In counter flow heat exchangers

Option A: Both the fluids at inlet (of heat exchanger where hot fluid enters) are in their coldest state
This is incorrect because in a counter flow heat exchanger, the hot fluid enters the exchanger in its hottest state, and the cold fluid enters the exchanger in its hottest state from the opposite end. Therefore, it is not possible for both fluids to be in their coldest state at the same inlet.

Option B: Both the fluids at inlet are in their hottest state
This is correct. In a counter flow heat exchanger, the hot fluid enters at its hottest state from one end, and the cold fluid enters at its hottest state from the opposite end. This creates a temperature gradient that facilitates efficient heat transfer throughout the exchanger.

Option C: Both the fluids at exit are in their hottest state
This is incorrect. In a counter flow heat exchanger, the fluids flow in opposite directions. At the exit, the hot fluid will be in its coldest state (after transferring heat) and the cold fluid will be in its coldest state (after receiving heat). Therefore, both fluids cannot be in their hottest state at the exit.

Option D: One fluid is in hottest state and other in coldest state at inlet
This is incorrect because, in a counter flow heat exchanger, both fluids enter at their respective hottest states from opposite ends. If one fluid is in its hottest state at the inlet, the other fluid will also be in its hottest state but from the opposite end, not at the same inlet.

Conclusion:

Option B is the correct answer because, in counter flow heat exchangers, both fluids enter the exchanger in their hottest states from opposite ends, which creates an optimal temperature gradient for heat transfer.