Engineering Science (XE) is a code of GATE paper and not an engineering branch. Students applying for Engineering Science paper can apply for various M.Tech courses in all IITs and NITs.
Students pursuing B.Tech or B. E. in any subject can appear for the Engineering Science paper, as long as they match it with the entry criteria to the M.Tech specialization of their choice. The test has 2 compulsory parts in Engineering Mathematics and General Aptitude. Then the student has to choose 2 from the 7 optional subjects. The subjects are Fluid Mechanics, Thermodynamics, Material Science, Solid Mechanics, Polymer Science, Food Technology and Atmospheric and Ocean Science.
Students who qualify in the GATE exam can apply to these colleges. GATE score is also valid for quite a few companies like ONGC, BSNL, GAIL, etc. Even private companies like L&T give preference to GATE qualified students.