How many different binary trees are possible with 'n' nodes?

This question was previously asked in
UGC NET Computer Science (Paper 2) 11 March 2023 Official Paper
View all UGC NET Papers >
  1. n-1
  2. 2n - 1
  3. 2n
  4. 2n - n

Answer (Detailed Solution Below)

Option 4 : 2n - n
Free
UGC NET Paper 1: Held on 21st August 2024 Shift 1
10.9 K Users
50 Questions 100 Marks 60 Mins

Detailed Solution

Download Solution PDF

The correct answer is 2n - n

EXPLANATION:

  • A binary tree allows for a maximum of two child nodes per parent node.
  • The formula (2n - n) can be used to ascertain the number of different binary trees that can be drawn given 'n' number of nodes.
  • As an example, when 'n' is equal to 1, applying the formula yields (21 - 1), which equals 1.
  • As an example, when 'n' is equal to 2, applying the formula yields (22 - 1), which equals 2.
  • As an example, when 'n' is equal to 3, applying the formula yields (23 - 1), which equals 5.
  • Therefore, when 'n' nodes, we can draw (2n - n) unique binary tree.


F1 Savita ENG 22-12-23 D03

Mistake PointsAbove question data is ambiguous so official answer key drop this question. We have updated the question. 

Latest UGC NET Updates

Last updated on Jun 12, 2025

-> The UGC NET June 2025 exam will be conducted from 25th to 29th June 2025.

-> The UGC-NET exam takes place for 85 subjects, to determine the eligibility for 'Junior Research Fellowship’ and ‘Assistant Professor’ posts, as well as for PhD. admissions.

-> The exam is conducted bi-annually - in June and December cycles.

-> The exam comprises two papers - Paper I and Paper II. Paper I consists of 50 questions and Paper II consists of 100 questions. 

-> The candidates who are preparing for the exam can check the UGC NET Previous Year Papers and UGC NET Test Series to boost their preparations.

More Tree Questions

Get Free Access Now
Hot Links: teen patti all app teen patti lotus teen patti chart teen patti 100 bonus