadrant is:

The function \[ f:\mathbb R\to\mathbb R,\qquad f(x)=|x| \] (\(\mathbb R\) is the set of real numbers) is: