In case it's only MBA in construction management then your best possible option is RICS Noida, the admissions take place through CAT/MAT scores followed by interview. Incase instead of MBA if you wish to do M.tech in construction management then you have two options.

First option: Take up GATE exam and pursue M.tech in construction management from any of the IITs or NITs.

Second Option: Register for L&T's Build India Scholarship exam and go for the same course i.e M.Tech. Under this scheme the full tuition fee will be waived off. But it covers only 4 colleges; IIT Delhi, IIT Madras, NIT Surathkal, NIT Trichy.

Also, you can consider going for NICMAR which offers PGP in construction management and other similar courses. In case of NICMAR they have their own admission details the complete detail of which you can find on their website.