Inequalities is an important topic in the Mathematics section in VITEEE exam. Practising this topic will increase your score overall and make your conceptual grip on VITEEE exam stronger.
This article gives you a full set of VITEEE PYQs for Inequalities with explanations for effective preparation. Practice of VITEEE Mathematics PYQs including Inequalities questions regularly will improve accuracy, speed, and confidence in the VITEEE 2026 exam.
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VITEEE PYQs for inequalities with Solutions
1.
If \[ f(x) = \frac{x + |x|}{x} \] then the value of \[ \lim_{x \to 0} f(x) \] is:- 0
- 2
- Does not exist
- None of these
2.
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:
-10
- -30
- 30
10
3.
For the binary operation defined on \( \mathbb{R} - \{1\} \) such that: \[ a b = \frac{a}{b + 1} \] which of the following is true?- Not associative
- Commutative
- Not commutative
- Both (A) and (B)
4.
The number of nonzero terms in the expansion of \[ (1 + 3\sqrt{2}x)^9 + (1 - 3\sqrt{2}x)^9 \] is:- 2
- 3
- 4
- 5
5.
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:- \( 1 \)
- \( -1 \)
- \( 2 \)
- None of these
6.
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?- South-West
- North-West
- South
- South-East
7.
The equations of the lines which cut off an intercept 1 from the y-axis and are equally inclined to the axes are:- \( x - y + 1 = 0, x + y + 1 = 0 \)
- \( x - y - 1 = 0, x + y - 1 = 0 \)
- \( x - y - 1 = 0, x + y + 1 = 0 \)
- None of these
8.
Evaluate the definite integral: \[ I = \int_{0}^{\frac{\pi}{2}} (\sqrt{\tan x} + \sqrt{\cot x})dx \]- \( \frac{\pi}{\sqrt{2}} \)
- \( \pi \sqrt{2} \)
- \( \frac{\pi}{2} \)
- \( \sqrt{2} \pi \)
9.
Evaluate the integral: \[ I = \int \frac{\sin^2 x - \cos^2 x}{\sin^2 x \cos^2 x} dx \]- \( \tan x + \cot x + C \)
- \( \csc x + \sec x + C \)
- \( \tan x + \sec x + C \)
- \( \tan x + \csc x + C \)
10.
If \[ \left| \frac{\sec(x - y)}{\sec(x + y)} \right| = a \] then \( \frac{dy}{dx} \) is:- \( -\frac{y}{x} \)
- \( \frac{x}{y} \)
- \( -\frac{x}{y} \)
- \( \frac{y}{x} \)
11.
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:- 1
- 2
- 3
- 4
12.
A parabola has the origin as its focus and the line \( x = 2 \) as the directrix. Then the vertex of the parabola is at:
- \( (0, 2) \)
- \( (1, 0) \)
- \( (0, 1) \)
- \( (2, 0) \)
13.
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:- \( 5x^2 + 3y^2 - 48 = 0 \)
- \( 3x^2 + 5y^2 - 15 = 0 \)
- \( 5x^2 + 3y^2 - 32 = 0 \)
- \( 3x^2 + 5y^2 - 32 = 0 \)
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14.
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?- \( \frac{7}{15} \)
- \( \frac{8}{15} \)
- \( \frac{4}{19} \)
- \( \frac{8}{19} \)
15.
The equation of the circle with centre (0,2) and radius 2 is \[ x^2 + y^2 - my = 0. \] The value of \( m \) is:- 1
- 2
- 4
- 3
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