The correct option in this case is A: Both A and R are true, and R is the correct explanation of A.

The assertion states that the frequency of floods in North Indian plains has increased during the last couple of decades, which is true. There have been numerous reports and studies indicating an increase in the occurrence of floods in the region, leading to significant damages to lives, property, and infrastructure.

The reason provided is that there has been a reduction in the depth of river valleys due to the deposition of silt. This is also true and provides a valid explanation for the increased frequency of floods. Over time, rivers carry sediment and deposit it along their banks, which can reduce the depth of the river valleys. As a result, during heavy rainfall events, the river channels may not have the capacity to accommodate the increased volume of water, leading to floods.

Therefore, in this case, both the assertion and the reason are true, and the reason provided is a correct explanation for the assertion.