He has no child __________ his wife.

[Tait-ka]

He has no child ------- his wife.
1. from
2. by
3. of
4. with

Which option is correct?

My guess is that 'by' is correct.

I took this MCQ (multiple choice question) from a past paper conducted by PPSC. It was held on 13/7/2025.
Please see here the paper description:

 

[emsr2d2]

Thank you for providing the full source and a screenshot. I have edited your title so that it shows the entire sentence.

It's a poor question because two choices are correct and lead to grammatical sentences (in BrE, at least). Most people here would say "with" but "by" is also correct. The latter has somewhat fallen out of use in general everyday speech.

Also, note that most native speakers would use the plural "children" after "no".

He has no children with/by his wife.

In addition, most of us would talk about the couple as a couple:

He and his wife have no kids.
She and her husband have no kids.