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If \( \Large \frac{1}{4} \times \frac{2}{6} \times \frac{3}{8} \times \frac{4}{10} \times \frac{5}{12} \times ..... \times \frac{31}{64}=\frac{1}{2^{x}} \), the value of x is

A) 31
B) 32
C) 36
D) 37

Correct Answer:



C) 36

Description for Correct answer:
\( \Large \frac{1}{4} \times \frac{2}{6} \times \frac{3}{8} \times \frac{4}{10} \times \frac{5}{12} \times ........ \times \frac{31}{64} = \frac{1}{2^{x}} \)

=> \( \Large \left(\frac{1}{2}\right)^{30} \times \left(\frac{1}{2}\right)^{6} \)

= \( \Large \left(\frac{1}{2}\right)^{30+6} = \frac{1}{2x} \)

or \( \Large \frac{1}{2^{36}} = \frac{1}{2x} \)

Therefore, x = 36

Part of solved Elementary Mathematics questions and answers : >> Elementary Mathematics

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