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`

Answer 1

`3/160`

Given : \[a \odot b = \frac{ab}{4}\]

\[3 \odot \left( \frac{1}{5} \odot \frac{1}{2} \right) = 3 \odot \left[ \frac{\left( \frac{1}{5} \right)\left( \frac{1}{2} \right)}{4} \right]\]
\[ = 3 \odot \left( \frac{1}{40} \right)\]
\[ = \frac{3\left( \frac{1}{40} \right)}{4}\]
\[ = \frac{3}{160}\]