List of top Mathematics Questions asked in CUET (UG)

If A = $\begin{bmatrix} 0 & 0 & \sqrt{3} \\ 0 & \sqrt{3} & 0 \\ \sqrt{3} & 0 & 0 \end{bmatrix}$, then |adj A| is equal to
If A and B are skew-symmetric matrices, then which one of the following is NOT true?
The feasible region is bounded by the inequalities: \[ 3x + y \geq 90, \quad x + 4y \geq 100, \quad 2x + y \leq 180, \quad x, y \geq 0 \] If the objective function is $ Z = px + qy $ and $ Z $ is maximized at points $ (6, 18) $ and $ (0, 30) $, then the relationship between $ p $ and $ q $ is:
If A is a square matrix and I is the identity matrix of same order such that A2 = I, then (A - I)3 + (A + I)3 - 3A is equal to
Let \( y=\sin(\cos(x^2)) \). Find \( \frac{dy}{dx} \) at \( x=\frac{\sqrt{\pi}}{2} \).
For a matrix $ A $ of order $ 3 \times 3 $, which of the following is true?
The total cost C(x) in Rupees associated with the production of x units of an item is given by C(x) = \(0.007x^3 - 0.003x^2 + 15x + 400\). The marginal cost when 10 items are produced is:
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
Corner points of a feasible bounded region are \((0, 10)\), \((4, 2)\), \((3, 7)\) and \((10, 6)\). Maximum value 50 of objective function \(z = ax + by\) occurs at two points \((0, 10)\) and \((10, 6)\). The value of \(a\) and \(b\) are:
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
If A and B are invertible matrices then which of the following statement is NOT correct?
If $\vec{a} + \vec{b} + \vec{c} = \vec{0}$ and $|\vec{a}| = 3, |\vec{b}| = 5, |\vec{c}| = 7$, then the angle between $\vec{a}$ and $\vec{b}$ is
If $A$ is a square matrix of order 3 and $A \cdot (\operatorname{Adj}(A)) = 10I$, then the value of $\frac{1}{25} |\operatorname{adj}(A)|$ is:
If \(\int \frac{(1 + x \log x)}{xe^{-x}} dx = e^x f(x) + C\), where C is constant of integration, then f(x) is
If $A$ is a square matrix of order 3 such that $|A| = 2$, then $|\operatorname{adj}(\operatorname{adj}(A))|$ is:
Let AX = B be a system of three linear equations in three variables. Then the system has
(A) a unique solution if |A| = 0
(B) a unique solution if |A| $\neq$ 0
(C) no solutions if |A| = 0 and (adj A) B $\neq$ 0
(D) infinitely many solutions if |A| = 0 and (adj A)B = 0
Choose the correct answer from the options given below:
If the function f(x) = $\begin{cases}\frac{k\cos x}{\pi - 2x} & ; x \neq \frac{\pi}{2} \\ 3 & ; x = \frac{\pi}{2} \end{cases}$ is continuous at x = $\frac{\pi}{2}$, then k is equal to
For a matrix $ A $ of order $ 3 \times 3 $, which of the following is true?
If $ A $ is a $ 2 \times 2 $ matrix and $ |A| = 4 $, then $ |A^{-1}| $ is:
A black and a red die are rolled simultaneously. The probability of obtaining a sum greater than 9, given that the black die resulted in a 5 is
If $ A $ is a square matrix such that $ \text{adj}(\text{adj}(A)) = A $, then $ |A| $ is:
Let A = [aij]2x3 and B = [bij]3x2, then |5AB| is equal to
The corner points of the feasible region associated with the LPP: Maximise Z = px + qy, p, q > 0 subject to 2x + y $\le$ 10, x + 3y $\le$ 15, x,y $\ge$ 0 are (0, 0), (5, 0), (3, 4) and (0, 5). If optimum value occurs at both (3, 4) and (0, 5), then
The area (in sq. units) of the region bounded by the parabola y2 = 4x and the line x = 1 is
If y = 3e2x + 2e3x, then $\frac{d^2y}{dx^2} + 6y$ is equal to