UPSC Maths Optional

13 chapters · 1,473 PYQs · 128 Theorems · 113 Proofs · Years 2000–2026

✅ PYQs updated till 2026
How this page works
Proofs + PYQ Main chapter — solutions & past questions Formulae That chapter’s formula & theorem sheet
Extra reference (not tied to one chapter)
Taylor & Maclaurin series · Euler’s identity
σ-notation cheat sheet + YouTube proof walkthrough
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Paper I — chapters

P1 · Ch 1
Linear Algebra
116 PYQs 15 Theorems 14 Proofs 5 Hot Topics
Proofs + PYQ Formulae
P1 · Ch 2
Calculus
117 PYQs 12 Theorems 11 Proofs 5 Hot Topics
Proofs + PYQ Formulae
P1 · Ch 3
Analytic Geometry
111 PYQs 5 Theorems 5 Proofs 4 Hot Topics
Proofs + PYQ Formulae
P1 · Ch 4
Ordinary Differential Equations
117 PYQs 6 Theorems 6 Proofs 5 Hot Topics
Proofs + PYQ Formulae
P1 · Ch 5
Dynamics & Statics
111 PYQs 7 Theorems 7 Proofs 5 Hot Topics
Proofs + PYQ Formulae
P1 · Ch 6
Vector Analysis
119 PYQs 7 Theorems 7 Proofs 4 Hot Topics
Proofs + PYQ Formulae

Paper II — chapters

P2 · Ch 1
Modern Algebra
113 PYQs 12 Theorems 11 Proofs 5 Hot Topics
Proofs + PYQ Formulae
P2 · Ch 2
Real Analysis
111 PYQs 19 Theorems 19 Proofs 6 Hot Topics
Proofs + PYQ Formulae
P2 · Ch 3
Complex Analysis
109 PYQs 9 Theorems 9 Proofs 5 Hot Topics
Proofs + PYQ Formulae
P2 · Ch 4
Linear Programming
106 PYQs 7 Theorems 6 Proofs 4 Hot Topics
Proofs + PYQ Formulae
P2 · Ch 5
Partial Differential Equations
121 PYQs 6 Theorems 6 Proofs 5 Hot Topics
Proofs + PYQ Formulae
P2 · Ch 6
Numerical Analysis
111 PYQs 6 Theorems 6 Proofs 4 Hot Topics
Proofs + PYQ Formulae
P2 · Ch 7
Mechanics & Fluid Dynamics
111 PYQs 7 Theorems 7 Proofs 4 Hot Topics
Proofs + PYQ Formulae