Sentence improvement – correlative conjunction and inversion with 'No sooner … than …': correct both the auxiliary inversion and the linker so it reads 'No sooner did he return home than his mother felt happy.'

Given sentence
'No sooner he had returned home then his mother felt happy.'

Concept/Approach
With negative/limiting adverbials like 'No sooner', English requires inversion (auxiliary before subject) and the fixed correlative '… than …' (not 'then'). Two accepted patterns are:• Past perfect: 'No sooner had he returned home than …'• Simple past with do-support: 'No sooner did he return home than …'

Step-by-step correction
1) Invert: 'did he return' (or 'had he returned').2) Replace 'then' → 'than'.3) Final (keyed): 'No sooner did he return home than his mother felt happy.'

Why other options fall short
'had he returned … when' → uses 'when' instead of the required 'than'.'he had returned … than' → lacks inversion.'No improvement' → keeps both errors.

Final Answer
did he return home than