List of top Mathematics Questions

If 3 and 4 are intercepts of a line \( L = 0 \), then the distance of \( L = 0 \) from the origin is:
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?
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:
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 \( a, b, c \) 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:
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:
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 sum of the series \( (1 + 2) + (1 + 2 + 2^2) + (1 + 2 + 2^2 + 2^3) + \cdots \) up to terms is:
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:
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:
Evaluate \( \left[ i^{18} + \frac{1}{i} \right]^{25} \):
If \( \sin 2x = 4 \cos x \), then \( x \) is equal to:
If \( x \) and \( y \) are acute angles, such that \[ \cos x + \cos y = \frac{3}{2} \quad \text{and} \quad \sin x + \sin y = \frac{3}{4}, \quad \text{then} \quad \sin(x + y) \text{ equals:} \]
Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral equals:
A student answers a multiple choice question with 5 alternatives, of which exactly one is correct. The probability that he knows the correct answer is \( p \), \( 0 < p < 1 \). If he does not know the correct answer, he randomly ticks one answer. Given that he has answered the question correctly, the probability that he did not tick the answer randomly is:
The expression \( \frac{\tan A + \cot A}{1 - \cot A} \) can be written as:
Five persons A, B, C, D and E are in queue of a shop. The probability that A and E are always together, is: