Correct option is B
Statements:
1. All sparrows are birds.
2. Some bird are animals.
3. All dogs are animals.
From the statement following Venn diagram can be –

Conclusions:
I. Some dogs are sparrows. (does not follow)
All sparrows are birds, some birds are animals and All dogs are animals, it implies that some dogs are sparrows does not follow.
as dogs and sparrow does not have a direct relation.
II. All animals are birds is a possibility. (follows)
Some birds are animals, it implies that All animals are birds is a possibility follows.
III. Some animals are sparrows. (does not follow)
All sparrows are birds, some birds are animal, it implies that some animals are sparrows does not follow.
Thus, Option B (Only conclusion II is true) is the correct answer.