What is the angle between the clock hands at 6 : 45?

Correct option is D

Given: The clock hands at 6:45.

FormulaUsed: $$\begin{vmatrix} 30H - \frac {11}{2}M \end{vmatrix}$$

= $$\begin{vmatrix} (30\times6) - \frac {11}{2}\times45 \end{vmatrix}$$

= $$\begin{vmatrix} 180 - \frac {495}{2} \end{vmatrix}$$

= $$180 - 247.5$$

= 67½°

Thus, correct option is (d).