List of top Mathematics Questions on inequalities asked in VITEEE

For the binary operation defined on R−{1} \mathbb{R} - \{1\} such that: ab=ab+1 a b = \frac{a}{b + 1} which of the following is true?
If ∣sec⁡(x−y)sec⁡(x+y)∣=a \left| \frac{\sec(x - y)}{\sec(x + y)} \right| = a then dydx \frac{dy}{dx} is:
The number of nonzero terms in the expansion of (1+32x)9+(1−32x)9 (1 + 3\sqrt{2}x)^9 + (1 - 3\sqrt{2}x)^9 is:
The sum of the series 11+2+12+3+13+4+… \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 x2+y2−my=0. x^2 + y^2 - my = 0. The value of m m is:
Evaluate the definite integral: I=∫0π2(tan⁡x+cot⁡x)dx I = \int_{0}^{\frac{\pi}{2}} (\sqrt{\tan x} + \sqrt{\cot x})dx
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 derivative of sin⁡−1(2x1+x2) \sin^{-1} \left(\frac{2x}{1 + x^2} \right) with respect to cos⁡−1(1−x21+x2) \cos^{-1} \left(\frac{1 - x^2}{1 + x^2} \right) is equal to:
Evaluate the integral: I=∫sin⁡2x−cos⁡2xsin⁡2xcos⁡2xdx I = \int \frac{\sin^2 x - \cos^2 x}{\sin^2 x \cos^2 x} dx
If f(x)=x+∣x∣x f(x) = \frac{x + |x|}{x} then the value of lim⁡x→0f(x) \lim_{x \to 0} f(x) is:
The solution set of the inequality 37−(3x+5)≥9x−8(x−3)is: 37 - (3x + 5) \geq 9x - 8(x - 3) { is:}
The equations of the lines which cut off an intercept 1 from the y-axis and are equally inclined to the axes are:
The distance between the parallel lines 3x−4y+7=0and3x−4y+5=0isab.Valueofa+bis: 3x - 4y + 7 = 0 \quad {and} \quad 3x - 4y + 5 = 0 { is } \frac{a}{b}. { Value of } a + b { is:}

A parabola has the origin as its focus and the line x=2 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 25 \sqrt{\frac{2}{5}} is:

The relationship between a a and b b so that the function f(x) f(x) defined by

f(x)={ax+1,if x≤3bx+3,if x>3 f(x) = \begin{cases} ax + 1, & \text{if } x \leq 3 \\ bx + 3, & \text{if } x > 3 \end{cases}

is continuous at x=3 x = 3 , is:

If the system of linear equations x+ky+3z=0,3x+ky−2z=0,2x+4y−3z=0 x + ky + 3z = 0, \quad 3x + ky - 2z = 0, \quad 2x + 4y - 3z = 0 has a non-zero solution  (x,y,z) (x, y, z) , then xzy2 \frac{xz}{y^2} is equal to:

The locus of a point that is equidistant from the lines x+y−22=0andx+y−2=0is: x + y - 2\sqrt{2} = 0 \quad {and} \quad x + y - \sqrt{2} = 0 { is:}

The equation of the hyperbola with vertices at

(0,±6)ande=53 (0, \pm 6) \quad \text{and} \quad e = \frac{5}{3}

is:

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

In a certain code, BANKER is written as LFSCBO. How will CONFER be written in that code?
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?
If | x2−x−6∣=x+2x^2 - x - 6 | = x + 2, then the values of xx are