SATHEE: Quantitative Aptitude Ques 1384

Quantitative Aptitude Ques 1384

Question: Find the value of $ m-n, $ if $ \frac{9^{n}\times 3^{2}\times {{( {3^{-\frac{n}{2}}} )}^{-2}}-{{(27)}^{n}}}{3^{3m}\times 2^{3}}=\frac{1}{27} $

Options:

A) $ 1 $

B) $ -2 $

C) $ -1 $

D) $ 2 $

Show Answer

Answer:

Correct Answer: A

Solution:

$ \frac{9^{n}\times 3^{2}\times {{({3^{-n/2}})}^{-2}}-{{(27)}^{n}}}{3^{3m}\times 2^{3}}=\frac{1}{27} $

$ \Rightarrow $ $ \frac{3^{2n}\times 3^{2}\times 3^{n}\times 3^{3n}}{3^{3m}\times 2^{3}}=\frac{1}{27} $
$ \Rightarrow $ $ \frac{{3^{3n+2}}-3^{3n}}{3^{3m}\times 8}=\frac{1}{27} $

$ \Rightarrow $ $ \frac{3^{3n}\times 8}{3^{3m}\times 8}=\frac{1}{{{(3)}^{3}}} $
$ \Rightarrow $ $ {{{{{(3)}^{3}}}}^{n-m}}={3^{-3}} $

$ \Rightarrow $ $ n-m=-1 $ or $ m-n=1 $

Quantitative Aptitude Ques 1383

Quantitative Aptitude Ques 1385

Quantitative Aptitude Ques 1384

Question: Find the value of $ m-n, $ if $ \frac{9^{n}\times 3^{2}\times {{( {3^{-\frac{n}{2}}} )}^{-2}}-{{(27)}^{n}}}{3^{3m}\times 2^{3}}=\frac{1}{27} $

Options:

Answer:

Solution:

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