List of top Mathematics Questions asked in VITEEE

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 distance of the point \( (-5, -5, -10) \) from the point of intersection of the line \[ r = -2i - j + 2k + \lambda(3i + 4j + 2k) \] and the plane \( r \cdot (i - j + k) = 5 \) is:

\[ \int_{\log \sqrt{n}}^{\log \sqrt{r}} 2x \sec^2\left( \frac{1}{3} \cdot 2x \right) \, dx \] is equal to:

What is the angle between the two straight lines \[ y = (2 - \sqrt{3})x + 5 \quad \text{and} \quad y = (2 + \sqrt{3})x - 7? \]

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?

The value of \( \tan^{-1} (1) + \tan^{-1} (0) + \tan^{-1} (2) + \tan^{-1} (3) \) is equal to:

Area bounded by the curve \( y = \log x \) and the coordinate axes 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 value of \( (1 + i)^4 \) is:

\[ \int \frac{2dx}{(e^x + e^{-x})^2} = ? \]

The angle of intersection of the curve \( y = x^2 \), \( dy = 7 - x^2 \) at \( (1, 1) \) is:

The angle formed by the positive Y-axis and the tangent to \( y = x^2 + 4x - 17 \) at \( (2, -3) \) 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:

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:

\( P = Q \) can also be written as:

Which of the following is an infinite set?

Let \[ \int \frac{x^{1/2}}{\sqrt{1 - x^3}} \, dx = \frac{3}{3} \, g(x) + C \] then

The equations \( 2x + 3y + 4 = 0 \), \( 3x + 4y + 6 = 0 \), and \( 4x + 5y + 8 = 0 \) are:

If the tangent at \( P(1, 1) \) on \( y^2 = x(2 - x) \) meets the curve again at \( Q \), then \( Q \) is:

Radius of the circle \( (x + 5)^2 + (y - 3)^2 = 36 \) is:

If \( f(x) = \frac{x}{1 + x^2} + \frac{x}{(1 + x^2)^2} + \cdots \) to infinity, then at \( x = 0, f(x) \)

The shortest distance between the lines \( x = y + 2 \), \( z = 6x - 6 \) and \( x + 1 = 2y = -12z \) 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