List of top Mathematics Questions asked in CUET (UG)

The value of \( \lambda \) for which the following system of equations has unique solution: \[ \lambda x+3y-z=1 \] \[ x+2y+z=2 \] \[ -\lambda x+y+2z=-1 \] are:

If \( A=\begin{bmatrix}2 & 3 \\ 5 & -2\end{bmatrix} \), then:

Evaluate: \( \begin{vmatrix} 1 & 2 & 3 \\ 0 & 1 & 4 \\ 5 & 6 & 0 \end{vmatrix} \)

If \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \), then \( A^{-1} \) is:

If \( X + Y = \begin{pmatrix} 5 & 3 \\ 0 & 7 \end{pmatrix} \) and \( X - Y = \begin{pmatrix} 7 & 1 2 & 3 \end{pmatrix} \). Then X and Y are

If $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$, then $\text{adj}(A)$ is:

Find the maximum value of $f(x) = -x^2 + 4x + 1$

For any square matrix $A$, $A \cdot \text{adj}(A) =$

Evaluate: $\int_0^{\pi/2}\sin x \, dx$

The feasible region of an LPP is always:

Evaluate: $\int \frac{1}{1 + x^2} \, dx$

A die is thrown twice. The probability of getting a sum equal to 8 is:

A bag contains 5 red and 3 blue balls. Two balls are drawn at random without replacement. The probability that both are red is:

Evaluate: $\int x \cdot e^x \, dx$

If $y = \log(\sin x) + \log(\cos x)$, then $\frac{dy}{dx}$ is:

Find the total number of distinct binary relations that can be defined over a set \( A \) containing exactly 3 elements.

Find the equation of the normal to the curve \( y = x^2 - x \) at the coordinate point position \( (1, 0) \).

Evaluate the value of the following definite integral using standard calculus integrations: \( \int_{0}^{1} x e^x \, dx \)

An unbiased coin is tossed twice. Let event \( A \) represent getting a head on the first toss, and event \( B \) represent getting a head on the second toss. Determine the mathematical relationship between events \( A \) and \( B \).

If \( A \) is a square matrix of order 3 such that its determinant is \( |A| = 3 \), calculate the value of the scalar matrix determinant represented by \( |2A| \).

Find the maximum value of the linear objective optimization function \[ Z = 4x + y \] evaluated over a feasible region bounded by the corner vertices: \[ (0,0), \ (3,0), \ (2,3), \ \text{and} \ (0,4). \]

Find the open interval across which the cubic polynomial function \( f(x) = 2x^3 - 3x^2 - 36x + 7 \) is classified as strictly decreasing.

Find the shortest distance between the two parallel straight lines whose vector position equations are given by: \[ \vec{r} = (\hat{i} + 2\hat{j} - 4\hat{k}) + \lambda(2\hat{i} + 3\hat{j} + 6\hat{k}) \] \[ \vec{r} = (3\hat{i} + 3\hat{j} - 5\hat{k}) + \mu(2\hat{i} + 3\hat{j} + 6\hat{k}) \]

If \( A \) is a non-singular square matrix of order \( 3 \times 3 \) such that its determinant is \( |A| = 5 \), find the absolute value of the determinant of its adjoint matrix, represented as \( |\text{adj}(A)| \).

Determine the exact expression for the Integrating Factor (I.F.) of the following first-order linear differential equation: \( \frac{dy}{dx} - y\tan x = e^x \)