Section 1: Calculus
A fundamental section with good weightage.
Topics
- Functions of two or more variables
- Continuity, partial derivatives
- Maxima and minima
- Multiple integrals
- Vector calculus (Gradient, Divergence, Curl)
Section 2: Linear Algebra
Topics
- Vector spaces over R and C
- Linear transformations
- Systems of linear equations
- Eigenvalues and eigenvectors
- Cayley-Hamilton Theorem
Section 3: Real Analysis
Topics
- Sequences and Series
- Metric spaces
- Connectedness, Compactness
- Completeness
- Uniform convergence
Other Important Sections
- Complex Analysis: Analytic functions, specialized integrals.
- Ordinary Differential Equations: First order & linear equations.
- Algebra: Groups, subgroups, normal subgroups.
- Functional Analysis: Normed linear spaces, Banach spaces.
- Numerical Analysis: Numerical solutions, integration.
- Partial Differential Equations: Method of separation of variables.
- Topology: Basis, dense sets, subsystem.
- Linear Programming: Simplex method, duality.
Exam Pattern
| Section | No. of Questions | Marks | Nature |
|---|---|---|---|
| General Aptitude | 10 | 15 | MCQ |
| Subject Questions | 55 | 85 | MCQ, MSQ, NAT |
| Total | 65 | 100 | 3 Hours |