@prateek111 you can’t construct the binary tree with all the other options other than **c**.

**To solve this question we have to look at two things: 1) In a binary tree, a node may have at most 2 children. 2) To construct binary tree from the given sequences above, innermost parenthesis should be worked first**

**In Option A :**

( 4 5 6 7 ) is there, which says that node 4 has got three children, which is wrong for a binary tree, and also in the question, only ( X Y Z ) is defined, i.e. a node X can have at most 2 children, which will be the roots of subtrees Y and Z.

**In Option B :**

After working on innermost (2 3 4), where 2 is a node of the binary tree, 3 is left subtree of node 2 and 4 is right subtree of node 2. From this we get (1 2 5 6). Here 2 has come from the root of subtree ( 2 3 4 ). Now again we don’t have any definition for ( 1 2 5 6). Hence invalid

**In Option D :**

(4567) doesn’t follow the rule (XYZ).

**In Option C:**

After working on ( 2 3 4) and ( 5 6 7 ) we get ( 1 2 5 ) where 2 has come from the root of subtree ( 2 3 4 ) and 5 has come from the root of subtree ( 5 6 7 ). Now, in ( 1 2 5 ) node 1 is the root of the binary tree, and subtree with root 2 is the left subtree and subtree with root 5 is the right subtree at root node 1. Hence it is giving valid binary tree.

So according to the representation we will only be able to draw binary tree for **option c**.

**Now look at the figures you have constructed. Since you were able to draw binary tree for ****options a & d** they also seem to be a valid binary tree because in your figure, both these trees follow the Rule of at most 2 childern.

I hope you understood how to solve this question.