In anaerobic respiration there is no consumption of oxygen and carbon dioxide is produced in most of the cases,
e.g., $C_6H_{12}O_{6}\xrightarrow{\text{ Zymase}} 2CO_2 + 2C_2H_5OH$
As $R.Q =\frac{\text{Volume of $CO_2$ evolved $2CO_2$}}{\text{ infinity}}$
$= \frac{2CO_2}{O}= $ infinity
Therefore, the respiratory quotient is infinity