List of top Mathematics Questions asked in CUET (UG)

If \( A \) is a square matrix and \( I \) is an identity matrix such that \( A^2 = A \), then \( A(I - 2A)^3 + 2A^3 \) is equal to:
\(\text{ If } \Delta = \begin{vmatrix} 1 & \cos x & 1 \\ -\cos x & 1 & \cos x \\ -1 & -\cos x & 1 \\ \end{vmatrix} , \text{ then:}\)
\((A)\space \Delta = 2(1 - \cos^2 x)\)
\((B)\space \Delta = 2(2 - \sin^2 x)\)
(C) Minimum value of ∆ is 2
(D) Maximum value of \( \Delta \) is 4
For \( I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \), if \( A = \begin{bmatrix} a & b \\ c & -a \end{bmatrix} \) be such that \( A^2 = I \), then:
If \[ A = \begin{bmatrix} 2 & 4 \\ x & 2 \end{bmatrix} \] and $A$ is singular, then $x$ is equal to:
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 \( A = \begin{bmatrix} -k & 0 \\ 0 & -k \end{bmatrix}, \, k \neq 0 \), then the value of \( m \) in \( (A^T)^4 = mA \) is:
If \[ \begin{bmatrix} 1 & 3 \\ 4 & 5 \end{bmatrix} \begin{bmatrix} x \\ 2 \end{bmatrix} = \begin{bmatrix} 5 \\ 6 \end{bmatrix}, \] then the value of \( x \) is:
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:
Which of the following are components of a time series?(A) Irregular component
(B) Cyclical component
(C) Chronological component
(D) Trend Component
Choose the correct answer from the options given below:
Mohan caught 100 frogs from a garden and measured their weights. The mean weight of these frogs is a :
The rate of change (in cm2/s) of the total surface area of a hemisphere with respect to the radius r at r = 3.
The function f(x) = |x| + |1 − x| is:
An equilateral triangle of side \( 4\sqrt{3} \) cm formed out of a sheet is converted into a rectangle such that there is no loss of the area of the triangle. Then the least perimeter of the rectangle (in cm) will be:
Match List-I with List-II:
Integrating factor of xdy − (y + 2x2)dx = 0
A firm anticipates an expenditure of ₹10,000 for a new equipment at the end of 5 years from now. How much should the firm deposit at the end of each quarter into a sinking fund earning interest 10% per year compounded quarterly to provide for the purchase?
[Use (1.025)20=1.7]
The integral of the function \( \frac{1}{9 - 4x^2} \) 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 \( y = e^{{2}\log_e t} \) and \( x = \log_3(e^{t^2}) \), then \( \frac{dy}{dx} \) is equal to:

Subject to constraints: 2x + 4y ≤ 8, 3x + y ≤ 6, x + y ≤ 4, x, y ≥ 0; The maximum value of Z = 3x + 15y is:
The direction cosines of the line which is perpendicular to the lines with direction ratios 1,-2,-2 and 0, 2, 1 are:
Which of the following cannot be the direction ratios of the straight line \(\frac{x - 3}{2} = \frac{2 - y}{3} = \frac{z + 4}{-1}\)?
\(\text{The area of the region enclosed between the curves } 4x^2 = y \text{ and } y = 4 \text{ is:}\)
The value of \(\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{dx}{1 + \tan^{18}x}\) is:
Match List-I with List-II:
List-IList-II
The derivative of \( \log_e x \) with respect to \( \frac{1}{x} \) at \( x = 5 \) is(I) -5
If \( x^3 + x^2y + xy^2 - 21x = 0 \), then \( \frac{dy}{dx} \) at \( (1, 1) \) is(II) -6
If \( f(x) = x^3 \log_e \frac{1}{x} \), then \( f'(1) + f''(1) \) is(III) 5
If \( y = f(x^2) \) and \( f'(x) = e^{\sqrt{x}} \), then \( \frac{dy}{dx} \) at \( x = 0 \) is(IV) 0
Choose the correct answer from the options given below :
The area of the region bounded by the lines \( \frac{x}{7\sqrt{3a}} + \frac{y}{b} = 4 \), \( x = 0 \), and \( y = 0 \) is: