test = pd.DataFrame({'days': [0,20,30,31,45,60]})

test['range1'] = pd.cut(test.days, [0,30,60], include_lowest=True)
#30 value is in [30, 60) group
test['range2'] = pd.cut(test.days, [0,30,60], right=False)
#30 value is in (0, 30] group
test['range3'] = pd.cut(test.days, [0,30,60])
print (test)
   days          range1    range2    range3
0     0  (-0.001, 30.0]   [0, 30)       NaN
1    20  (-0.001, 30.0]   [0, 30)   (0, 30]
2    30  (-0.001, 30.0]  [30, 60)   (0, 30]
3    31    (30.0, 60.0]  [30, 60)  (30, 60]
4    45    (30.0, 60.0]  [30, 60)  (30, 60]
5    60    (30.0, 60.0]       NaN  (30, 60]