List of top Mathematics Questions asked in VITEEE

In a culture, the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000 if the rate of growth of bacteria is proportional to the number present?
If the angle \( \theta \) between the line \[ \frac{x + 1}{2} = \frac{z - 2}{2} = \frac{y + 4}{\sqrt{n}} \] and the plane \( 2x - y + z + 4 = 0 \) is such that \( \sin \theta = \frac{1}{3} \), then the value of \( n \) is:
The value of \( \tan^{-1} (1) + \tan^{-1} (0) + \tan^{-1} (2) + \tan^{-1} (3) \) is equal to:
The angle of intersection of the curve \( y = x^2 \), \( dy = 7 - x^2 \) at \( (1, 1) \) is:
The value of \( (1 + i)^4 \) is:
The relation \( R \) defined on the set \( A = \{1, 2, 3, 4, 5\} \) by \( R = \{(x, y) : |x^2 - y^2|<16 \} \) is given by:
The angle formed by the positive Y-axis and the tangent to \( y = x^2 + 4x - 17 \) at \( (2, -3) \) is:
\[ \int \frac{2dx}{(e^x + e^{-x})^2} = ? \]
Area bounded by the curve \( y = \log x \) and the coordinate axes is:
If \( (-4, 5) \) is one vertex and \( 7x - y + 8 = 0 \) is one diagonal of a square, then the equation of second diagonal is:
Which of the following is an infinite set?
The domain of the function \[ \sqrt{2x - 5x^2 + 6} + \sqrt{2x + 8 - x^2} \] is:
If \( \mathbf{a} = 2i - 2j + k \) and \( \mathbf{c} = -i + 2k \), then \( \mathbf{a} \times \mathbf{c} \) is equal to:
Let \[ \int \frac{x^{1/2}}{\sqrt{1 - x^3}} \, dx = \frac{3}{3} \, g(x) + C \] then
\( P = Q \) can also be written as:
The shortest distance between the lines \( x = y + 2 \), \( z = 6x - 6 \) and \( x + 1 = 2y = -12z \) is:
If \( f(x) = \frac{x}{1 + x^2} + \frac{x}{(1 + x^2)^2} + \cdots \) to infinity, then at \( x = 0, f(x) \)
If the tangent at \( P(1, 1) \) on \( y^2 = x(2 - x) \) meets the curve again at \( Q \), then \( Q \) is:
The equations \( 2x + 3y + 4 = 0 \), \( 3x + 4y + 6 = 0 \), and \( 4x + 5y + 8 = 0 \) are:
Radius of the circle \( (x + 5)^2 + (y - 3)^2 = 36 \) is:
The value of \( c \) in Rolle’s Theorem for the function \( f(x) = e^x \sin x, x \in [0, \pi] \) is:
A die is thrown $10$ times, the probability that an odd number will come up at least one time is
Let \( f \) be the function defined by \[ f(x) = \begin{cases} x^2 - 1, & x \neq 1 \\ x^2 - 2|x-1|^{-1}, & x = 1 \end{cases} \] The function is continuous at:

The equation of the plane which bisects the angle between the planes \[ 3x - 6y + 2z + 5 = 0 \quad \text{and} \quad 4x - 12y + 32z - 3 = 0 \] \(\text{which contains the origin is:}\)

If \[ \left( \frac{a}{b} \right)^2 + \left( \frac{b}{a} \right)^2 = 676, \quad \left| \mathbf{b} \right| = 2, \quad \text{then} \left| \mathbf{a} \right| \(\text{ is equal to:}\)