List of top Mathematics Questions asked in CUET (UG)

Find the adjoint of \[ A= \begin{pmatrix} 1& 2\\ 3& 4 \end{pmatrix} \]

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

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

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 \[ x+y\le10,\qquad x,y\ge0 \]

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

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

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

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:

The relation \(R\) on the set of real numbers defined by \[ R=\{(a,b):a\leq b^2\} \] is:
• [(A)] Reflexive
• [(B)] Not symmetric
• [(C)] Neither reflexive nor transitive
• [(D)] Transitive Choose the correct answer from the options given below:

For the L.P.P. Maximize \[ z=10x+6y \] subjected to: \[ 3x+y\leq12 \] \[ 2x+5y\leq34 \] \[ x,y\geq0 \] Then the feasible region represented by system of inequalities is:

If \[ \begin{bmatrix} 2x+1 & 5x \\ 0 & y^2+1 \end{bmatrix} = \begin{bmatrix} x+3 & 10 \\ 0 & 26 \end{bmatrix} \] then the possible values of \(x+y\) are:

If \[ y= \left( x^{\sin x} \right)^{\tan x}, \] then find \[ \dfrac{dy}{dx}. \]