A binary tree T has 20 leaves. The number of nodes in T having two children is ______.

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Official answer: 19

Trees

In any binary tree, the number of leaf nodes $L$ (nodes with degree 0) and the number of internal nodes with degree 2 ( $n_2$ ) are related by the property:

L = n_2 + 1

Given $L = 20$ :

n_2 = L - 1 = 20 - 1 = 19

Thus, the number of nodes in $T$ having two children is 19.

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This Trees previous year question is Q10 of the GATE CSE 2015 Set 2 paper. Find more GATE CSE PYQs on Trees in Programming and Data Structures, or browse all GATE CSE PYQs.

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Trees in GATE CSE

Trees has 13 GATE CSE PYQs across 11 papers from 2012 to 2026. 5 of them are 1-mark NAT questions like this one, and it is the only one in GATE CSE 2015 Set 2.

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.