List of top Mathematics Questions asked in CUET (UG)

If a random variable \(X\) has probability distribution \[ P(X=x)=kx, \] \[ x=1,2,3,4, \] then the value of \(k\) is:

The differential equation of the family of curves \[ y=ce^{2x} \] is:

If \[ \int_{0}^{1}(3x^2+2x+1)\,dx=k, \] then the value of \(k\) is:

If \[ z=\frac{1+i}{1-i}, \] then \(z^8\) equals:

The number of 5-digit numbers that can be formed using the digits \(1,2,3,4,5,6\) without repetition and divisible by \(5\) is:

Find the distance from the point \[ (1,1,1) \] to the plane \[ x+y+z=3. \]

Calculate \[ \int e^x\,dx. \]

If \[ P(A)=0.5, \qquad P(B)=0.3, \qquad P(A\cap B)=0.1, \] find \[ P(A|B). \]

Find the rate of change of the area of a circle with respect to its radius \(r\) when \[ r=3\text{ cm}. \]

Find \[ \frac{dy}{dx} \] if \[ y=\log(\sin x). \]

Find the value of \[ \cos\left(\sin^{-1}\left(\frac{1}{2}\right)\right). \]

Is \[ f(x)=x^2 \] continuous at \(x=0\)?

Minimize \[ Z=2x+3y \] subject to \[ x+y\ge5, \qquad x,y\ge0. \]

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

Find the angle between the vectors \[ \vec{a}=\hat{i}+\hat{j}-\hat{k} \] and \[ \vec{b}=\hat{i}-\hat{j}+\hat{k}. \]

Let \(A\) and \(B\) be two \(3\times3\) matrices such that \[ A^2-4A+3I=O \] and \[ B=A^{-1}+2A. \] Find the determinant of \(B\) if \(\det(A)=3\).

Given a matrix \(A\) of order \(3\times3\). If \[ |A|=3 \] then the value of \[ |A(\operatorname{adj}A)| \] is:

Find the local maximum point of the function \[ f(x)=-x^3+3x+1 \]

Let \( R \) be a relation on \( \{1,2,3\} \) defined by \[ R=\{(1,1),(2,2),(3,3),(1,2)\} \] Identify the properties satisfied by \(R\).

For vectors \( \vec{a}=3\hat{i}-\hat{j}+2\hat{k} \) and \( \vec{b}=\hat{i}+2\hat{j}-\hat{k} \), find the scalar projection of \( \vec{a} \) onto \( \vec{b} \).

Find the domain of the function \( f(x)=\sin^{-1(3x-1) \).}

A bag has 4 red and 6 black balls. Two balls are drawn without replacement. What is the probability that the second is red given the first was black?

Maximize \( Z = 5x + 3y \) subject to \( x + y \le 6 \) and \( x, y \ge 0 \). Where does the maximum value occur?

For the linear differential equation \[ \frac{dy}{dx} + \frac{2}{x}y = x^2 \] calculate the integrating factor (I.F.).

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