Let's analyze both statements to determine their correctness with respect to the concept of polygenic inheritance.

Statement I: When many alleles of a single gene govern a character, it is called polygenic inheritance.

This statement is incorrect. Polygenic inheritance involves multiple genes (each with two or more alleles) contributing to a single phenotype, rather than many alleles of a single gene. So, this statement misrepresents the definition of polygenic inheritance.

Statement II: In Polygenic inheritance, the effect of each allele is additive.

This statement is correct. In polygenic inheritance, each allele of the different genes that contribute to a trait typically has a small, additive effect on the phenotype. For example, characteristics like human height and skin color are determined by the cumulative effect of multiple genes.

Based on the above analysis:

Option A

Statement I is true but Statement II is false

Option B

Statement I is false but Statement II is true

Option C

Both Statement I and Statement II are true

Option D

Both Statement I and Statement II are false

The correct answer is Option B: Statement I is false but Statement II is true.