GATE CS 2004 Q52 — File Organization and Indexing (B and B+ Trees)

In a $\text{B}^+$ tree, an internal node of order $P$ (where $P$ is the maximum number of child pointers) contains:

• At most $P$ child pointers
• At most $P - 1$ search key values

Let:

• $P$ be the order of the internal node.
• $V_p = 6\text{ bytes}$ (size of a child pointer).
• $V_k = 14\text{ bytes}$ (size of a search key value).
• $B = 512\text{ bytes}$ (block size).

To fit the internal node within a single disk block, the total size must satisfy the inequality:

Substituting the given values:

Since the order $P$ must be an integer, the maximum possible value is $P = 26$.

Therefore, the order of the internal node is 26 (Option C).