List of top Mathematics Questions asked in VITEEE

If the vertex of a parabola is $ (2, -1) $ and the equation of its directrix is \[ 4x - 3y = 21, \] then the length of its latus rectum is:

If \[ f(x) = \frac{x + |x|}{x} \] then the value of \[ \lim_{x \to 0} f(x) \] is:

In a certain code, BANKER is written as LFSCBO. How will CONFER be written in that code?

What was the cost price of the suitcase purchased by Samir? I. Samir got a 25 percent concession on the labelled price. II. Samir sold the suitcase for Rs. 2000 with 25 percent profit on the labelled price.

An accurate clock shows 8 O'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 20:00 (8 O'clock in the evening)?

The eccentricity of the curve $ 2x^2 + y^2 - 8x - 2y + 1 = 0 $ is:

The sum of the first n terms of the series $$ 1^2 + 2 \cdot 2^2 + 3^2 + 2 \cdot 4^2 + 5^2 + 2 \cdot 6^2 + \cdots $$ is $$ \frac{n(n + 1)^2}{2} \quad \text{when n is even. When n is odd the sum is} $$

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

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:

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:

The value of the definite integral

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

is:

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

The following determinant is equal to:

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

If $ 12\cot^2 \theta - 31\csc \theta + 32 = 0 $, then the value of $ \sin \theta $ is:

Coin is tossed till heads is obtained what is expectation of no. of coin tosses

Find the probability of getting the sum as a perfect square number when two dice are thrown together.

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 \[ 3x - 4y + 7 = 0 \quad {and} \quad 3x - 4y + 5 = 0 { is } \frac{a}{b}. { Value of } a + b { is:} \]

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:

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

For what value of $ k $, does the equation \[ 9x^2 + y^2 = k(x^2 - y^2 - 2x) \] represent the equation of a circle?

If \[ \frac{n + 2C8}{n - 2P4} = \frac{57}{16}, { then the value of } n { is:} \]

To fill 12 vacancies, there are 25 candidates of which five are from the scheduled caste. If 3 of the vacancies are reserved for scheduled caste candidates while the rest are open to all, then the number of ways in which the selection can be made is:

The point diametrically opposite to the point $ P(1, 0) $ { on the circle} \[ x^2 + y^2 + 2x + 4y - 3 = 0 { is:} \]

Let $ R $ be a relation on the set $ \mathbb{N} $ defined by \[ \{(x, y) \mid x, y \in \mathbb{N}, \, 2x + y = 41\}. \] {Then, $ R $ is:}