List of top Mathematics Questions

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:
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 \( \left[ i^{18} + \frac{1}{i} \right]^{25} \):
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 \( \sin 2x = 4 \cos x \), then \( x \) is equal to:
The expression \( \frac{\tan A + \cot A}{1 - \cot A} \) can be written as:
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:
Five persons A, B, C, D and E are in queue of a shop. The probability that A and E are always together, is:
The equation of a plane passing through the line of intersection of the planes \( x + 2y + 3z = 2 \) and \( x - y + z = 3 \) and at a distance \( \frac{2}{\sqrt{3}} \) from the point \( (3, 1, -1) \) is:
The point of intersection of the lines \( \frac{x - 1}{3} = \frac{y - 2}{-3} = \frac{z - 3}{4} \) and \( \frac{x - 4}{5} = \frac{y - 1}{2} = \frac{z - 1}{-2} \) is:
The angle between the lines \( 2x = 3y - z \) and \( 6x = -y - 4z \) is:
The integral of \( \int \frac{dx}{x^2[1 + x^4]^{3/4}} \) is:
The integral \( \int \frac{2^x}{\sqrt{1 - 4^x}} \, dx \) is equal to:
The integral \( \int_{\pi/2}^{-\pi/2} \sin x \, dx \) is:
The line \( \frac{x - 2}{3} = \frac{y - 3}{4} = \frac{z - 4}{5} \) is parallel to the plane:
The value of \( \lim_{x \to 0} \frac{ax^3 + bx^2 + cx}{3x^2} \), where \( a, b, c > 0 \), is:
The approximate value of \( f(5.001) \), where \( f(x) = x^3 - 7x^2 + 15 \), is:
Find the center and radius of the circle given by the equation \( 2x^2 + 2y^2 + 3x + 4y + 9 = 0 \).
What will be the equation of the circle whose center is \( (1, 2) \) and which passes through the point \( (4, 6) \)?