STUDY MATERIAL · GATE DA
GATE Calculus and Optimization: questions and notes
Calculus and Optimization questions from 3 GATE papers (2024–2026) with the official answers, each solved step by step, plus notes for each topic, a formula sheet and practice questions.
- previous-year questions
- 13previous-year questions
- solved step by step
- 13solved step by step
- GATE papers, 2024–2026
- 3GATE papers, 2024–2026
- topics with notes
- 3topics with notes
TOPICS
Three topics, in the order they are taught
Taken from the official GATE 2027 syllabus. Each topic has notes, the formulas you need, its previous-year questions with the official answers and step-by-step solutions, and practice questions.
Limits, continuity and differentiability
This topic covers how a function of one real variable behaves near a point: whether a limit exists, whether the function is continuous there, and whether it has a derivative.
6 previous-year questions · 9 marks · 5 practice questions
Taylor series
A Taylor series writes a smooth function of one real variable as an infinite polynomial in powers of (x - a), built from its derivatives at the point a.
2 previous-year questions · 2 marks · 6 practice questions
Maxima, minima and single-variable optimisation
Maxima and minima locate where a function of one variable turns from rising to falling or the reverse, and single-variable optimisation uses that to find the best value of a quantity.
5 previous-year questions · 8 marks · 6 practice questions
QUESTIONS BY TOPIC AND YEAR
13 questions, by topic and year
How many questions each topic had in the DA papers of each year. This shows what was asked, not what will be asked. We placed each question under a topic ourselves; the exam paper does not label topics. Every question links back to its paper.
| Topic | 2024 | 2025 | 2026 | Total |
|---|---|---|---|---|
| Limits & continuity | 3 | 3 | · | 6 |
| Taylor series | · | 1 | 1 | 2 |
| Maxima & minima | 2 | 2 | 1 | 5 |
All three GATE DA papers are included: 2024 (IISc Bengaluru), 2025 (IIT Roorkee) and 2026 (IIT Guwahati), each with its final answer key.
Calculus and Optimization formulas by topic
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THE OFFICIAL SYLLABUS
What each paper lists under Calculus and Optimization
From the GATE 2027 syllabus PDF: all of DA Section 3, “Calculus and Optimization”. It is limited to functions of a single variable.
GATE DA
Functions of a single variable, limit, continuity and differentiability, Taylor series, maxima and minima, optimization involving a single variable.
IF YOU WOULD RATHER TALK IT THROUGH