The correct option is (b) The base current IB, cannot increase further
For explanation I would say: At saturation, the collector-to-emitter voltage is the minimum drop possible occurring due to the non-zero internal resistance of the BJT. Since it cannot decrease further, the current IC cannot increase further. The BJT is said to be saturated. However, the base current, IB, can keep increasing with the input voltage and hence, in saturation, the relation IC = βIB is not satisfied.