GATE Fundamentals — Mathematics & General Aptitude
Engineering Mathematics (Common to All Papers — 13–15 marks)
Linear Algebra
•Matrix operations: addition, multiplication, transpose, inverse
•Determinant: |A| = 0 means singular (non-invertible)
•Eigenvalues: det(A - λI) = 0
•Cayley-Hamilton theorem: every matrix satisfies its own characteristic equation
•Rank: number of non-zero rows in row echelon form
Calculus
•Limits, continuity, differentiability
•Maxima/minima: f'(x) = 0, check f''(x)
•Integration: area under curve, volume of revolution
•Multiple integrals: change order of integration, Jacobian
Discrete Mathematics (CS Paper)
•Propositional logic: AND, OR, NOT, implications, equivalences
•Predicate logic: universal (∀) and existential (∃) quantifiers
•Set theory: union, intersection, complement, power set, Cartesian product
•Relations: reflexive, symmetric, transitive, equivalence
•Graph theory: degree, path, cycle, tree, spanning tree, Euler/Hamiltonian
Probability & Statistics
•P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
•Conditional probability: P(A|B) = P(A ∩ B)/P(B)
•Bayes' theorem: P(A|B) = P(B|A)·P(A)/P(B)
•Distributions: Binomial, Poisson, Normal (Gaussian)
•Mean, variance, standard deviation
General Aptitude — Key Topics
Verbal Ability
•Reading comprehension: identify main idea, tone, inference
•Grammar: subject-verb agreement, tense consistency, articles
•Vocabulary: synonyms, antonyms, fill in the blanks
•Sentence correction and completion
Numerical Ability
•Arithmetic: percentage, profit/loss, ratio, time-work, speed-distance
•Number theory: divisibility, HCF, LCM, remainders
•Series: arithmetic progression (AP), geometric progression (GP)
•Data interpretation: tables, bar charts, pie charts, line graphs
Logical Reasoning
•Syllogisms, Venn diagrams
•Blood relations, directions
•Coding-decoding
•Critical reasoning: assumptions, conclusions, arguments
GATE Preparation Strategy
3-Phase Approach
Phase 1 (Months 1–4): Concept Building
•Complete all subjects from standard references
•Make concise notes per topic
•Solve previous year questions after each chapter
Phase 2 (Months 5–7): Practice
•Subject-wise test series (aim: 80%+ accuracy per subject)
•Focus on weak areas identified from tests
•Revise formulas and theorems weekly
Phase 3 (Months 8–10): Full Tests
•Attempt 2 full mocks per week
•Review every wrong answer — understand root cause
•Time management: allocate based on marks per question
•Final 2 weeks: only revision, no new topics
Standard References
| Subject (CS) | Reference |
|---|
|-------------|-----------|
| DS & Algorithms | CLRS (Introduction to Algorithms), Narasimha Karumanchi |
|---|---|
| OS | Galvin (Operating System Concepts) |
| DBMS | Korth (Database System Concepts) |
| Computer Networks | Tanenbaum, Forouzan |
| TOC | Peter Linz (Introduction to Formal Languages) |
| Compiler Design | Aho, Lam, Sethi, Ullman (Dragon Book) |
| Digital Logic | Morris Mano |
| Discrete Maths | Kenneth Rosen |