List of top Mathematics Questions on inequalities asked in VITEEE

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

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

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

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

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:

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

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

The equations of the lines which cut off an intercept 1 from the y-axis and are equally inclined to the axes are:

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

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:

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:

Kailash faces towards north. Turnings to his right, he walks 25 metres. He then turns to his left and walks 30 metres. Next, he moves 25 metres to his right. He then turns to the right again and walks 55 metres. Finally, he turns to the right and moves 40 metres. In which direction is he now from his starting point?

The solution set of the inequality \[ 37 - (3x + 5) \geq 9x - 8(x - 3) { is:} \]

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

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:

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

The equation of the hyperbola with vertices at

\[ (0, \pm 6) \quad \text{and} \quad e = \frac{5}{3} \]

is:

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

The locus of a point that is equidistant from the lines \[ x + y - 2\sqrt{2} = 0 \quad {and} \quad x + y - \sqrt{2} = 0 { is:} \]

Which of the following inequality is true for $ x>0 $?

If | $x^2 - x - 6 | = x + 2$, then the values of $x$ are