I chose Mathematics and Physics as optional subjects as I had a considerable exposure to the topics in their syllabi from my study since classes +1, +2 upto college level.

The books I referred for Mathematics are as follows:

Paper I

1. Linear Algebra:

Linear Algebra by Vasishtha and Sharma (Krishna Series)

Matrices by Vasishtha and Vasishtha (Krishna Series)

2. Calculus:

Differential Calculus by Shanti Narayan (S. Chand)

Integral Calculus by Shanti Narayan (S. Chand)

A Course of Mathematical Analysis by Shanti Narayan (S. Chand)

3. Analytic Geometry:

Analytical Solid Geometry by Shanti Narayan (S. Chand)

4. Ordinary Differential Equations:

Ordinary and Partial Differential Equations by M.D. Raisinghania (S. Chand)

Laplace Transforms:

Brilliant Tutorials

Advanced Engineering Mathematics by Erwin Kreyszig

5. Statics:

Statics (Krishna Series)

Dynamics:

Dynamics (Krishna Series)

6. Vector Analysis:

Vector Calculus (Krishna Series)

Curves in Space :

Calculus by Thomas & Finney

Paper II

1. Algebra:

Abstract Algebra by Khanna and Bhambri

Topics in Algebra by I. N. Herstein

2. Real Analysis:

Elements of Real Analysis by MD Raisinghania (S. Chand)

3. Complex Analysis:

Functions of a Complex Variable (Krishna Series)

4. Linear Programming:

Linear Programming (Krishna Series)

5. Partial Differential Equations:

Ordinary and Partial Differential Equations by M.D. Raisinghania (S. Chand)

Boundary Value Problems:

Advanced Engineering Mathematics by Erwin Kreyszig

6. Numerical Analysis and Computer Programming:

Numerical Methods by Jain, Jain and Iynger

7. Mechanics:

Rigid Dynamics Volume I & II (Krishna Series)

Fluid Dynamics:

M.D. Raisinghania (S. Chand)