GATE

When selecting subjects for the GATE entrance examination, choose the subject that is most closely related to your engineering discipline and career aspirations, as you can only choose one or two subjects relevant to your field from the available options, depending on your specific goals and the GATE paper combination rules; always consult the official GATE syllabus and paper codes to confirm which subjects are available for your chosen branch. 
Key factors to consider when choosing GATE subjects:
Your Engineering Degree:

Choose a subject that is directly related to your undergraduate engineering degree.
Career Goals:
If you want to pursue a certain career route, such as M.Tech .

Yes, a GATE-qualified student with an MA in English can apply for a PhD programme and may receive a stipend. Although GATE is mainly linked with the engineering and technology fields, some institutions may allow the acceptance of GATE scores in interdisciplinary programs, including those of humanities.
Stipend Details:
Stipend Amount: PhD students are paid a monthly stipend of 31,000 for the first two years as Junior Research Fellows (JRF). It increases to 35,000 in subsequent years as a Senior Research Fellow (SRF).
Eligibility: Candidates who had earned a valid GATE score and were registered at approved PhD programs at participating GATE institutions, became eligible for the stipend.
Application Process
Candidates should check on certain eligibility criteria and processes regarding applications for the interested universities, as policies do tend to vary. Best advisable would be to consult admissions offices of the respective universities if they have any questions as concerns applying with an MA in English.

If you have already finished your M.Tech from an IIT, you are usually exempted from appearing for GATE for a PhD programme in most institutes and even IITs. Several IITs as well as other research-oriented institutes relax the GATE requirement for M.Tech holders, particularly from IITs, considering that you have a strong academic record and research potential. However, the general rules for PhD admission vary from institute to institute and department to department. It is prudent to check the individual PhD admission guidelines of the IIT or other institutes you're interested in to confirm whether any other entrance exams or qualifications are needed.