GATE

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.

First of all, I don't know what is your department. So, I cannot tell you subject wise strategy. It is very difficult to prepare for GATE within 7 months, if you didn't study well during your previous semester. But, it is not Impossible. So going through basic strategy
Make detailed syllabus and sort out the subjects that you know well.
First of all, finish those subjects that you are interested in. You have 1011 Subjects appox. including engineering maths. Make a detail time table and divide all the subjects within 7 months. If you are finding any subject very hard to understand then you can skip 1 or 2 subject. Its is not an bad idea because time is too short. Don't Skip Engineering Mathematics. It cover 15% of total GATE marks. You can make weekly target and give revision at the end of the week
You can study 34 subject at once. At the end of the day you know your strength and weekness very well. Prepare a routine accordingly and follow them.
Best of luck.

Solve at-least last 10 years Previous Papers. It will make you get the idea about the type of Questions being asked in the Exam. Focus more on 2 mark questions. They boost your Score exponentially.
Practice as many Mock-tests as you can (that too as per the Standard pattern of the GATE Exam).
Keep your fundamentals and concepts clear. The Questions asked in the GATE Exam are mostly based on the fundamental concepts. By giving these you will actually know about question pattern and gain experience for giving objective kind of test and also you will be able to measure your standard as per other student so that you can change yourself better to crack the exam.