1. Tom is the youngest of his brothers.

2. Tom is youngest of his brothers.
(Are both OK? Which one is grammatical?)

3. This book was most helpful for my homework.

4.This book was the most helpful for my homework.
(Which one is grammatical? Do we have to use 'the' or not in this case?)

1 and 2 mean the same thing.

#1 is better, but it's unexplainable! It's just the normal placement of words.

1. Both sentences are grammatically correct, but they have slightly different meaning.

In the first sentence, "Tom is the youngest of his brothers," the use of the definite article "the" suggests that Tom is the youngest out of a specific group of brothers. This implies that Tom has multiple brothers and he is the youngest one among them.

In the second sentence, "Tom is youngest of his brothers," the absence of the definite article "the" suggests a more general statement. It implies that Tom is young compared to his brothers, without specifying that he is the absolute youngest.

2. Both sentences are grammatically correct, but they convey slightly different meanings.

In the first sentence, "This book was most helpful for my homework," the adverb "most" is used to emphasize the degree of helpfulness that the book provided for your homework. This suggests that the book was extremely helpful or significantly more helpful than any other book.

In the second sentence, "This book was the most helpful for my homework," the use of the definite article "the" implies that you are comparing this book with other books and stating that it was the most helpful among them.

The choice between using "most" and "the most" depends on the specific context or emphasis you want to convey.