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which is correct option? does answer depends on the definition of levels?

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Simple. Given answer is correct. Why are you confused ?  Root lies at 0th level or 1st level tht does not matter. No need of definition.
They have given NUMBER of levels...

one level ... 2^0 = 1 leaf
two levels...2^1 = 2 leaves
.
Level number 'x'.. you need definition
x levels... no need of definition... you can assume root as 1 here.

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