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Question #40620

Difficulty: 8/10 | 🟢 Free

The Question

Consider the binomial expansion of $(|x-2| + |x-5|)^{15}$ . If the $6^{\text{th}}$ term is the strictly numerically greatest term in the expansion, then the sum of all possible integral values of $x$ is:

Options

A.
17
B.
21
C.
13
D.
26

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

General Term Formulation|Numerically Greatest Term|Modulus Sign Dependency

Why This Question Is Tricky

Common Mistakes

This question tests the 'Modulus Sign Dependency' trap in the context of the Numerically Greatest Term (NGT).

Students typically apply the standard NGT ratio test and obtain an inequality for the terms.

However, the presence of modulus functions creates a non-linear ratio $|x-5|/|x-2|$ .

The lethal trap occurs when candidates blindly drop the modulus signs (assuming $x > 5$ ) and solve the simplified inequality, which yields only the interval $(7.5, 9.5)$ and the integers 8 and 9.

By failing to account for the sign flip inside the modulus, they completely miss the secondary valid regime $(3.875, 4.0625)$ generated by the negative branch, thereby missing the integer 4 and arriving at the trap answer 17.

Squaring the inequality or rigorous piecewise analysis is required to bypass this discontinuity.

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Binomial Theorem - Class 11
Concept	General Term Formulation
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free