Aspire's Library
A Place for Latest Exam wise Questions, Videos, Previous Year Papers,
Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Consider the following statements:
A. The number of labelled binary trees possible with $n$ nodes is $\frac{(2n)!}{(n+1)!}$
B. The number of binary search trees possible with $n$ nodes is $\frac{(2n)!}{(n+1)!n!}$
C. The number of unlabeled binary trees possible with $n$ nodes is $\frac{C(2n,n)}{(n+1)!}$
D. The number of simple, undirected and labelled graphs possible with $n$ vertices is $2^{\frac{n(n-1)}{2}}$
Solution
A is correct.
Number of labelled binary trees with $n$ nodes:
$=C_n\times n!$
$=\frac{(2n)!}{(n+1)!n!}\times n!$
$=\frac{(2n)!}{(n+1)!}$
B is correct.
Number of binary search trees with $n$ nodes:
$=C_n=\frac{(2n)!}{(n+1)!n!}$
C is incorrect.
Correct formula for unlabeled binary trees is:
$C_n=\frac{1}{n+1}C(2n,n)$
D is correct.
Number of simple undirected labelled graphs:
$=2^{\frac{n(n-1)}{2}}$
So, correct option is:
$\boxed{(b)\ \text{A, B and D are only correct}}$
Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
Ask Your Question or Put Your Review.
