no article + noun + of noun - Article Question

[vcolts]

Ex1. Parts of your work can be used for the next project.

Ex2. Parts of your book can be used for your essay.

Ex3. Part of your donation will be given to the children of the victims.

Ex4. Part of the annual budget will be spent for reconstructing the dam.

Ex5. Parts of the computer can be donated to the school.

Ex6. The parts of the computer can be donated to the school.
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I was taught/conditioned to add an article in front of nouns of something/someone most of the time.

Q1. Are all of the above grammatically correct? (In another words, an article is not necessasry in all of the cases above (except Ex6), right?)

Q2. If I understand correctly, you do not need to add "the" in front of nouns of something unless you mean particular things, right? (in the case of parts of the computer vs. the parts of the computer)

Thanks in advance!

[bhaisahab]

Ex1. Parts of your work can be used for the next project.

Ex2. Parts of your book can be used for your essay.

Ex3. Part of your donation will be given to the children of the victims.

Ex4. Part of the annual budget will be spent for reconstructing the dam.

Ex5. Parts of the computer can be donated to the school. Some of the parts can be donated.

Ex6. The parts of the computer can be donated to the school. All of the parts can be donated.
=====

I was taught/conditioned to add an article in front of nouns of something/someone most of the time.

Q1. Are all of the above grammatically correct? (In another words, an article is not necessary in all of the cases above (except Ex6), right?)

Q2. If I understand correctly, you do not need to add "the" in front of nouns of something unless you mean particular things, right? (in the case of parts of the computer vs. the parts of the computer)

Thanks in advance!

They are all grammatically correct.