@abhishekjuly,
Wow Ab you're not alone by any means. With a BS in journ and erstwhile career some 75 years in the field, I'm still not sure
Don't know why I
don't like 1a) but
1b) Millions of people are searching for houses for their families in Delhi. Is okay. However we'd be more likely to "In Delhi(,) millions…."
Often I shoot for singular: Millions (of people) are searching for a house for the (their) family in Delhi
Another example shooting for singular: By the millions a family in Delhi is searching for a house
2)
both just awkward and somehow not entirely clear. Let's see……
2a) is okay except it should be "number" and you can skip" than the people", "so", and "for them"
Many people were trying to get a cup of coffee for themselves, but as cups were less in number, many of them could not get one
Many were trying to get a cup of coffee(,) but because cups were less in number some were unsuccessful (denied)
Many tried to get a cup of coffee but were unsuccessful since the cups were less in number
Don't like 2b) because it seems to imply some of those fellas wanted more than one cup
Also the "so" is equivocal: Does it mean "therefore" or "very"; and too many "many's"
Many people were trying to get a cups of coffee for themselves, but cups were less in number; so many could not get one
Almost everyone was trying to get a cup of coffee, but cups were less in number; so many could not get one (went without)