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Question #41289

Difficulty: 8/10 | 🟢 Free

The Question

Let $A = [a_{i,j}]$ be a $15 \times 15$ matrix defined as: $a_{i,j} = \begin{cases} 0 & \text{if } i \neq j \\ 2^{\left| \frac{1}{30} - \frac{1}{i(i+1)} \right|} & \text{if } i = j \end{cases}$ The value of $48 \log_2 (\det A)$ is equal to:

Options

A.
21
B.
43
C.
48
D.
86

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

Triangular/Diagonal Matrix Shortcut|Method of Differences|Modulus Sign Dependency

Why This Question Is Tricky

Common Mistakes

This question tests the evaluation of the determinant of a diagonal matrix whose entries form a series under a modulus function.

The core trap is the 'Modulus Sign Dependency'.

Students often blindly apply the Method of Differences to the entire sequence without checking for critical points where the argument of the absolute value changes sign.

By setting the constant term to $1/30$ , which equals the 5th term of the telescoping sequence, the sum must be split into two distinct piecewise intervals.

Ignoring this critical point and evaluating the sum directly yields the incorrect trap answer of 21.

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Determinants - Class 12
Concept	Triangular/Diagonal Matrix Shortcut
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free