An ideal gas in a heat engine operate between two thermal reservoirs in a cyclic process. Absolute temperature of hot reservoir is $T_H$ and cold reservoir is $T_c$  . There is no heat exchange of gas with surrounding except with thermal reservoirs. Then choose the correct option(s).

If the cycle is reversible, then then the entropy of gas increases in every cycle

If the cycle is irreversible, then efficiency of the engine is smaller then   $1-\frac{T_c}{T_H}$ 
 

If the cycle is irreversible, then the entropy of gas decreases in every cycle

If the cycle is reversible, then efficiency of the engine is   $1-\frac{T_c}{T_H}$