List of top Mathematics Questions asked in CUET (UG)

Let A = $\begin{bmatrix 1 & 2 & 1 \\ 1 & 3 & 2 \\ 2 & 4 & 1 \end{bmatrix}$ and Mij, Aij respectively denote the minor, co-factor of an element aij of matrix A, then which of the following are true?}
(A) M22 = -1
(B) A23 = 0
(C) A32 = 3
(D) M23 = 1
(E) M32 = -3
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Let A = [aij]2x3 and B = [bij]3x2, then |5AB| is equal to

If A and B are invertible matrices then which of the following statement is NOT correct?

for $|x| < 1$, sin(tan-1x) equal to

The solution of the differential equation $\log_e(\frac{dy}{dx}) = 3x + 4y$ is given by

The probability distribution of a random variable X is given by
\begin{tabular}{|c|c|c|c|} \hline X & 0 & 1 & 2 \\ \hline P(X) & $1 - 7a^2$ & $\frac{1}{2}a + \frac{1}{4}$ & $a^2$ \\ \hline \end{tabular}
If a > 0, then P(0 $<$ x $\le$ 2) is equal to

Let f: R $\rightarrow$ R be defined as f(x) = 10x. Then (Where R is the set of real numbers)

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

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

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 interval, on which the function f(x) = x2e-x is increasing, is equal to

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) $(1 + x^2)\frac{dy}{dx} + 2xy = 2$
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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

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

If y = 3e2x + 2e3x, then $\frac{d^2y}{dx^2} + 6y$ is equal to

Let A = [aij]n x n be a matrix. Then Match List-I with List-II
List-I
(A) AT = A
(B) AT = -A
(C) |A| = 0
(D) |A| $\neq$ 0
List-II
(I) A is a singular matrix
(II) A is a non-singular matrix
(III) A is a skew symmetric matrix
(IV) A is a symmetric matrix
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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: