Summary
Free PDF of official NCERT answers for Class 12 Mathematics Part I, covering all exercises across Chapters 1–6 — from Relations & Functions through Application of Derivatives. No sign-up required.
This answer key provides final answers to every exercise in the NCERT Class 12 Mathematics Part I textbook. It covers Chapter 1 (Exercises 1.1, 1.2, Miscellaneous), Chapter 2 (Exercises 2.1, 2.2, Miscellaneous), Chapter 3 (Exercises 3.1–3.4, Miscellaneous), Chapter 4 (Exercises 4.1–4.5, Miscellaneous), Chapter 5 (Exercises 5.1–5.7, Miscellaneous, plus Supplementary Material on derivatives of exponential and logarithmic functions), and Chapter 6 (Exercises 6.1–6.3, Miscellaneous).
Key points & formulas
- 01Chapter 1 — Relations & Functions: answers for Exercises 1.1 and 1.2 (reflexivity, symmetry, transitivity, injectivity, surjectivity) and Miscellaneous Exercise.
- 02Chapter 2 — Inverse Trigonometric Functions: answers for Exercises 2.1 and 2.2 (principal value branches, identities) and Miscellaneous Exercise.
- 03Chapter 3 — Matrices: answers for Exercises 3.1 through 3.4 (order, operations, transpose, symmetric/skew-symmetric) and Miscellaneous Exercise.
- 04Chapter 4 — Determinants: answers for Exercises 4.1 through 4.5 (minors, cofactors, adjoint, inverse, solving linear systems) and Miscellaneous Exercise.
- 05Chapter 5 — Continuity & Differentiability: answers for Exercises 5.1 through 5.7 (continuity, implicit/parametric/logarithmic differentiation, second-order derivatives) and Miscellaneous Exercise, plus Supplementary Material (Theorem 5 — derivatives of ex and loge x).
- 06Chapter 6 — Application of Derivatives: answers for Exercises 6.1 through 6.3 (rates of change, increasing/decreasing functions, maxima and minima) and Miscellaneous Exercise.
- 07Covers all chapter-end Miscellaneous Exercises for Chapters 1–6, giving complete practice coverage for the Part I syllabus.
Frequently asked questions
01Is this NCERT Class 12 Maths Part I answer key PDF free to download?
Yes — the PDF is free to view and download directly from this page. No account or sign-up is needed.
02Which chapters are covered in the NCERT Class 12 Maths Part I answers?
The answer key covers all six chapters of Part I: Chapter 1 (Relations & Functions), Chapter 2 (Inverse Trigonometric Functions), Chapter 3 (Matrices), Chapter 4 (Determinants), Chapter 5 (Continuity & Differentiability), and Chapter 6 (Application of Derivatives).
03Does this PDF include answers to Miscellaneous Exercises?
Yes — every Miscellaneous Exercise for Chapters 1 through 6 is included alongside the numbered exercises.
04How many exercises are covered in Chapter 5 (Continuity & Differentiability)?
Chapter 5 has seven exercises (5.1–5.7), a Miscellaneous Exercise, and a Supplementary Material section covering derivatives of exponential and logarithmic functions — all included in this answer key.
05Are answers to Chapter 4 determinants and matrix inverse problems included?
Yes — Exercises 4.1 through 4.5 cover determinants, minors and cofactors, adjoint, inverse of a matrix, and solving systems of linear equations using matrices. All answers and Miscellaneous Exercise answers are included.
06Does the Class 12 Maths Part I answer key cover Application of Derivatives?
Yes — Chapter 6 covers rates of change (Exercise 6.1), increasing and decreasing functions (Exercise 6.2), and maxima and minima (Exercise 6.3), along with the Miscellaneous Exercise.
07Where can I find NCERT Class 12 Maths answers for inverse trigonometric functions?
Chapter 2 answers are in this PDF — Exercises 2.1 and 2.2 give principal values and results of inverse trig identities, and the Miscellaneous Exercise is also included.
08Is this the official NCERT answer key or a third-party solution guide?
This is the official NCERT-published answer key reprinted from the Part I textbook (Reprint 2026-27). It provides final answers, not step-by-step solutions.
09Does the PDF include answers for Chapter 3 Matrices, including symmetric and skew-symmetric matrix problems?
Yes — Exercises 3.1 through 3.4 and the Miscellaneous Exercise for Chapter 3 are all covered, including problems on matrix operations, transpose, symmetric and skew-symmetric decomposition.
10Can I use these answers to check my work for CBSE Class 12 board exam preparation?
Yes — this is the standard answer key for all Part I textbook exercises. It is best used to verify final answers after attempting problems yourself, covering all topics that appear in the CBSE Class 12 board exam from Chapters 1–6.
More chapters in Mathematics Part I
This is the complete Mathematics Part I Chapter 9 as published by NCERT — every diagram, solved example, and exercise included, free. Browse all CBSE Class 12 textbooks.
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