GATE CS 2025 Set 1 Q11 — File Organization and Indexing (B and B+ Trees)

A $B^+$ tree with $5$ nodes and a maximum capacity of $3$ keys per node must have a $2$-level structure consisting of:

• $1$ Root node containing $3$ keys (fully occupied).
• $4$ Leaf nodes containing the data keys.

When the value $23$ is inserted into its corresponding leaf node:

1. The target leaf node is already full (containing $3$ keys), causing it to split into two nodes.
2. This split requires pushing/copying a key up to the parent (the root node).
3. Since the root node is also completely full with $3$ keys, it overflows and must also split.
4. Splitting the root node creates a new root, which increases the height of the tree by $1$.

Thus, at least one node splits (Option B) and the height of the tree increases (Option D).