List of top Mathematics Questions asked in VITEEE

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 \( b^2 \geq 4ac \) 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 simultaneous equations \( Kx + 2y = 1 \), \( K(1 - y) - 2x = 2 \) and \( K + 2y = 3 \) have only one solution when

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

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 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

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

The equation of a directrix of the ellipse \( \frac{x^2}{16} + \frac{y^2}{25} = 1 \) is

If the normal at \( (a^2, 2a^2) \) on the parabola \( y^2 = 4ax \), meets the parabola again at \( (a^2, 2a^2) \), then

The length of the straight line \( x - 3y = 1 \) intercepted by the hyperbola \( x^2 - 4y^2 = 1 \) is

The curve described parametrically by \[ x = t^2 + 2t - 1, \quad y = 3t + 5 \] represents

If \( \sin^{-1} x + \sin^{-1} y = \frac{\pi}{2} \), then \( \cos^{-1} x + \cos^{-1} y \) is equal to

If the normal to the curve \( y = f(x) \) at \( (3, 4) \) makes an angle \( \frac{3\pi}{4} \) with the positive x-axis, then \( f'(3) \) is equal to