UGC NET Computer Science July 2018 - II Question 29

Question 29

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29. A 5-ary tree is tree in which every internal node has exactly 5 children. The number of left (leaf) nodes in such a tree with 8 internal nodes will be :

Options:

1. (1) 30
2. (2) 33
3. (3) 45
4. (4) 125

Answer : (2) 33

Explanation Question 29

The question ask about total number of leaf nodes in 5-ary tree with 8 internal nodes

In above image you can check that number of leaf nodes are 33 and internal nodes are 8. Each internal nodes has exactly 5 children.

You can derive formula to calculate leaf and internal nodes in such complete tree.

In a complete n-ary tree,
Number Of leaf nodes, L = ( n − 1) ∗ I + 1 where L is No. of leaves and I is No. of Internel nodes

Here n = 5, I = 8
Therefore,
Number Of leaf nodes, L = ( n − 1) ∗ I + 1
= (5 - 1) * 8 + 1
= 4 * 8 + 1
= 33

You can also check this video here

According to UGC NET Answer key.
This question remains cancelled and marks awarded to all candidates appeared in the test.

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