List of top Mathematics Questions asked in VITEEE

The number of students who take both the subjects mathematics and chemistry is 30. This represents 10% of the enrolment in mathematics and 12% of the enrolment in chemistry. How many students take at least one of these two subjects?
Let \( f(x) \) be defined as: \[f(x) = \begin{cases} 3 - x, & x<-3 \\ 6, & -3 \leq x \leq 3 \\ 3 + x, & x>3 \end{cases}\]
Let \( \alpha \) be the number of points of discontinuity of \( f(x) \) and \( \beta \) be the number of points where \( f(x) \) is not differentiable. Then, \( \alpha + \beta \) is:
If \( f(x) \) defined as given below, is continuous on \( R \), then the value of \( a + b \) is equal to: % Function Definition \[f(x) = \begin{cases} \sin x, & x \leq 0 \\ x^2 + a, & 0<x<1 \\ bx + 3, & 1 \leq x \leq 3 \\ -3, & x>3 \end{cases}\]
Let \( n(A) = m \) and \( n(B) = n \), if the number of subsets of \( A \) is 56 more than that of subsets of \( B \), then \( m + n \) is equal to:
The probability that a card drawn from a pack of 52 cards will be a diamond or a king is:
The argument of the complex number \[ \left( \frac{i}{2} - \frac{2}{i} \right) \] is equal to:
The lines $$ p(p^2 + 1)x - y + q = 0 \quad {and} \quad (p^2 + 1)^2 x + (p^2 + 1)y + 2q = 0 $$ are perpendicular to a common line for:
Find the missing number in the sequence: \[ 285, 253, 221, 189, ? \]
The area of the parallelogram whose diagonals are \[ \mathbf{d_1} = \frac{3}{2} \hat{i} + \frac{1}{2} \hat{j} - \hat{k}, \quad \mathbf{d_2} = 2 \hat{i} - 6 \hat{j} + 8 \hat{k} \] is:
If \( |\mathbf{a}| = 3 \), \( |\mathbf{b}| = 4 \), then the value of \( \lambda \) for which \( \mathbf{a} + \lambda \mathbf{b} \) is perpendicular to \( \mathbf{a} - \lambda \mathbf{b} \) is:

If 

and $(A + B)^2 = A^2 + B^2$ then $x + y$ is:

For which toy category has there been a continuous increase in production over the years?
Eccentricity of ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ if it passes through point $(9, 5)$ and $(12, 4)$ is:
The angle between the two lines: \[ \frac{x + 1}{2} = \frac{y + 3}{2} = \frac{z - 4}{-1} \] \[ \frac{x - 4}{1} = \frac{y + 4}{2} = \frac{z + 1}{2} \] is:
The particular solution of \[ \log \frac{dy}{dx} = 3x + 4y, \quad y(0) = 0 \] is:
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:
What is the percentage drop in the production of Ludo from 1992 to 1994?
Evaluate the integral: \[ I = \int \frac{\sin^2 x - \cos^2 x}{\sin^2 x \cos^2 x} dx \]
The derivative of \[ \sin^{-1} \left(\frac{2x}{1 + x^2} \right) \] with respect to \[ \cos^{-1} \left(\frac{1 - x^2}{1 + x^2} \right) \] is equal to:
Evaluate the definite integral: \[ I = \int_{0}^{\frac{\pi}{2}} (\sqrt{\tan x} + \sqrt{\cot x})dx \]
If \[ \left| \frac{\sec(x - y)}{\sec(x + y)} \right| = a \] then \( \frac{dy}{dx} \) is:
Bag P contains 6 red and 4 blue balls, and Bag Q contains 5 red and 6 blue balls. A ball is transferred from Bag P to Bag Q, and then a ball is drawn from Bag Q. What is the probability that the ball drawn is blue?
The sum of the series \[ \frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \dots \] up to 15 terms is:
The equation of the circle with centre (0,2) and radius 2 is \[ x^2 + y^2 - my = 0. \] The value of \( m \) is:
For the binary operation defined on \( \mathbb{R} - \{1\} \) such that: \[ a b = \frac{a}{b + 1} \] which of the following is true?