List of top Questions asked in CUET (UG)

The area (in sq. units) of the region bounded by the curve \( y = x^5 \), the x-axis and the ordinates x = -1 and x = 1 is equal to
The area (in sq. units) of the region bounded by y = $2\sqrt{1-x^2}$, x $\in$ [0,1] and x-axis is equal to
Let A = [aij]2x3 and B = [bij]3x2, then |5AB| is equal to
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

Match List-I with List-II

List-IList-II
(A) \( f(x) = |x| \)(I) Not differentiable at \( x = -2 \) only
(B) \( f(x) = |x + 2| \)(II) Not differentiable at \( x = 0 \) only
(C) \( f(x) = |x^2 - 4| \)(III) Not differentiable at \( x = 2 \) only
(D) \( f(x) = |x - 2| \)(IV) Not differentiable at \( x = 2, -2 \) only


Choose the correct answer from the options given below:

Let \( y=\sin(\cos(x^2)) \). Find \( \frac{dy}{dx} \) at \( x=\frac{\sqrt{\pi}}{2} \).

Match List-I with List-II

List-IList-II
(A) The minimum value of \( f(x) = (2x - 1)^2 + 3 \)(I) 4
(B) The maximum value of \( f(x) = -|x + 1| + 4 \)(II) 10
(C) The minimum value of \( f(x) = \sin(2x) + 6 \)(III) 3
(D) The maximum value of \( f(x) = -(x - 1)^2 + 10 \)(IV) 5


Choose the correct answer from the options given below:

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
for $|x| < 1$, sin(tan-1x) equal to
Let A = $\begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}$ and I = $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$. If AT + A = I, then
If A and B are skew-symmetric matrices, then which one of the following is NOT true?
If A and B are invertible matrices then which of the following statement is NOT correct?
The area (in sq. units) of the region bounded by the parabola y2 = 4x and the line x = 1 is
Which of the following are linear first order differential equations?
(A) $\frac{dy}{dx} + P(x)y = Q(x)$
(B) $\frac{dx}{dy} + P(y)x = Q(y)$
(C) $(x - y)\frac{dy}{dx} = x + 2y$
(D) $(1 + x^2)\frac{dy}{dx} + 2xy = 2$
Choose the correct answer from the options given below:
The solution of the differential equation $\log_e(\frac{dy}{dx}) = 3x + 4y$ is given by
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
Consider the LPP: Minimize Z = x + 2y subject to 2x + y $\ge$ 3, x + 2y $\ge$ 6, x, y $\ge$ 0. The optimal feasible solution occurs at
Let f: R $\rightarrow$ R be defined as f(x) = 10x. Then (Where R is the set of real numbers)
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 y = 3e2x + 2e3x, then $\frac{d^2y}{dx^2} + 6y$ is equal to
The interval, on which the function f(x) = x2e-x is increasing, is equal to
If the maximum value of the function f(x) = $\frac{\log_e x}{x}$, x > 0 occurs at x = a, then a2f''(a) is equal to
$\int_{1}^{4} |x - 2| dx$ is equal to
The integral I = $\int \frac{e^{5\log_e x} - e^{4\log_e x}}{e^{3\log_e x} - e^{2\log_e x}} dx$ is equal to