UPSC

Hi Saumy,
Yes, you can opt for mathematics as an optional subject for UPSC civil services examination. Some of the popular books for the paper I are:
Linear Algebra :
Schaums outline on Linear Algebra: this book has explained linear algebra in a far better and simpler manner than Krishna Series. Due to its clarity, it can be read quickly also.
Krishna Series on Matrices
Calculus :
Krishna Series on Differential calculus
Krishna Series on Integral calculus
Mathematical Analysis by Malik and Arora : a must read book for both Paper I and II
Analytical Geometry :
Krishna Series on Analytical Geometry : this book is better than Shantinarayan and has many solved examples
Krishna Series on Analytical Solid Geometry : for Conicoids, Generating Lines
Ordinary Differential Equations:
Ordinary and Partial Differential Equations by MD Raisinghania
Advanced Differential Equations by MD Raisinghania : required for Laplace Transforms (Paper-I) and Boundary value problems (Paper-II)
Dynamics and Statics
Krishna Series on Statics
Krishna Series on Dynamics
Vector Analysis
Krishna Series on Vector Calculus (~ 330 pages)
Schaums outline on Vector Analysis
For Paper II:
Abstract Algebra: This being my favourite topic, I had referred many books. But as many candidates find this topic tough, I would suggest referring to following books.
Abstract Algebra, Group Theory by R Kumar (Vardhaman Publications)
Abstract Algebra, Ring Theory by R Kumar (Vardhaman Publications)
Abstract Algebra by Joseph Gallian (optional)
Real Analysis:
Mathematical Analysis by Malik and Arora
Real Analysis by MD Raisinghania
Complex Analysis:
Krishna Series
Linear Programming:
Operations Research by JK Sharma or Kanti Swarup or Krishna Series
Partial Differential Equations:
ODE and PDE by MD Raisinghania
Engineering Maths by Grewal : for boundary value problems
Advanced Differential Equations by M.D Raisinghania (for boundary value problems)
Numerical Analysis and Computer programming:
Numerical Methods by Jain and Iyengar (but questions are not coming from this book from past few years)
Numerical Analysis chapter from Grewal, Engineering Mathematics
For Algorithms and flowcharts, I am having soft copy of a book which I will share.
Mechanics and Fluid Dynamics:
Fluid Dynamics by MD Raisinghania
Krishna Series, Dynamics for Moment of Inertia and D Alemberts Principle
Krishna Series, Rigid Dynamics for Lagrangian and Hamiltonian

Hi Katra,
UPSC preparation requires constant mentoring and guidance. Most of the coaching institutes follow a very generic approach where they cover syllabus through classes and notes. Most of the students are not aware of the requirements of the competition, changing trends and pattern. They should be facilitated to find their approach to crack every stage of the competition. The 50% of this competition is psychological where one's composure and mental equanimity actually helps to crack it in limited time frame. So, coaching institute can only guide you to an extent, but major hard work has to be done by you.
The coaching centers are famous according to different stages of examination: prelims, mains and interview. Though a lot of free material is available online, which can easily help you prepare for examination like Mrunal, Insight, etc. Some of the best coaching institutes are:
Vision IAS
Vajiram
ALS
Khan Study Group
Chanakya IAS Academy

1. Try to be creative. when you will write an essay or when you will answer descriptive question try to show your creativity. whatever you will write in the paper write intelligently.
2. Choose the subject for civil service main examination according to your stream of study. in which subject you have good knowledge choose only that subject. first read the syllabus of each paper then choose the paper according to your knowledge.
3. Do not be tensed at the time of examination. if the question is tough then it is tough for everyone. so you should not worry about you. whatever you will know just answer them.
4. Try to be prepare for English language paper. to do good in this paper you must have good knowledge in English. So, you must be prepare very well for the English subject.