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Free, original, step-by-step NCERT Solutions for Class 12 Mathematics, matching the current 2026-27 CBSE syllabus.
Each chapter below is solved question by question, in the order it appears in the textbook, so you can follow along page by page instead of jumping between sites. Click a chapter's Solutions link for the full worked answers, Extra Questions for additional practice beyond the textbook, and Revision Notes for a quick summary before a test.
Chapter 1: Relations and Functions – Free PDF Download
Chapter 1 of Class 12 Mathematics opens the book with relations and functions -- the language used throughout the rest of the syllabus (Chapter 2 Inverse Trigonometric Functions builds directly on the invertible-function ideas here). In the current 2026-27 rationalised syllabus this chapter has Exercise 1.1 (16 ques...
Solutions | Extra Questions | Revision Notes
Chapter 2: Inverse Trigonometric Functions – Free PDF Download
Complete, verified solutions to the NCERT Class 12 Maths Chapter 2 (Inverse Trigonometric Functions) exercise questions. These Class 12 Mathematics Chapter 2 solutions are also useful as quick revision notes before exams. 2.1 Find the principal value of sin⁻¹(−1/2).Ans: sin⁻¹(−1/2) = −π/6, since sin(−π/6) = −1/2 and...
Solutions | Extra Questions | Revision Notes
Chapter 3: Matrices – Free PDF Download
Complete, verified solutions to the NCERT Class 12 Maths Chapter 3 (Matrices) exercise questions. These Class 12 Mathematics Chapter 3 solutions are also useful as quick revision notes before exams. 3.1 In the matrix A = [[2,5,19,-7],[35,-2,5/2,12],[√3,1,-5,17]], write (i) the order, (ii) the number of elements, (ii...
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Chapter 4: Determinants – Free PDF Download
Complete, verified solutions to the NCERT Class 12 Maths Chapter 4 (Determinants) exercise questions. These Class 12 Mathematics Chapter 4 solutions are also useful as quick revision notes before exams. 4.1 Evaluate the determinant |2 4; -5 -1|.Ans: (2)(-1) - (4)(-5) = -2 + 20 = 18.
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Chapter 5: Continuity and Differentiability – Free PDF Download
Complete, verified solutions to the NCERT Class 12 Maths Chapter 5 (Continuity and Differentiability) exercise questions. These Class 12 Mathematics Chapter 5 solutions are also useful as quick revision notes before exams. 5.1 Prove that the function f(x)=5x-3 is continuous at x=0, at x=-3 and at x=5.Ans: f is a pol...
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Chapter 6: Applications of Derivatives – Free PDF Download
Complete, verified solutions to the NCERT Class 12 Maths Chapter 6 (Applications of Derivatives) exercise questions. These Class 12 Mathematics Chapter 6 solutions are also useful as quick revision notes before exams. 6.1 Find the rate of change of the area of a circle with respect to its radius r when r=3cm and r=4...
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Chapter 7: Integrals – Free PDF Download
Chapter 7 of Class 12 Maths is Integrals, the reverse process of differentiation. It covers indefinite and definite integrals, integration techniques, and the Fundamental Theorem of Calculus. These Class 12 Mathematics Chapter 7 solutions are also useful as quick revision notes before exams. If d/dx[F(x)]=f(x), then...
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Chapter 8: Applications of Integrals – Free PDF Download
Chapter 8 of Class 12 Maths is Applications of Integrals. It uses definite integrals to compute the area under curves, between curves, and bounded by circles/parabolas/ellipses. These Class 12 Mathematics Chapter 8 solutions are also useful as quick revision notes before exams. The area bounded by y=f(x), the x-axis...
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Chapter 9: Differential Equations – Free PDF Download
Chapter 9 of Class 12 Maths is Differential Equations. It covers the order and degree of differential equations, forming them, and solving first-order first-degree equations by variable separation, homogeneous methods, and linear equations. These Class 12 Mathematics Chapter 9 solutions are also useful as quick revi...
Solutions | Extra Questions | Revision Notes
Chapter 10: Vectors – Free PDF Download
Chapter 10 of Class 12 Maths is Vectors, covering vector representation, algebra, dot and cross products, and their geometric applications. These Class 12 Mathematics Chapter 10 solutions are also useful as quick revision notes before exams. A vector has both magnitude and direction, denoted a or with an arrow. Posi...
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Chapter 11: Three-Dimensional Geometry – Free PDF Download
Chapter 11 of Class 12 Maths is Three-Dimensional Geometry. It extends vector concepts to lines and planes in 3D space, covering direction cosines/ratios, equations of lines and planes, and distances/angles between them. These Class 12 Mathematics Chapter 11 solutions are also useful as quick revision notes before e...
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Chapter 12: Linear Programming – Free PDF Download
Chapter 12 of Class 12 Maths is Linear Programming. It covers formulating real-world optimization problems as linear programming problems (LPPs) and solving them graphically. These Class 12 Mathematics Chapter 12 solutions are also useful as quick revision notes before exams. An LPP involves optimizing (maximizing o...
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Chapter 13: Probability – Free PDF Download
Chapter 13 of Class 12 Maths is Probability, the final chapter of the syllabus. It covers conditional probability, multiplication theorem, independent events, Bayes theorem, and probability distributions. These Class 12 Mathematics Chapter 13 solutions are also useful as quick revision notes before exams. The condit...
Solutions | Extra Questions | Revision Notes
| Chapter | NCERT Solutions | Revision Notes | Extra Questions (HOTS) |
|---|---|---|---|
| Ch 1: Relations and Functions – Free PDF Download | Solutions | Revision Notes | Extra Questions |
| Ch 2: Inverse Trigonometric Functions – Free PDF Download | Solutions | Revision Notes | Extra Questions |
| Ch 3: Matrices – Free PDF Download | Solutions | Revision Notes | Extra Questions |
| Ch 4: Determinants – Free PDF Download | Solutions | Revision Notes | Extra Questions |
| Ch 5: Continuity and Differentiability – Free PDF Download | Solutions | Revision Notes | Extra Questions |
| Ch 6: Applications of Derivatives – Free PDF Download | Solutions | Revision Notes | Extra Questions |
| Ch 7: Integrals – Free PDF Download | Solutions | Revision Notes | Extra Questions |
| Ch 8: Applications of Integrals – Free PDF Download | Solutions | Revision Notes | Extra Questions |
| Ch 9: Differential Equations – Free PDF Download | Solutions | Revision Notes | Extra Questions |
| Ch 10: Vectors – Free PDF Download | Solutions | Revision Notes | Extra Questions |
| Ch 11: Three-Dimensional Geometry – Free PDF Download | Solutions | Revision Notes | Extra Questions |
| Ch 12: Linear Programming – Free PDF Download | Solutions | Revision Notes | Extra Questions |
| Ch 13: Probability – Free PDF Download | Solutions | Revision Notes | Extra Questions |
Also see the Class 12 NCERT Books catalog for the official textbook PDF.
Frequently Asked Questions
Are these Class 12 Mathematics solutions updated for the 2026-27 syllabus?
Yes, every chapter listed above is checked against the current NCERT Mathematics textbook for the 2026-27 CBSE session.
Do you also have Extra Questions and Revision Notes for Class 12 Mathematics?
Yes — wherever published, Extra Questions and/or Revision Notes are linked next to the matching chapter above.
Are these Class 12 Mathematics NCERT Solutions available in Hindi medium?
Hindi-medium solutions for Class 12 Mathematics are being added progressively. In the meantime, this English-medium solution can be used alongside your Hindi-medium NCERT textbook, since the questions and chapter numbering are identical.