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The number of possible binary trees with $4$ nodes is

1. $12$
2. $13$
3. $14$
4. $15$

Since its not mentioned whether the nodes are labelled or not, so taking un-labelled nodes in general,

maximum number of binary trees = 2nCn / n+1

This gives 14 binary trees which is option C

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$\textit{There is one binary tree with one node. }$

$\textit{There are two differently shaped trees with two nodes. }$

$\textit{There are 14 different (shaped) binary trees with four nodes.}$

$\textit{These different trees are shown below.}$

https://www.geeksforgeeks.org/total-number-of-possible-binary-search-trees-with-n-keys/

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