NIMCET 2013 Question Paper with solutions

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Question : 24 of 120

Marks: +1, -0

The value of

9^{1/3} .9^{1/9} .9^{1/{27}}

... ∞ is

3
6
9
N.O.T

Solution:

9^{1/3}⋅9^{1/9}⋅9^{1/27}......

=9^{1/3+1/9+1/27+..}

9(1/3/{1-/3})

[∵a+ar+ar^2+...∞=a/{1-r}]

=9^{(1/3/{3-1}/3)}=9^{1/3{/}2/3}=9^{1/3×3/2}=9^{1/2}=3

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