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Question #40630

Difficulty: 8/10 | 🟢 Free

The Question

Let $f(x) = |x - 2|^{17} + |x + 2|^{17}$ . For $x \in (-2, 2)$ , $f(x)$ can be expressed as a polynomial $P(x) = \sum_{r=0}^{17} C_r x^r$ . Find the value of $r$ for which $C_r$ is maximum.

Options

A.
4
B.
5
C.
6
D.
8

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

Coefficient of x^r in Expansion|Greatest Binomial Coefficient|Modulus Sign Dependency

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to handle modulus sign dependency in binomial expansions.

A common trap is to ignore the domain $x \in (-2, 2)$ and incorrectly expand $|x - 2|^{17}$ as $(x - 2)^{17}$ .

This flawed approach yields the polynomial $Q(x) = (x - 2)^{17} + (x + 2)^{17}$ , where the surviving terms have odd powers of $x$ , leading to an incorrect maximum coefficient at $r = 5$ .

By correctly applying the modulus definition $|x - 2| = 2 - x$ , the surviving terms shift to even powers of $x$ , changing the polynomial entirely and shifting the maximum coefficient to $r = 6$ .

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Binomial Theorem - Class 11
Concept	Coefficient of x^r in Expansion
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free