###### GATE 2007

October 24, 2023###### GATE 2007

October 24, 2023# GATE 2007

Question 13 |

The maximum number of binary trees that can be formed with three unlabeled nodes is:

1 | |

5 | |

4 | |

3 |

Question 13 Explanation:

Total number of binary trees possible for n nodes is

C(n) = (2n)!/(n+1)!n!

C(n) = (2(3))!/(3+1)!3! = 6×5×4×3×2×1/4×3×2×1×3×2 = 5

Total no. of possible trees is 5.

Total = 5

C(n) = (2n)!/(n+1)!n!

C(n) = (2(3))!/(3+1)!3! = 6×5×4×3×2×1/4×3×2×1×3×2 = 5

Total no. of possible trees is 5.

Total = 5

Correct Answer: B

Question 13 Explanation:

Total number of binary trees possible for n nodes is

C(n) = (2n)!/(n+1)!n!

C(n) = (2(3))!/(3+1)!3! = 6×5×4×3×2×1/4×3×2×1×3×2 = 5

Total no. of possible trees is 5.

Total = 5

C(n) = (2n)!/(n+1)!n!

C(n) = (2(3))!/(3+1)!3! = 6×5×4×3×2×1/4×3×2×1×3×2 = 5

Total no. of possible trees is 5.

Total = 5

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