The correct sentence is given as "We've to go to study". That is not correct English. Have cannot be contracted when it is emphasized.
"We have to go study" is a much more idiomatic sentence than "We have to go to study."
I agree that "We have to go study" is what would normally be said. I think sometimes there is too much emphasis on word to word translation, which results in sentences that are a bit unnatural.
As an English (England) speaker I would say "We have to go to study"
Maybe in US English. The latter is more natural for me as a British English speaker. It's good to have all the options out there though.
Why is जाना not जाने used with the plural हमें ? Thanks!