List of top Mathematics Questions asked in COMEDK UGET

If \( \lim_{x \to \infty} \left( 1 + \frac{a}{x} + \frac{b}{x^2} \right)^{2x} = e^2 \), then:

If for any \( 2 \times 2 \) square matrix \( A \), \( A(\text{adj} A) = \begin{bmatrix} 8 & 0 \\ 0 & 8 \end{bmatrix} \), then find the value of \( \det(A) \).

If \( A = \begin{bmatrix} 2 - k & 2 \\ 1 & 3 - k \end{bmatrix} \) is a singular matrix, then the value of \( 5k - k^2 \) is:

If \( A = \begin{bmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{bmatrix} \), then \( |A| \cdot \text{adj}(A) \) is equal to:

If \( A = \{3, 5, 7\} \) and \( B = \{1, 2, 3, 5\} \), then \( A \times B \cap B \times A \) is equal to:

The argument of \( \dfrac{1 - i\sqrt{3}}{1 + i\sqrt{3}} \) is:

\( (i + \sqrt{3})^{100} + (i - \sqrt{3})^{100} + 2^{100} \) is equal to:

The total number of terms in the expansion of \( (x + y)^{100} + (x - y)^{100} \):

The coefficient of \( x^{20} \) in the expansion of \( (1 + 3x + 3x^2 + x^3)^{20} \):

If A, B, and C are three mutually exclusive and exhaustive events such that \( P(A) = 2P(B) = 3P(C) \). What is \( P(B) \)?

What is \( \frac{\cos \theta}{1 - \tan \theta} + \frac{\sin \theta}{1 - \cot \theta} \) equal to?

The point \( (-3, -2) \) lies

Find the general solution of \( \sin 2x + \cos x = 0 \).

If \( f(x) + 2f(1 - x) = x^2 + 5 \) for all real values of \( x \), then \( f(x) \) is given by:

If \( ^nC_3 = 220 \), then \( n = \ ? \)

There are 12 points in a plane out of which 3 points are collinear. How many straight lines can be drawn by joining any two of them?

Evaluate $\left[i^{22} + \left(\dfrac{1}{i}\right)^{25}\right]^3$

The maximum of \( Z \) is where, \( Z = 4x + 2y \) subject to constraints \[ 4x + 2y \geq 46, \quad x + 3y \leq 24, \quad x, y \geq 0 \]

If \( p = \hat{i} + \hat{j}, q = 4\hat{k} - \hat{j} \) and \( r = \hat{i} + \hat{k} \), then the unit vector in the direction of \( 3p + q - 2r \) is

The first and fifth terms of an A.P. are -14 and 2 respectively and the sum of its $n$ terms is 40. The value of $n$ is

If \( U_{n+1} = 3U_n - 2U_{n-1} \) and \( U_0 = 2, U_1 = 3 \), then \( U_n \) is equal to

If \( 4^n + 15n + P \) is divisible by 9 for all \( n \in \mathbb{N} \), then the least negative integral value of \( P \) is

\( (2^{3n} - 1) \) is divisible by

Five persons A, B, C, D and E are in queue at a shop. The probability that A and B are always together is.

The probability of choosing randomly a number \( c \) from the set \( \{1, 2, 3, \dots, 9\} \) such that the quadratic equation \( x^2 + 4x + c = 0 \) has real roots, is