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Question
If the binary operation ⊙ is defined on the set Q+ of all positive rational numbers by \[a \odot b = \frac{ab}{4} . \text{ Then }, 3 \odot \left( \frac{1}{5} \odot \frac{1}{2} \right)\] is equal to __________ .
Options
`3/160`
`5/160`
`3/10`
`3/40`
Solution
`3/160`
Given : \[a \odot b = \frac{ab}{4}\]
\[3 \odot \left( \frac{1}{5} \odot \frac{1}{2} \right) = 3 \odot \left[ \frac{\left( \frac{1}{5} \right)\left( \frac{1}{2} \right)}{4} \right]\]
\[ = 3 \odot \left( \frac{1}{40} \right)\]
\[ = \frac{3\left( \frac{1}{40} \right)}{4}\]
\[ = \frac{3}{160}\]
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