List of top Mathematics Questions asked in CUET (UG)

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
If $A$ is a square matrix of order 3 such that $|A| = 2$, then $|\operatorname{adj}(\operatorname{adj}(A))|$ 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
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 = $\begin{bmatrix} 0 & 0 & \sqrt{3} \\ 0 & \sqrt{3} & 0 \\ \sqrt{3} & 0 & 0 \end{bmatrix}$, then |adj A| is equal to
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
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

The probability distribution of the random variable X is given by

X0123
P(X)0.2k2k2k

Find the variance of the random variable \(X\).

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:
The rate of change of area of a circle with respect to its circumference when radius is 4cm, is
The function f(x) = tanx - x
If A and B are any two events such that P(B) = P(A and B), then which of the following is correct

If A is any event associated with sample space and if E1, E2, E3 are mutually exclusive and exhaustive events. Then which of the following are true? 

(A) \(P(A) = P(E_1)P(E_1|A) + P(E_2)P(E_2|A) + P(E_3)P(E_3|A)\) 
(B) \(P(A) = P(A|E_1)P(E_1) + P(A|E_2)P(E_2) + P(A|E_3)P(E_3)\) 
(C) \(P(E_i|A) = \frac{P(A|E_i)P(E_i)}{\sum_{j=1}^{3} P(A|E_j)P(E_j)}, \; i=1,2,3\) 
(D) \(P(A|E_i) = \frac{P(E_i|A)P(E_i)}{\sum_{j=1}^{3} P(E_i|A)P(E_j)}, \; i=1,2,3\) 

Choose the correct answer from the options given below:

How many minimum number of times must a man toss a fair coin so that the probability of having at least one head is more than 90%?

Let A and B be two events such that: \[ P(A) = 0.8, \quad P(B) = 0.5, \quad P(B|A) = 0.4 \]

Match List-I with List-II:

List-IList-II
(A) \(P(A \cap B)\)(I) 0.2
(B) \(P(A|B)\)(II) 0.32
(C) \(P(A \cup B)\)(III) 0.64
(D) \(P(A')\)(IV) 0.98
How many minimum number of times must a man toss a fair coin so that the probability of having at least one head is more than 90%?
If A and B are any two events such that P(B) = P(A and B), then which of the following is correct
If A is any event associated with sample space and if E\textsubscript{1}, E\textsubscript{2}, E\textsubscript{3} are mutually exclusive and exhaustive events. Then which of the following are true?
(A) $P(A) = P(E_1)P(E_1|A) + P(E_2)P(E_2|A) + P(E_3)P(E_3|A)$
(B) $P(A) = P(A|E_1)P(E_1) + P(A|E_2)P(E_2) + P(A|E_3)P(E_3)$
(C) $P(E_i|A) = \frac{P(A|E_i)P(E_i){\sum_{j=1}^{3} P(A|E_j)P(E_j)}, i=1,2,3$}
(D) $P(A|E_i) = \frac{P(E_i|A)P(E_i){\sum_{j=1}^{3} P(E_i|A)P(E_j)}, i=1,2,3$}
Choose the correct answer from the options given below: