GATE CSE 2025 Session 2 Q13: Internal nodes in a full binary tree with n nodes

Consider a binary tree $T$ in which every node has either zero or two children. Let $n > 0$ be the number of nodes in $T$ .

Which ONE of the following is the number of nodes in $T$ that have exactly two children?

Try it: multiple choice: exactly one correct option

Wrong answer costs 1/3 mark in GATE.

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Answer: B (official GATE 2025 final answer key)

Concept used: In a full binary tree, leaves = internal nodes + 1.

First step: Let $i$ be the internal nodes; then there are $i + 1$ leaves and $n = 2i + 1$ .

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Source: official GATE 2025 Session 2 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key