List of top Mathematics Questions asked in VITEEE

The equation of the plane which bisects the angle between the planes \[ 3x - 6y + 2z + 5 = 0 \quad {and} \quad 4x - 12y + 3z - 3 = 0 { which contains the origin is:} \]

The value of the definite integral

\[ \int_0^{\frac{\pi}{2}} \log(\tan x) \, dx \]

is:

The point \( (t^2 + 2t + 5, 2t^2 + t - 2) \) { lies on the line} \( x + y = 2 \) { for:}

If the system of linear equations \[ x + ky + 3z = 0, \quad 3x + ky - 2z = 0, \quad 2x + 4y - 3z = 0 \] has a non-zero solution  \( (x, y, z) \), then \( \frac{xz}{y^2} \) is equal to:

The total number of 3-digit numbers, the sum of whose digits is even, is equal to:
If \( \alpha, \beta \) are the roots of the equation \( ax^2 + bx + c = 0 \), then \[ \frac{\alpha}{a\beta + b} + \frac{\beta}{a\alpha + b} = \]
If \( 12\cot^2 \theta - 31\csc \theta + 32 = 0 \), then the value of \( \sin \theta \) is:
The locus of a point that is equidistant from the lines \[ x + y - 2\sqrt{2} = 0 \quad {and} \quad x + y - \sqrt{2} = 0 { is:} \]
If \[ \frac{1}{q + r}, \quad \frac{1}{r + p}, \quad \frac{1}{p + q} \] {are in A.P., then:}

The variance of the data \( 2, 4, 6, 8, 10 \) is:

The equation of the hyperbola with vertices at

\[ (0, \pm 6) \quad \text{and} \quad e = \frac{5}{3} \]

is:

The function \( f : \mathbb{R} \to \mathbb{R} \) defined by \( f(x) = x^2 + x \) is:

The relationship between \( a \) and \( b \) so that the function \( f(x) \) defined by

\[ f(x) = \begin{cases} ax + 1, & \text{if } x \leq 3 \\ bx + 3, & \text{if } x > 3 \end{cases} \]

is continuous at \( x = 3 \), is:

The local minimum value of the function \[ f(x) = 3 + |x|, \quad x \in \mathbb{R} \] is:

The sum of the first n terms of the series \[ 1^2 + 2.2^2 + 3^2 + 2.4^2 + 5^2 + 2.6^2 + \cdots \] {is} \[ \frac{n(n + 1)^2}{2} { when n is even. When n is odd the sum is} \]
The fourth, seventh, and tenth terms of a G.P. are \( p, q, r \) respectively, then:
The modulus of \( (1 + i\sqrt{3})(2 + 2i) \) / \( (\sqrt{3} - i) \) is:

The value of the integral \[ \int_0^{\frac{\pi}{2}} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} \, dx \] is:

The following determinant is equal to:

\[ \begin{vmatrix} \sin^2 x & \cos^2 x & 1 \\ \cos^2 x & \sin^2 x & 1 \\ -10 & 12 & 2 \end{vmatrix} \]

A parabola has the origin as its focus and the line \( x = 2 \)  as the directrix. Then the vertex of the parabola is at:

The area enclosed between the graph of \( y = x^3 \) { and the lines} \[ x = 0, \, y = 1, \, y = 8 { is:} \]
The distance between the parallel lines \[ 3x - 4y + 7 = 0 \quad {and} \quad 3x - 4y + 5 = 0 { is } \frac{a}{b}. { Value of } a + b { is:} \]
Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (-3, 1) and has eccentricity \( \sqrt{\frac{2}{5}} \) is:

For the parabola \( y^2 = -12x \), the equation of the directrix is  \( x = a \). The value of  \( a \) is:

What was the ratio between the ages of P and Q four years ago? I. The ratio between the present ages of P and Q is 3 : 4. II. The ratio between the present ages of Q and R is 4 : 5.