To evaluate the given statements about dicotyledonous leaves, let's break down each statement and understand its validity.

Statement I: In a dicotyledonous leaf, the adaxial epidermis generally bears more stomata than the abaxial epidermis.

This statement is generally false. In most dicotyledonous leaves, the abaxial (lower) epidermis typically has more stomata than the adaxial (upper) epidermis. This adaptation helps in efficient gas exchange while minimizing water loss as the lower surface is less exposed to direct sunlight.

Statement II: In a dicotyledonous leaf, the adaxially placed palisade parenchyma is made up of elongated cells, which are arranged vertically and parallel to each other.

This statement is true. The palisade parenchyma in dicotyledonous leaves is located on the adaxial (upper) side and consists of elongated cells aligned vertically and parallel to each other. This arrangement is crucial for maximizing light absorption for photosynthesis.

Based on the explanation above, the correct evaluation of the given statements is:

Option B: Statement I is false but Statement II is true.