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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


\[\frac{243^{\frac{n}{5} \times} 3^{2n+1}}{9^{n} \times 3^{n-1}}=?\]

A) 1

B) 3

C) 9

D) 27


Given that \[10^{0.48}=x,10^{0.70}=y\] and \[x^{2}=y^{2}\], then the value of z is close to:

A) 1.45

B) 1.88

C) 2.9

D) 3.7


If \[2^{n-1}+2^{n+1}=320\] then n is equal to:

A) 6

B) 8

C) 5

D) 7


If \[\frac{9^{n} \times 3^{5} \times \left(27\right)^{3}}{3 \times \left(81\right)^{4}}=27\], then the value of n is:

A) 0

B) 2

C) 3

D) 4


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