M.Tech

For all the details related to GATE exam, check the link below :
https://www.shiksha.com/engineering/exams/gate

Yes, they do have.

In M.Tech (Part Time) you have to attend classes twice a week only. Fees is less and can be paid in installments.

Some of the popular colleges which offer M.Tech courses in solar energy are as follows:n1) School of Engineering, University of Petroleum and Energy Studies, Dehradunn2) TERI University, Delhin3) SRM Institute of Science and Technology, Chennai - Kattankulathur Campusn4) Rajasthan Technical University, Kotan5) College of Engineering- Anna University (CEG, Guindy), Guindy, Chennain6) University of Petroleum and Energy Studies, Dehradunn7) Maulana Azad National Institute of Technology, Bhopal.

Hello Manirathinam,
First, congratulations on completing B.Tech. You need to take the GATE in the process to get admission into the good colleges for the M.Tech. The M.Tech will allow you to go for the lectureship or Master's degree in your field. The GATE exam is an entrance exam for the selection of the candidates in the IIT, NIT or other top institutes for M.Tech. There are other exams like IIT JAM CSIR NET exams for the science stream candidates. You can take a look all the options and appear for the exam according to your eligibility.

Since Chemistry is a division of Science, hence, you can definitely apply for the examination. For more details regarding GATE examination, please go through the following website:
http://www.iitk.ac.in/gate/gate2011/eligibility.php.