List of top Mathematics Questions asked in CUET (UG)

If \( A \), \( B \), and \( C \) are three singular matrices given by \[ A = \begin{bmatrix} 1 & 4 \\ 3 & 2 \end{bmatrix}, \quad B = \begin{bmatrix} 3b & 5 \\ a & 2 \end{bmatrix}, \quad \text{and} \quad C = \begin{bmatrix} a + b + c & c + 1 \\ a + c & c \end{bmatrix}, \] then the value of \( abc \) is:

If \(\tan^{-1}\left(\frac{2}{3 - x + 1}\right) = \cot^{-1}\left(\frac{3}{3x + 1}\right)\), then which one of the following is true?

If \((\vec{a} - \vec{b}) \cdot (\vec{a} + \vec{b}) = 27\) and \(|\vec{a}| = 2|\vec{b}|\), then \(|\vec{b}|\) is:

The angle between two lines whose direction ratios are proportional to \(1, 1, -2\) and \((\sqrt{3} - 1), (-\sqrt{3} - 1), -4\) is:

Let \( R \) be the relation over the set \( A \) of all straight lines in a plane such that \( l_1 \, R \, l_2 \iff l_1 \) is parallel to \( l_2 \). Then \( R \) is:

Which one of the following represents the correct feasible region determined by the following constraints of an LPP?
\[ x + y \geq 10, \quad 2x + 2y \leq 25, \quad x \geq 0, \quad y \geq 0 \]

Which of the following cannot be the direction ratios of the straight line \(\frac{x - 3}{2} = \frac{2 - y}{3} = \frac{z + 4}{-1}\)?

There are two bags. Bag-1 has 4 white and 6 black balls, and Bag-2 has 5 white and 5 black balls. A die is rolled, and if it shows a multiple of 3, a ball is drawn from Bag-1; otherwise, from Bag-2. If the ball drawn is not black, the probability it was not drawn from Bag-2 is:

For the function $f(x) = 2x^3 - 9x^2 + 12x - 5, x \in [0, 3]$, match List-I with List-II:

List-I	List-II
(A) Absolute maximum value	(I) 3
(B) Absolute minimum value	(II) 0
(C) Point of maxima	(III) -5
(D) Point of minima	(IV) 4

For the differential equation \((x \log x) \, dy = (\log x - y) \, dx\):
(A) Degree of the given differential equation is 1.
(B) It is a homogeneous differential equation.
(C) Solution is \(2y \log x + A = (\log x)^2\), where \(A\) is an arbitrary constant.
(D) Solution is \(2y \log x + A = \llog(\ln x)\), where \(A\) is an arbitrary constant.

The direction cosines of the line which is perpendicular to the lines with direction ratios 1,-2,-2 and 0, 2, 1 are:

\(\text{ If } f(x) = \sin x + \frac{1}{2} \cos 2x \text{ in } \left[ 0, \frac{\pi}{2} \right], \text{ then:}\)
(A) \(f'(x) = \cos x - \sin 2x\)
(B)The critical points of the function are \(x = \frac{\pi}{6}\) and \(x = \frac{\pi}{2}\)
(C) The minimum value of the function is 2
(D) The maximum value of the function is \(\frac{3}{4}\)

\(\text{ If } \Delta = \begin{vmatrix} 1 & \cos x & 1 \\ -\cos x & 1 & \cos x \\ -1 & -\cos x & 1 \\ \end{vmatrix} , \text{ then:}\)
\((A)\space \Delta = 2(1 - \cos^2 x)\)
\((B)\space \Delta = 2(2 - \sin^2 x)\)
(C) Minimum value of ∆ is 2
(D) Maximum value of \( \Delta \) is 4

\(\text{The matrix }\) \(\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{bmatrix} \text{ is a:}\)
(A) Scalar matrix
(B) Diagonal matrix
(C) Skew-symmetric matrix
(D) Symmetric matrix

For a square matrix } A_{n \times n}:
(A) \( |\text{adj } A| = |A|^{n-1} \) 
(B) \( |A| = |\text{adj } A|^{n-1} \) 
(C) \( A (\text{adj } A) = |A| \) 
(D) \( |A^{-1}| = \frac{1}{|A|} \) 
$\text{Choose the \textbf{correct} answer from the options given below:}$

If the random variable X has the following distribution:

X	0	1	2	otherwise
P(X)	k	2k	3k	0

Match List-I with List-II:

Choose the correct answer from the options given below: