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GATE DA 2026 Q41: B+ tree root after inserting 3

Question

Consider a B+ Tree where the maximum number of key values in each leaf node is 2 and the maximum number of pointers in each non-leaf node is 3. Let the content of the B+ Tree be as shown in the figure.

B+ tree: root with keys 5 and 8; leaves [1, 5], [7, 8], [9, 12] linked left to right, last leaf pointing to NULL
Tap the figure to enlarge

Which of the following options denotes the key value(s) stored in the root node after inserting a key value 3 in the given B+ Tree?

Try it: multiple choice: exactly one correct option

Select one option
Wrong answer costs 2/3 mark in GATE.
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Answer: A (official GATE 2026 final answer key)

Concept used: B+ tree insertion: an overfull leaf splits and pushes a separator up; an overfull internal node splits and pushes its middle key up.

First step: 3 goes into leaf [1, 5], which overflows and splits; the root then needs 4 pointers (3 keys), so it splits around its middle key.

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Source: official GATE 2026 DA question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key

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