The height of a binary tree is the maximum number of edges in any root to leaf path. The maximum number of nodes in a binary tree of height $h$ is:
$2^h -1$
$2^{h-1} -1$
$2^{h+1} -1$
$2^{h+1}$
At maximum tree is given as above
So maximum height = 2 (15 - > 10 -> 8) or other all are same height
Put h = 2 in option and find number of nodes
A- 2^{2} -1 = 3 wrong
B- 2^{1}-1 = 1 wrong
C- 2^{3}-1 = 7 correct
D- 2^{3} = 8 wrong
SO option C is correct option
height H=0 ( only root node ) , no of node N=1=2^{0}
H=1 , N=2^{1}
... so on
total =2^{0 }+2^{1}+2^{2}+.......2^{H }=2^{H+1}-1
Ans is C
Gatecse
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