Official PYQ · 2002Q2.23File Organization and Indexing (B and B+ Trees)MCQ1 mark

GATE CS 2002 Q2.23 — File Organization and Indexing (B and B+ Trees)

A $B^+$ - tree index is to be built on the Name attribute of the relation STUDENT. Assume that all the student names are of length $8$ bytes, disk blocks are of size $512$ bytes, and index pointers are of size $4$ bytes. Given the scenario, what would be the best choice of the degree (i.e. number of pointers per node) of the $B^+$ - tree?

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Answer: C

To find the best choice of the degree (number of pointers per node, $p$ ) of the $B^+$ -tree, we need to ensure that the total size of an internal node does not exceed the disk block size.

Let:

Disk block size ( $B$ ) = $512$ bytes
Key size ( $K$ ) = $8$ bytes (length of student name)
Pointer size ( $P$ ) = $4$ bytes

An internal node of a $B^+$ -tree with degree $p$ contains:

$p$ pointers
$p - 1$ keys

The total size of the node must satisfy the following inequality:

p \cdot P + (p - 1) \cdot K \le B

Substituting the given values into the inequality:

p \cdot 4 + (p - 1) \cdot 8 \le 512

4p + 8p - 8 \le 512

12p \le 520

p \le \frac{520}{12} \approx 43.33

Since the degree $p$ must be an integer, the maximum possible value is:

p = 43

Therefore, the best choice for the degree of the $B^+$ -tree is 43.

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Published 10 Oct 2026

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