List of top Mathematics Questions asked in VITEEE

Amplitude of $\frac{1+\sqrt{3}i}{\sqrt{3}+1}$ is :

The vector equation of the symmetrical form of equation of straight line $\frac{x-5}{3} = \frac{y+4}{7} = \frac{z-6}{2}$ is

The solution of $\frac{dv}{dt} +\frac{k}{m}v = -g$ is

The interval in which the function $f\left(x\right) = \frac{4x^{2}+1}{x}$ is decreasing is :

If the parabola $y^2 = 4ax$ passes through the point $(1, -2)$, then the tangent at this point is

The set of points of discontinuity of the function \[ f(x) = \sin (2 \sin x) \sin^2 x \] is given by

The angle between a pair of tangents drawn from a point \( T \) to the curve \[ x^2 + y^2 + 4x - 6y - 9 = 3x + 1 \] is

If matrix \( A = \begin{pmatrix} 3 & 2 & 4 \\1 & 2 & -1 \end{pmatrix} \) and

If vectors \( \mathbf{i} + \mathbf{j} + \mathbf{k} \) and \( \mathbf{i} + \mathbf{j} + \mathbf{k} \) are coplanar, then find

The volume \( V \) and depth \( x \) of water in a vessel are connected by the relation \[ V = 5x - \frac{x^2}{6} \] and the volume of water is increasing, at the rate of 5 cm\(^3\)/sec, when \( x = 2 \) cm. The rate at which the depth of water is increasing is

The parabola having its focus at (3, 2) and directrix along the y-axis has its vertex at

The tangent lines to the curve \( y^2 = 4ax \) at points where \( x = a \), are

The conditional \( (P \land Q) \Rightarrow P \) is

If \( f(x) = \cos x + 1 \) and \( f'(x) = 2 \cos x \), then \[ \int_0^\frac{\pi}{2} f(x)dx \] is equal to

The rank of the matrix \[ \begin{pmatrix} 1 & 2 & 5 \\ 2 & 4 & 4 \\ 3 & 6 & 6 \end{pmatrix} \] is

The distance of the point \( (1, -2, 3) \) from the plane \( x - y + z = 5 \) measured parallel to the line \[ \frac{x}{2} = \frac{y}{3} = \frac{z - 1}{6} \] is

If the eccentricity of the hyperbola \[ x^2 - y^2 \cos^2 \alpha = 25 \] is \( \sqrt{5} \), then the eccentricity of the ellipse \[ x^2 \cos^2 \alpha + y^2 = 5 \] is equal to:

The condition that the line \( \frac{x}{p} + \frac{y}{q} = 1 \) be normal to the parabola \( y^2 = 4ax \) is

The area bounded by \( f(x) = x^2, 0 \leq x \leq 1 \), and \( g(x) = x + 2, 1 \leq x \leq 2 \) and x-axis is

The line which passes through the origin and intersects the two lines \[ \frac{x - 1}{2} = \frac{y - 3}{4} = \frac{z - 14}{4} \] is

If \( u_n = \int_0^{\frac{\pi}{4}} \tan \theta d\theta \), then \( u_{n+2} \) is:

A random variable \( X \) has the probability distribution \[ P(X) = \{ 0.15, 0.23, 0.12, 0.10, 0.20, 0.07, 0.06, 0.08 \} \] For the events \( E = \{ X \text{ is a prime number} \} \) and \( F = \{ X<4 \} \), then \( P(E \cup F) \) is

Ten different letters of an alphabet are given, words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated is

The value of \( \tan^{-1} \left( \frac{1}{2} \right) + \tan^{-1} \left( \frac{1}{3} \right) \) is

Let A be the centre of the circle \( x^2 + y^2 - 2x - 4y - 20 = 0 \), and B(1, 7) and D(4, -2) are points on the circle then, if tangents are drawn at B and D, which meet at C, then area of quadrilateral ABCD is