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Question #40428

Difficulty: 8/10 | 🟢 Free

The Question

Let $S$ be the set of all integers $x \in [0, 15]$ satisfying the inequality $\left[ \frac{2x^2 - 7x + 5}{x^2 - 3x - 4} \right] \ge 2$ where $[t]$ denotes the greatest integer less than or equal to $t$ . Find the sum of all elements in $S$ .

Options

A.
81
B.
87
C.
91
D.
48

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

Greatest Integer Function (GIF)|Maximum/Minimum of Quadratic Expressions|Cross Multiplication Trap

Why This Question Is Tricky

Common Mistakes

This question tests the 'Cross Multiplication Trap' within the context of the Greatest Integer Function.

Students often correctly deduce that $[y] \ge 2 \implies y \ge 2$ , but then incorrectly cross-multiply the denominator $x^2 - 3x - 4$ without considering its sign.

This illegal operation leads to the erroneous linear inequality $2x^2 - 7x + 5 \ge 2x^2 - 6x - 8 \implies x \le 13$ .

This traps the student into including spurious integers like 0, 1, 2, and 3, where the denominator is actually negative (which would have flipped the inequality sign).

By forcing the student to evaluate the sum of the integers, the trap directly leads to the incorrect options 91 or 87.

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Relations and Functions - Class 11
Concept	Greatest Integer Function (GIF)
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free