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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...
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Chapter 2: Inverse Trigonometric Functions – Free PDF Download
Inverse trigonometric functions answer the reverse question: given a ratio, which angle produced it? Chapter 2 works through the NCERT exercise problems on evaluating these functions, their principal value branches, and key identities. Note: under the 2023 CBSE syllabus rationalisation, Exercise 2.2 and the Miscella...
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Chapter 3: Matrices – Free PDF Download
Matrices organise numbers into rows and columns so that operations like addition and multiplication can be applied to entire arrays at once. This chapter's exercises cover matrix algebra, transpose, and symmetric/skew-symmetric matrices, solved step by step below. Practice matrix operations (addition, multiplication...
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Chapter 4: Determinants – Free PDF Download
A determinant is a single number computed from a square matrix that reveals whether the matrix is invertible and shows up throughout geometry, calculus, and systems of linear equations. This chapter's exercises are solved step by step below, following the exact numbering used in the current (2026-27 session) NCERT t...
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Chapter 5: Continuity and Differentiability – Free PDF Download
Before a function can be differentiated, it first has to be continuous. Chapter 5 builds on that idea with exercises on checking continuity, applying the chain rule, and working with logarithmic and implicit differentiation, all solved here. Master the standard derivative formulas and chain rule cold before attempti...
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Chapter 6: Applications of Derivatives – Free PDF Download
Derivatives aren't just abstract slopes — they help find rates of change, maxima and minima, and approximate values. This chapter's exercises apply derivatives to real problems, worked through step by step below. 1. Find the rate of change of the area of a circle with respect to its radius r when (a) r=3cm (b) r=4cm...
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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. If d/dx[F(x)]=f(x), then ∫f(x)dx=F(x)+C, where C is the constant of integration. This is the indefinite integral.
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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. The area bounded by y=f(x), the x-axis, and the lines x=a, x=b is Area=∫ab|f(x)|dx (the modulus ensures a positive area even if the curve d...
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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. A differential equation involves derivatives of a dependent variable with re...
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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. A vector has both magnitude and direction, denoted a or with an arrow. Position vectors locate points relative to the origin. Unit vectors i, j, k represent the coordinate axes.
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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. If a line makes angles α,β,γ with the x,y,z axes, cosα,cosβ,cosγ are its direction cosines (l,m,...
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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. An LPP involves optimizing (maximizing or minimizing) a linear objective function Z=ax+by, subject to a set of linear constraints (inequalitie...
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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. The conditional probability of event A given event B has occurred is P(A|B)=P(A∩B)/P(B), provided P(B)>0.
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.