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Question #40536

Difficulty: 8/10 | 🟢 Free

The Question

Find the set of all real values of $x$ satisfying the inequality: $\frac{x^2 - x - 2}{[x]} \ge x + 1$ where $[ \cdot ]$ denotes the greatest integer function.

Options

A.
$[-1, 0)$
B.
$\emptyset$
C.
$(-\infty, -1] \cup [1, \infty)$
D.
$[1, \infty)$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Specialist

Targeted practice for niche, high-difficulty concepts that frequently appear in JEE Advanced exams.

Concepts Behind This Question

Denominator Restriction|Cross Multiplication Trap|Greatest Integer Function Traps

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to handle inequalities involving variable denominators inside a Greatest Integer Function (GIF).

The primary trap is the impulse to cross-multiply or cancel the common factor $(x+1)$ without considering its sign, which leads to the empty set.

Furthermore, students must recognize that $x - [x] = \{x\}$ , making the factored term $\{x\} - 2$ strictly negative.

Failing to flip the inequality sign when dividing by this negative term leads directly to the trap option $(-\infty, -1] \cup [1, \infty)$ .

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Linear Inequalities - Class 11
Concept	Denominator Restriction
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free