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If \[2^{x}=3^{y}=6^{-z}\], then \[\left( \frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)\] is equal to?

A) 0

B) 1

C) 3/2

D) -1/2


If \[2^{x}=\sqrt[3]{32}\] , then x is equal to?.

A) 5

B) 3

C) 3/5

D) 5/3


If  \[3^{(x-y)}=27 \]  and \[3^{(x+y)}=243 \], then x is equal to?

A) 0

B) 2

C) 4

D) 6


if abc= 1, then \[\left(\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}\right)=?\]

A) 0

B) 1

C) 1/ab

D) ab


Number of prime numbers in \[\frac{6^{12}\times 35^{28}\times 15^{16}}{14^{12}\times 21^{11}}is:\]

A) 56

B) 66

C) 112

D) none of this


Name of prime factors in \[\left(216\right)^{\frac{3}{5}}\times \left(2500\right)^{\frac{2}{5}}\times \left(300\right)^{\frac{1}{5}}\]

A) 6

B) 7

C) 8

D) none of this