List of top Mathematics Questions asked in COMEDK UGET

If matrix A = [ 2 -2 ] [ -2 2 ] and A² = pA, then the value of p is:
If for any 2 × 2 square matrix A, we have A ⋅ adj(A) = [8 0; 0 8], then the value of det(A) is:
If 3 and 4 are intercepts of a line \( L = 0 \), then the distance of \( L = 0 \) from the origin is:
The distance of the point \( (1, 2) \) from the line \( x + y + 5 = 0 \) measured along the line parallel to \( 3x - y = 7 \) is:
The slopes of the lines, which make an angle 45° with the line \( 3x - y = -5 \), are:
Middle term in the expansion of \( \left( x^2 + \frac{1}{x^2} + 2 \right)^n \) is:
If \( a, b, c \) are in AP, \( b - a, c - b \) and \( a \) are in GP, then \( a : b : c \) is:
How many numbers greater than 40000 can be formed from the digits 2, 4, 5, 5, 7?
If a polygon of \( n \) sides has 275 diagonals, then \( n \) is equal to:
Out of 8 given points, 3 are collinear. How many different straight lines can be drawn by joining any two points from these 8 points?
The number of triangles which can be formed by using the vertices of a regular polygon of \( (n + 3) \) sides is 220. Then, \( n \) is equal to:
If two pairs of lines \( x^2 - 2mxy - y^2 = 0 \) and \( x^2 - 2nxy - y^2 = 0 \) are such that one of them represents the bisector of the angles between the other, then:
Evaluate \( 3^n - 7n - 1 \) is divisible by:
If \( 49^n + 16n + P \) is divisible by 64 for all \( n \in \mathbb{N} \), then the least negative integral value of \( P \) is:
The value of \[ 1! + 2! + 2! + 3! + 3! + \cdots + n \cdot n! \] is:
The solution of the differential equation \( \sec^2 x \, \tan y \, dx + \sec y \, \tan x \, dy = 0 \) is:
The solution of the differential equation \[ y \frac{dy}{dx} = x \left[ \frac{y^2}{x^2} + \varphi \left( \frac{y^2}{x^2} \right) \right] \] is:
The solution of the differential equation \[ (1 + y^2) + (x - e^{\tan^{-1} y}) \frac{dy}{dx} = 0 \] is:
The sum of the series \( (1 + 2) + (1 + 2 + 2^2) + (1 + 2 + 2^2 + 2^3) + \cdots \) up to terms is:
Evaluate \( \left[ i^{18} + \frac{1}{i} \right]^{25} \):
Total number of elements in the power set of a set \( A \) containing 15 elements is:
If \( A = \{1, 2, 5, 6\} \) and \( B = \{1, 2, 3\} \), then \( A \times B \cap B \times A \) is equal to:
Using mathematical induction, the numbers \( a_n \)'s are defined by \( a_0 = 1 \), \( a_{n+1} = 3n^2 + n + a_n \), \( (n \geq 0) \). Then, \( a_n \) is equal to:
If \( f(x) \) satisfies the relation \( 2f(x) + f(1 - x) = x^2 \) for all real \( x \), then \( f(x) \) is:
The expression \( \frac{\tan A + \cot A}{1 - \cot A} \) can be written as: