The solution of $\left|x+\frac{1}{x}\right|>2$ is

Important Questions on Inequalities and Modulus

EASY

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 1 - Inequalities and Modulus>DPP>Q 13

The solution of the inequality $\frac{|x+2|-\left|x\right|}{\sqrt{8-x^3}}\ge 0$ is

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 1 - Inequalities and Modulus>DPP>Q 14

If $\left|\frac{12x}{4x^2+9}\right|\le 1$, then

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 1 - Inequalities and Modulus>DPP>Q 15

Let $a, b, c$ and $d$ be real numbers, such that $|a-b|=2, |b-c|=3$ and $|c-d|=4$. Then, the sum of all possible values of $|a-d|$ is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 1 - Inequalities and Modulus>DPP>Q 16

The number of solutions of the equations $\sqrt{x^2}-\sqrt{(x-1{)}^2}+\sqrt{(x-2{)}^2}=\sqrt{5}$ is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 1 - Inequalities and Modulus>DPP>Q 17

If $\left|x^2-2x-8\right|+\left|x^2+x-2\right|=3|x+2|$, then the set of all real values of $x$ is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 1 - Inequalities and Modulus>DPP>Q 18

The number of integers satisfying the equation $\left|x\right|+\left|\frac{4-x^2}{x}\right|=\left|\frac{4}{x}\right|$ is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 1 - Inequalities and Modulus>DPP>Q 19

The equation $\left|2ax-3\right|+\left|ax+1\right|+\left|5-ax\right|=\frac{1}{2}$ possesses

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 1 - Inequalities and Modulus>DPP>Q 20

The set of values of $x$ satisfying $\left|\frac{x^2-5x+4}{x^2-4}\right|\le 1$ is: