List of top Questions asked in CUET (UG)

Given: \(y = a + b(x - 2022)\) is the least-squares straight-line trend.

Year (x)20202021202220232024
Profit (Rs. '000) (y)23452
If y = 3e2x + 2e3x, then $\frac{d^2y}{dx^2} + 6y$ is equal to
What is the mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on 1 face?
Which one of the following set of constraints does the given shaded region represent?
If A = $\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$ and B = $\begin{bmatrix} 1 & 0 \\ 1 & 0 \end{bmatrix}$ then the matrix AB is equal to
If \(e^y = \log x\), then which of the following is true?
Let f: R $\rightarrow$ R be defined as f(x) = 10x. Then (Where R is the set of real numbers)
Let A = \{1, 2, 3\}. Then, the number of relations containing (1, 2) and (1, 3), which are reflexive and symmetric but not transitive, is

The probability distribution of a random variable X is given by

X012
P(X)\(1 - 7a^2\)\(\tfrac{1}{2}a + \tfrac{1}{4}\)\(a^2\)


If \(a > 0\), then \(P(0 < X \leq 2)\) is equal to

Let f: R $\rightarrow$ R be defined as f(x) = 10x. Then (Where R is the set of real numbers)
Let A = $\begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}$ and I = $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$. If AT + A = I, then
The absolute maximum value of $y = x^{3} - 3x + 2$, for $0 \leq x \leq 2$, is:
The slope of the normal to the curve y = \(2x^2\) at x = 1 is:
A tub contains 60 litres of milk. From this tub, 6 litres of milk was taken out and replaced with water. This whole process was repeated further two more times. How much milk is there in the tub now?
The solution of the differential equation $\log_e(\frac{dy}{dx}) = 3x + 4y$ is given by
If the maximum value of the function f(x) = $\frac{\log_e x}{x}$, x > 0 occurs at x = a, then a2f''(a) is equal to
If \(A = \begin{bmatrix} 3 & 7 \\ 4 & -2 \end{bmatrix}\), \(X = \begin{bmatrix} \alpha \\ -2 \end{bmatrix}\), \(B = \begin{bmatrix} 7 \\ 32 \end{bmatrix}\) and \(AX = B\), then the value of the \(\alpha\) is
Let $\vec{a} = \hat{i} + 4\hat{j}$, $\vec{b} = 4\hat{j} + \hat{k}$ and $\vec{c} = \hat{i} - 2\hat{k}$. If $\vec{d}$ is a vector perpendicular to both $\vec{a}$ and $\vec{b}$ such that $\vec{c} \cdot \vec{d} = 16$, then $|\vec{d}|$ is equal to
The slope of the normal to the curve y = \(2x^2\) at x = 1 is:
Direction cosines of a vector perpendicular to $ \mathbf{a} = \hat{i} + 2\hat{j} + 3\hat{k} $ and $ \mathbf{b} = 2\hat{i} - \hat{j} + \hat{k} $ are:
If vectors $ \mathbf{u}, \mathbf{v}, $ and $ \mathbf{w} $ satisfy $ \mathbf{u} + \mathbf{v} + \mathbf{w} = 0 $, and $ \mathbf{u} $ and $ \mathbf{v} $ are unit vectors, while $ |\mathbf{w}| = \sqrt{3} $, then the angle between $ \mathbf{v} $ and $ \mathbf{w} $ is:
If A and B are invertible matrices then which of the following statement is NOT correct?
PQ and RS are common tangents to two circles intersecting at A and B. A and B, when produced on both sides, meet the tangents PQ and RS at X and Y, respectively. If \(AB = 3\) cm and \(XY = 5\) cm, then PQ is:
Let \(e^{\alpha y} + e^{\beta y} + \gamma x^2 + \delta \log|x| + C = 0\), where \(C \in \mathbb{R}\) be a particular solution of the differential equation \(x(e^{2y} - 1)dy + (x^2 - 1)e^y dx = 0\) and passes through the point (1, 1). The value of \((\alpha + \beta + \gamma + \delta - C)\) is
If \(B\) is a non-singular \(4 \times 4\) matrix and \(A\) is its adjoint such that \(|A| = 125\), then \(|B|\) is: