List of top Mathematics Questions asked in VITEEE

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:

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:

If the function \[ f(x) = \begin{cases} 1, & x \leq 2 \\ ax + b, & 2 < x < 4 \\ 7, & x \geq 4 \end{cases} \] is continuous at \( x = 2 \) and \( x = 4 \), then the values of \( a \) and \( b \) are:

For the binary operation defined on \( \mathbb{R} - \{1\} \) such that: \[ a b = \frac{a}{b + 1} \] which of the following is true?

Find the missing number in the sequence: \[ 285, 253, 221, 189, ? \]

The domain of the function \[ f(x) = \frac{1}{\sqrt{9 - x^2}} \] is:

The number of distinct real roots of the equation: \[ x^7 - 7x - 2 = 0 \] is:

Evaluate: \[ \cos^{-1} \frac{1}{2} + \sin^{-1} (1) + \tan^{-1} \frac{1}{\sqrt{3}} \]

The number of nonzero terms in the expansion of \[ (1 + 3\sqrt{2}x)^9 + (1 - 3\sqrt{2}x)^9 \] is:

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:

If \[ \left| \frac{\sec(x - y)}{\sec(x + y)} \right| = a \] then \( \frac{dy}{dx} \) is:

The particular solution of \[ \log \frac{dy}{dx} = 3x + 4y, \quad y(0) = 0 \] 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 equation of the circle with centre (0,2) and radius 2 is \[ x^2 + y^2 - my = 0. \] The value of \( m \) is:

Evaluate the integral: \[ I = \int \frac{\sin^2 x - \cos^2 x}{\sin^2 x \cos^2 x} dx \]

The minimum value of the function \[ y = x^4 - 2x^2 + 1 \] in the interval \( \left[\frac{1}{2}, 2 \right] \) is:

Evaluate the definite integral: \[ I = \int_{0}^{\frac{\pi}{2}} (\sqrt{\tan x} + \sqrt{\cot x})dx \]