GATE is the entrance exam for admission to Masters programmes for Engineering and Science Graduates. JEE Advanced is the entrance exam for admission to IITs, NITs,etc. for B.Tech programmes. GATE is for PG courses and JEE Advanced is for B.Tech courses. Both of them are different. If you want to study B.E/B.Tech in IIT Madras, you should write JEE Advanced and if you want to study Master's programme, you should write GATE exam.