Correct Answer: $\frac{9}{10}$

Solution : $\tan A = 3$
$⇒\tan A = \frac{\text{Perpendicular}}{\text{Base}}= \frac{3}{1}$
By Pythagoras Theorem,
Hypotenuse ² = Perpendicular ² + Base ²
Perpendicular = 3 and Base = 1
⇒ Hypotenuse ² = 3 ² + 1 ²
⇒ Hypotenuse ² = 10
⇒ Hypotenuse = $\sqrt{10}$
⇒ cos A = $\frac{\text{Base}}{\text{Hypotenuse}}=\frac{1}{\sqrt{10}}$
⇒ sin A = $\frac{3}{\sqrt{10}}$
So, 3 sin A cos A $= 3 × \frac{3}{\sqrt{10}}$ × $\frac{1}{\sqrt{10}}=\frac{9}{10}$
Hence, the correct answer is $\frac{9}{10}$.