List of top Mathematics Questions asked in VITEEE

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

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

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

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

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

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

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

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

A and B are events such that \( P(A \cup B) = 3/4 \), \( P(A) = 1/4 \), and \( P(A \cap B) = 2/3 \). Then the probability that \( P(A \cap B) \) is

\[ \int \left[ f'(x) \left( g(x) \right)^2 \right] dx \] is equal to:

The difference between greatest and least value of \[ f(x) = 2 \sin x + \sin 2x, \, x \in \left[ 0, \frac{3\pi}{2} \right] \] is

A and B are two independent witnesses (i.e., there is no collision between them) in a case. The probability that A will speak the truth is \( x \) and the probability that B will speak the truth is \( y \). A and B agree in a certain statement. The probability that the statement is true is

If \( x = -\frac{7}{3} \), then \( x^4 \) is

The range of the function \[ f(x) = \frac{1}{2 - \cos 3x} \] is

The area bounded by \( y = |x| \), \( y = 0 \) and \( |x| = \frac{1}{2} \) will be:

Value of \[ \int_0^{\pi/2} \frac{\sqrt{\sin x}}{\sin x + \cos x} \, dx \]

The solution of the differential equation \[ \log x \frac{dy}{dx} + x = \sin 2x \] is