I am in US for the whole last year. My wife and children came to US on Feb 24 and went back to India to attend a marriage on August 14th and did not return back to US for the rest of the year. This makes their stay in US less than 183 days by some 10 days. Can I claim the tax exemption for them or not.

Thank you very much in advance

If you are nonresident from India, you do not get any exemption for dependents.
When did you enter US on J1?