Why does the coefficient of performance of a refrigerator become infinity?

The equation $\beta = \frac{Q_2}{Q_1 - Q_2}$ is true or false?

The coefficient of performance of a refrigerator is $5$. If the temperature inside the freezer is $-20^{\circ}C$,the temperature of the surroundings to which it rejects heat is ........ $^{\circ}C$.

$A$ Carnot freezer takes heat from water at $0\,^{\circ}C$ inside it and rejects it to the room at a temperature of $27\,^{\circ}C$. The latent heat of ice is $336 \times 10^3\, J\,kg^{-1}$. If $5\, kg$ of water at $0\,^{\circ}C$ is converted into ice at $0\,^{\circ}C$ by the freezer,then the energy consumed by the freezer is close to

$A$ Carnot engine,having an efficiency of $\eta = 1/10$ as a heat engine,is used as a refrigerator. If the work done on the system is $10 \ J$,the amount of energy absorbed from the reservoir at a lower temperature is ....... $J$.

The coefficient of performance of a refrigerator is defined as: