List of top Mathematics Questions

If \( x \sin \left( \frac{y}{x} \right) \, dy = \sin \left( \frac{y}{x} \right) - x \, dx \) and \( y(1) = \frac{\pi}{2} \), then the value of \( \cos \left( \frac{y}{x} \right) \) is

The function \( f(x) = x^2 e^{-x} \), \( x>0 \). Then the maximum value of \( f(x) \) is

The value of \( \int_0^\infty \frac{dx}{(a^2 + x^2)^7} \) is equal to

The product of all values of \( \cos(\alpha) + i \sin(\alpha) )^{3/5} \) is equal to

The imaginary part of \( \frac{(1+i)^2}{i(2i-1)} \) is

If \( H \) is the harmonic mean between \( P \) and \( Q \), then the value of \[ \frac{H}{P} + \frac{H}{Q} \] is

If \( \theta \) is the angle between the lines \( AB \) and \( AC \) where A, B, and C are the three points with coordinates \( (1, 2, -1) \), \( (2, 0, 3) \), \( (3, -1, 2) \) respectively, then \[ \sqrt{62} \cos \theta \] is equal to

If \( \vec{a} \) and \( \vec{b} \) are two unit vectors, then the vector \[ (\vec{a} + \vec{b}) \times (\vec{a} \times \vec{b}) \] is parallel to the vector

If \( b^2 \geq 4ac \) for the equation \( ax^4 + bx^2 + c = 0 \), then all the roots of the equation will be real if

If \( x>0 \) and \( \log x + \log \left( \log x \right) + \log \left( \log \log x \right) + \dots = 4 \), then \[ x \text{ equals} \]

The number of real roots of the equation \[ \left( x + \frac{1}{x} \right)^3 + \frac{1}{x} = 0 \] is

The simultaneous equations \( Kx + 2y = 1 \), \( K(1 - y) - 2x = 2 \) and \( K + 2y = 3 \) have only one solution when

If \( X \) is a Poisson variate such that \[ 2P(X = 0) + P(X = 2) = 2P(X = 1), \text{ then } E(X) \] is equal to

If \( G^{*} \) is a group and the order of an element \( a \in G \) is 10, then the order of the inverse of \( a \) is

Everybody in a room shakes hands with everybody else. The total number of handshakes in the room is

The differential equation of the system of all circles of radius r in the XY plane is

The general solution of the differential equation \[ \frac{d^2 y}{dx^2} + \frac{dy}{dx} + y = 2e^{3x} \] is given by

The solution of the differential equation \[ \frac{dy}{dx}(x - y^3) = 0 \] is

The number of positive integral solutions of the equation \( x_1 + x_2 + x_3 + x_4 = 1050 \) is

Let \( A = \{ 1, 2, 3, \dots, n \} \) and \( B = \{ a, b, c, \dots \} \), then the number of functions from A to B that are onto is

The value of the integral \[ \int e^x \left( \frac{1 - x}{1 + x^2} \right)^2 dx \] is

The angle between the tangents at those points on the curve \( x = t^2 + 1 \) and \( y = t^2 - t - 6 \) where it meets the x-axis is

The value of \( \int_{1}^{4} |x - 3| \, dx \) is equal to

The area of the region bounded by the straight lines \( x = 0 \) and \( x = 2 \) and the curves \( y = 2x^2 \) and \( y = 2x - x^2 \) is equal to

If \( (x + y) \sin u = x^2 y^2 \), then \( x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} \) is