Let $${S_1} = \left\{ {x \in R - \{ 1,2\} :{{(x + 2)({x^2} + 3x + 5)} \over { - 2 + 3x - {x^2}}} \ge 0} \right\}$$ and $${S_2} = \left\{ {x \in R:{3^{2x}} - {3^{x + 1}} - {3^{x + 2}} + 27 \le 0} \right\}$$. Then, $${S_1} \cup {S_2}$$ is equal to :

$$( - \infty , - 2] \cup [1,2]$$

JEE Main · Quantitative Aptitude

JEE Main Inequalities Questions with Answers and Solutions

Solve real inequalities questions with step-by-step solutions — free preview, no login required.

Inside view · free preview

JEE Main Inequalities practice

Topic-wise practice4 questions 5 min

1Preview question 1 of 4 · instant answer reveal

STATEMENT - 1 : For every natural number

n \ge 2,

${1 \over {\sqrt 1 }} + {1 \over {\sqrt 2 }} + ........ + {1 \over {\sqrt n }} > \sqrt n .

$ STATEMENT - 2 : For every natural number $

n \ge 2,

$, $

\sqrt {n\left( {n + 1} \right)} < n + 1.

Choose one answer to reveal the solution.

This is a 4-question preview. The full 4-question timed test opens after free signup.

What visitors can use on this page

The preview questions and their step-by-step solutions are public. The full inequalities test, saved progress, performance reports, Maya AI chat, friend battles and the personalised plan open the signup modal.

JEE Main Inequalities practice FAQ

Can I solve these JEE Main Inequalities questions for free?

Yes. The preview questions, answers and step-by-step solutions on this page are free to read without any login.

What opens after free signup?

Signup unlocks the full JEE Main Inequalities topic test, saved attempts, performance analysis, Maya AI doubt-chat, friend challenges and a personalised study plan.

Are the solutions explained step by step?

Yes. Every question here carries a worked solution so you understand the method, not just the final answer.

Prepare together, not alone

JEE Main Inequalities practice

What visitors can use on this page

JEE Main Inequalities practice FAQ

Prepare together, not alone

JEE Main Inequalities practice

What visitors can use on this page

JEE Main Inequalities practice FAQ