Concept:
A p-n junction diode contains a depletion region around the junction.
Due to diffusion of charge carriers, a built-in electric field is established across the junction which creates a potential barrier known as the barrier potential.
This barrier potential opposes the further diffusion of majority charge carriers.
The behaviour of the diode depends upon whether it is forward biased or reverse biased.
Assertion Analysis:
In forward biasing,
\[
p\text{-side} \rightarrow \text{positive terminal}
\]
and
\[
n\text{-side} \rightarrow \text{negative terminal}.
\]
The external applied voltage opposes the built-in potential barrier.
As a consequence, the depletion region becomes thinner and the barrier potential decreases.
Because the barrier potential is reduced, majority charge carriers can cross the junction more easily, resulting in a large forward current.
Therefore, the statement
\[
\text{``barrier potential increases''}
\]
is incorrect.
The barrier potential actually decreases during forward biasing.
Hence, the Assertion is FALSE.
Reason Analysis:
The built-in potential of the junction and the externally applied forward-bias voltage act in opposite directions.
The purpose of forward biasing is precisely to oppose and reduce the junction barrier.
Therefore the statement that the applied voltage acts in the same direction as the built-in potential is incorrect.
In reality,
\[
\text{Forward Bias Voltage}
\]
acts opposite to
\[
\text{Built-in Potential}.
\]
Hence the Reason is also FALSE.
Relationship Between Assertion and Reason:
Since the Assertion is false and the Reason is also false, the given pair falls under the category:
\[
\text{Assertion False, Reason False}.
\]
Final Answer:
\[
\boxed{(D)}
\]