GATE

NIFT conducts its own entrance exam which happens in two stages:
1. General Ability Test (GAT)-This exam comprises 4 sections namely Quantitative Ability, Logical Reasoning, English Language Comprehension and General Knowledge.
2. Creative Ability Test CAT This test is administered to judge the intuitive ability, power of observation in concept development and design ability of the candidate. An important aspect of the test is the creative and innovative use of colour & illustration skills. Both the tests are important and mandatory to attend. Both take place on the same day and it's for all because NIFT has compulsory entrance test so a student who wants to take admission has to go through the test without the test and clearing it cannot go through so yes the fee for NIFT students and entrance exam is a must.

Firstly, you must know that GATE maths is not that of a very high level as we encounter in many examinations such as JEE Main/Advance etc. But it is not as easy as engineering maths either. It tests for the basic application of proper mathematical techniques. Your main objective for preparing math for GATE should be concentrating on basics and application of these basics in a variety of problems. Try to concentrate on important topics such as Linear Algebra, Calculus, Differential Equation, Probability and Statistics etc. You will that out that 4 out of 5 questions will be from these topics. As far as material is concerned there is no need of going for a dedicated text book. Refer you engineering text books topic wise and then solve all the previous year GATE papers starting from 2007. After your preparation is completed try solving questions from mock papers form Madeeasy, Gateforum etc. This surely will help, if you are aiming at getting a good score in math. Hope it helps.

The only answer to your question is YES. Every one who can out an sincere effort can excel in GATE exam and I can give you numerous examples for itfirst is me (AIR73), then my college senior who secured AIR 34, another friend with AIR 32 and so on. The only thing Common in our preparation was :
Specific book list and notes that we prepared in beginning of our preparation and stuck to it till the end. Stopped all the Redundant activities. Regular practice. Continuous interaction with faculty members and batchmates to identify where we lag. Honesty while attempting the TEST SERIES. SO I would just say that you can surely crack GATE with excellent rank, all you require is continuous hardwork and faith in yourself that you can do it and no matter what, never get demotivated.