Hey Vijay.

If you already have a undergraduate degree and want to pursue LLB a 3 year LLB programme is more suitabke for you.

CLAT is an entrance exam for admission in five year Integrated course of law like BA LLB, BCOM LLB, BBA LLB etc. These 5 year Integrated courses combine an undergraduate degree like BA, BCOM, BBA etc with law. CLAT does not offer any 3 year LLB courses. If you pursue CLAT after completion of graduation it would be wasting 2 years. Hence you can go for other good colleges and entrance tests for admission in 3 year LLB.

DU LLb- Delhi University

MH CET- GLC Mumbai, ILS Pune and other law colleges in Maharashtra

PU LLB- Panjab University,Chandigarg

TS LAWCET- Law colleges in Tamil Nadu

BHU LLB- Banaras Hindu University.

BVP LLB- Bharatiya Vidyapeeth University

LSAT- Private Law colleges like O.P. Jindal Global Law school, IIT Kharagpur etc 

Yes it is possible to crack Such law entrances in 1 month preparation but it would be better if you start earlier. 

Best of luck