Question

If the binary operation $\ast$ is defined on the set $Q^{+}$ of all positive rational numbers by $a\ast b=\frac{ab}{4}$. Then, $3\left(\frac{1}{5}\ast \frac{1}{2}\right)$ is equal to

• A. $\frac{3}{160}$
• B. $\frac{5}{160}$
• C. $\frac{3}{10}$
• D. $\frac{3}{40}$

Answer 1

Answer: (A)

Given that $a\ast b=\frac{ab}{4}\forall a$, $b\in Q^{\prime }$
$\therefore 3\ast \left(\frac{1}{5}\ast \frac{1}{2}\right)<br/>=3\ast \left\{\frac{\frac{1}{5}\times \frac{1}{2}}{4}\right\}$
$=3\ast \frac{1}{40}$
$=\frac{\left(3\times \frac{1}{40}\right)}{4}$
$=\frac{3}{160}$