List of top Mathematics Questions asked in CUET (UG)

If \( p, q, r \) are distinct, then the value of \[ \begin{vmatrix} p & p^2 & 1 + p^3 \\ q & q^2 & 1 + q^3 \\ r & r^2 & 1 + r^3 \\ \end{vmatrix} \] is:

For \[ f(x) = \int \frac{e^x}{\sqrt{4 - e^{2x}}} \, dx, \] if the point $\left(0, \frac{\pi}{2}\right)$ satisfies $y = f(x)$, then the constant of integration of the given integral is:

If \( A = \begin{bmatrix} 2 & 3 \\ 1 & -4 \end{bmatrix} \) and \( B = \begin{bmatrix} 1 & -2 \\ -1 & 3 \end{bmatrix} \), then \( B^{-1} A^{-1} \) is equal to:

The domain of \( f(x) = \cos^{-1}(7x) \) is:

For \( a, b > 0 \), if \( P = \begin{bmatrix} 0 & -a \\ 2a & b \end{bmatrix} \) and \( Q = \begin{bmatrix} b & a \\ -b & 0 \end{bmatrix} \) are two matrices such that \( PQ = \begin{bmatrix} 2 & 0 \\ 3 & 8 \end{bmatrix} \), then the value of \( (a + b)^{ab} \) is:

If \[ A = \begin{bmatrix} 2 & 4 \\ x & 2 \end{bmatrix} \] and $A$ is singular, then $x$ is equal to:

If \( P(A) = 0.4 \), \( P(B) = 0.8 \) and \( P(A | B) = 0.6 \), then \( P(A \cup B) \) is:

Let $A$ be a matrix such that $A^2 = I$, where $I$ is an identity matrix. Then $(I + A)^4 - 8A$ is equal to:

Given \[ A = \begin{bmatrix} 0 & \alpha & \beta \\ -\alpha & 0 & \gamma \\ -\beta & -\gamma & 0 \end{bmatrix}, \] the matrix $A$ is a:
(A) square matrix
(B) diagonal matrix
(C) symmetric matrix
(D) skew-symmetric matrix .
Choose the correct answer from the options given below:

Match List-I with List-II.

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If \(P = \begin{bmatrix} 5 & 3 \\ -1 & -2 \end{bmatrix}\) satisfies the equation \(P^2 - 3P - 7I = 0\), where \(I\) is an identity matrix of order 2, then \(P^{-1}\) is:

If \(A = \begin{bmatrix} 3 & 2 \\ -1 & 1 \end{bmatrix}  \quad \text{and} \quad  B = \begin{bmatrix} -1 & 0 \\ 2 & 5 \\ 3 & 4 \end{bmatrix},\)then \((BA)^T\) is equal to:

Two events \(X\) and \(Y\) are such that \(P(X) = \frac{1}{3}\), \(P(Y) = n\), and the probability of occurrence of at least one event is 0.8. If the events are independent, then the value of \(n\) is:

If \( A = \begin{bmatrix} K & 4 \\ 4 & K \end{bmatrix} \) and \( |A^3| = 729 \), then the value of \( K^8 \) is:

Match List-I with List-II:

List-I	List-II
(A) 4î − 2ĵ − 4k̂	(I) A vector perpendicular to both î + 2ĵ + k̂ and 2î + 2ĵ + 3k̂
(B) 4î − 4ĵ + 2k̂	(II) Direction ratios are −2, 1, 2
(C) 2î − 4ĵ + 4k̂	(III) Angle with the vector î − 2ĵ − k̂ is cos⁻¹(1/√6)
(D) 4î − ĵ − 2k̂	(IV) Dot product with −2î + ĵ + 3k̂ is 10

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If the solution of the differential equation \[ \frac{dy}{dx} = \frac{ax + 3}{2y + 5} \] represents a circle, then $a$ is equal to:

The integrating factor of the differential equation \[ (y \log_e y) \frac{dx}{dy} + x = 2 \log_e y \] is:

The value of \( \lambda \) for which the lines \(\frac{2 - x}{3} = \frac{3 - 4y}{5} = \frac{z - 2}{3}\) and  \(\frac{x - 2}{-3} = \frac{2y - 4}{3} = \frac{2 - z}{\lambda}\) are perpendicular is:

The area of the parallelogram, whose adjacent sides are given by the vectors \(\vec{a} = 2\hat{i} - \hat{j} + 5\hat{k}\) and \(\vec{b} = 2\hat{i} + \hat{j} + 2\hat{k}\), is:

The remainder when \(6^{1029}\) is divided by 7 is:

Relation \( R \) on the set \( A = \{1, 2, 3, \ldots, 13, 14\} \) defined as \( R = \{(x, y) : 3x - y = 0\} \) is:

A pair of dice is rolled . If the two numbers appearing on them are different the probability that
Match List-I with List-II
 

LIST-I(EVENT)	LIST-II(PROBABILITY)
(A) The sum of the number is greater than 11	(i) 0
(B) The sum of the number is 4 or less	(ii) 1/15
(C) The sum of the number is 4	(iii) 2/15
(D) The sum of the number is 4	(iv) 3/15

Choose the correct answer from the option given below

Minimize $Z = -50x + 20y$ subject to the constraints: \[ 2x - y \geq -5, \quad 3x + y \geq 3, \quad 2x - 3y \leq 12, \quad x \geq 0, \quad y \geq 0. \] Then which of the following is/are true:
(A) Feasible region is unbounded.
(B) $Z$ has no minimum value.
(C) The minimum value of $Z$ is 100.
(D) The minimum value of $Z$ is -300.

The shortest distance (in units) between the lines \(\frac{1 - x}{1} = \frac{2y - 10}{2} = \frac{z + 1}{1}\) and  \(\frac{x - 3}{-1} = \frac{y - 5}{1} = \frac{z - 0}{1}\) is: