OP Malhotra Class 12 Mathematics Solutions, Step-by-Step

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Here are free ISC Solutions for Class 12 Mathematics, updated for 2026-27. Written by expert teachers, these step-by-step answers help you understand the topic and do well in your 2026 tests.

What Makes These Class 12 Mathematics Solutions Useful

  • Full coverage: every question at the end of each chapter has a solved answer.
  • Follows 2026-27 rules: every answer matches the current ISC guidelines for Class 12 Mathematics.
  • Step-by-step help: hard topics and tough questions are broken down clearly, so ideas are easy to follow.
  • Marks in mind: these answers follow the official marking style, so you know how to write well in 2026.

Chapter-Wise Class 12 Mathematics Solutions PDF (2026-27)

Click the chapter links below to view or download the full ISC solutions for Class 12 Mathematics. Pick any chapter to begin getting ready for your 2026 exams.

Class 12 ISC Mathematics (OP Malhotra / S.Chand) - Chapter Framework

Comprehensive senior-secondary mathematical architecture aligned with the ISC board curriculum, mastering calculus, matrices, vectors, and three-dimensional geometry.

Relations, Functions & AlgebraModule 1
Equivalence relations, inverse trigonometric functions, matrix operations, properties of determinants, adjoints, and inverse matrices.
Differential & Integral CalculusModule 2
Continuity, differentiability, mean value theorems, tangents/normals, increasing/decreasing functions, indefinite integrals, and definite integrals.
Differential Equations, Vectors & 3DModule 3
Order/degree equations, variable separation, homogeneous differential equations, vector algebra, scalar/vector products, and lines/planes in space.
Board Exam Problem Sets (HOTS)High Yield
Linear programming optimization, probability distributions, Bayes' theorem, and rigorous multi-step problem sets structured for ISC board success.
Chapter 1 Relations
Chapter 01 Relations ISC Solutions Exercise 1
Chapter 10 Mean Value Theorems
Chapter 10 Mean Value Theorems ISC Solutions Exercise 10 (A)
Chapter 10 Mean Value Theorems ISC Solutions Chapter Test
Chapter 10 Mean Value Theorems ISC Solutions Exercise 10 (B)
Chapter 11 Applications of Derivatives
Chapter 11 Applications of Derivatives ISC Solutions Exercise 11 (D)
Chapter 11 Applications of Derivatives ISC Solutions Exercise 11 (C)
Chapter 11 Applications of Derivatives ISC Solutions Exercise 11 (B)
Chapter 11 Applications of Derivatives ISC Solutions Exercise 11 (A)
Chapter 12 Maxima and Minima
Chapter 12 Maxima and Minima ISC Solutions Exercise 12 (A)
Chapter 12 Maxima and Minima ISC Solutions Exercise 12 (C)
Chapter 12 Maxima and Minima ISC Solutions Exercise 12 (B)
Chapter 12 Maxima and Minima Revision
Chapter 12 Maxima and Minima Revision ISC Solutions Revision Exercise
Chapter 13 Indefinite Integral 1
Chapter 13 Indefinite Integral 1 ISC Solutions Exercise 13 (B)
Chapter 13 Indefinite Integral 1 ISC Solutions Exercise 13 (A)
Chapter 14 Indefinite Integral 2
Chapter 14 Indefinite Integral 2 ISC Solutions Exercise 14 (B)
Chapter 14 Indefinite Integral 2 ISC Solutions Exercise 14 (A)
Chapter 14 Indefinite Integral 2 ISC Solutions Exercise 14 (E)
Chapter 14 Indefinite Integral 2 ISC Solutions Exercise 14 (D)
Chapter 14 Indefinite Integral 2 ISC Solutions Exercise 14 (C)
Chapter 15 Indefinite Integral 3
Chapter 15 Indefinite Integral 3 ISC Solutions Exercise 15 (C)
Chapter 15 Indefinite Integral 3 ISC Solutions Exercise 15 (B)
Chapter 15 Indefinite Integral 3 ISC Solutions Exercise 15 (A)
Chapter 15 Indefinite Integral 3 ISC Solutions Exercise 15 (G)
Chapter 15 Indefinite Integral 3 ISC Solutions Exercise 15 (F)
Chapter 15 Indefinite Integral 3 ISC Solutions Exercise 15 (E)
Chapter 15 Indefinite Integral 3 ISC Solutions Exercise 15 (D)
Chapter 16 Definite Integrals
Chapter 16 Definite Integrals ISC Solutions Exercise 16 (B)
Chapter 16 Definite Integrals ISC Solutions Exercise 16 (A)
Chapter 16 Definite Integrals ISC Solutions Exercise 16 (D)
Chapter 16 Definite Integrals ISC Solutions Exercise 16 (C)
Chapter 17 Differential Equations
Chapter 17 Differential Equations ISC Solutions Exercise 17 (E)
Chapter 17 Differential Equations ISC Solutions Exercise 17 (D)
Chapter 17 Differential Equations ISC Solutions Exercise 17 (C)
Chapter 17 Differential Equations ISC Solutions Exercise 17 (B)
Chapter 17 Differential Equations ISC Solutions Exercise 17 (A)
Chapter 17 Differential Equations ISC Solutions Exercise 17 (G)
Chapter 17 Differential Equations ISC Solutions Exercise 17 (F)
Chapter 18 Probability
Chapter 18 Probability ISC Solutions Exercise 18 (D)
Chapter 18 Probability ISC Solutions Exercise 18 (C)
Chapter 18 Probability ISC Solutions Exercise 18 (B)
Chapter 18 Probability ISC Solutions Exercise 18 (A)
Chapter 19 Bayes Theorem
Chapter 19 Bayes Theorem ISC Solutions Exercise 19
Chapter 2 Functions
Chapter 02 Functions ISC Solutions Exercise 2 (C)
Chapter 02 Functions ISC Solutions Exercise 2 (B)
Chapter 02 Functions ISC Solutions Exercise 2 (A)
Chapter 20 Theoretical Probability Distribution
Chapter 20 Theoretical Probability Distribution ISC Solutions Exercise 20 (C)
Chapter 20 Theoretical Probability Distribution ISC Solutions Exercise 20 (B)
Chapter 20 Theoretical Probability Distribution ISC Solutions Exercise 20 (A)
Chapter 20 Theoretical Probability Distribution ISC Solutions Exercise 20 (D)
Chapter 21 Vectors
Chapter 21 Vectors ISC Solutions Exercise 21 (C)
Chapter 21 Vectors ISC Solutions Exercise 21 (B)
Chapter 21 Vectors ISC Solutions Exercise 21 (A)
Chapter 21 Vectors ISC Solutions Chapter Test
Chapter 22 Vectors
Chapter 22 Vectors ISC Solutions Exercise 22 (A)
Chapter 22 Vectors ISC Solutions Exercise 22 (C)
Chapter 22 Vectors ISC Solutions Exercise 22 (B)
Chapter 23 Three Dimensional Geometry
Chapter 23 Three Dimensional Geometry ISC Solutions Exercise 23 (D)
Chapter 23 Three Dimensional Geometry ISC Solutions Exercise 23 (C)
Chapter 23 Three Dimensional Geometry ISC Solutions Exercise 23 (B)
Chapter 23 Three Dimensional Geometry ISC Solutions Exercise 23 (A)
Chapter 23 Three Dimensional Geometry ISC Solutions Exercise 23 (F)
Chapter 23 Three Dimensional Geometry ISC Solutions Exercise 23 (E)
Chapter 24 The Plane
Chapter 24 The Plane ISC Solutions Exercise 24 (E)
Chapter 24 The Plane ISC Solutions Exercise 24 (D)
Chapter 24 The Plane ISC Solutions Exercise 24 (C)
Chapter 24 The Plane ISC Solutions Exercise 24 (B)
Chapter 24 The Plane ISC Solutions Exercise 24 (A)
Chapter 24 The Plane ISC Solutions Exercise 24 (F)
Chapter 25 Application of Integrals
Chapter 25 Application of Integrals ISC Solutions Exercise 25 (B)
Chapter 25 Application of Integrals ISC Solutions Exercise 25 (A)
Chapter 26 Application of Calculus in Commerce and Economics
Chapter 26 Application of Calculus in Commerce and Economics ISC Solutions Exercise 26 (C)
Chapter 26 Application of Calculus in Commerce and Economics ISC Solutions Exercise 26 (B)
Chapter 26 Application of Calculus in Commerce and Economics ISC Solutions Exercise 26 (A)
Chapter 26 Application of Calculus in Commerce and Economics ISC Solutions Exercise 26 (F)
Chapter 26 Application of Calculus in Commerce and Economics ISC Solutions Exercise 26 (E)
Chapter 26 Application of Calculus in Commerce and Economics ISC Solutions Exercise 26 (D)
Chapter 27 Linear Regression
Chapter 27 Linear Regression ISC Solutions Exercise 27
Chapter 28 Linear Programming
Chapter 28 Linear Programming ISC Solutions Exercise 28 (C)
Chapter 28 Linear Programming ISC Solutions Exercise 28 (B)
Chapter 28 Linear Programming ISC Solutions Exercise 28 (A)
Chapter 3 Binary Operations
Chapter 03 Binary Operations ISC Solutions Exercise 3 (C)
Chapter 03 Binary Operations ISC Solutions Exercise 3 (B)
Chapter 4 Inverse Trigonometric Functions
Chapter 04 Inverse Trigonometric Functions ISC Solutions Exercise 4
Chapter 5 Determinants
Chapter 05 Determinants ISC Solutions Exercise 5 (C)
Chapter 05 Determinants ISC Solutions Exercise 5 (B)
Chapter 05 Determinants ISC Solutions Exercise 5 (A)
Chapter 05 Determinants ISC Solutions Exercise 5 (D)
Chapter 6 Matrices
Chapter 06 Matrices ISC Solutions Exercise 6 (E)
Chapter 06 Matrices ISC Solutions Exercise 6 (D)
Chapter 06 Matrices ISC Solutions Exercise 6 (J)
Chapter 06 Matrices ISC Solutions Exercise 6 (C)
Chapter 06 Matrices ISC Solutions Exercise 6 (I)
Chapter 06 Matrices ISC Solutions Exercise 6 (B)
Chapter 06 Matrices ISC Solutions Exercise 6 (H)
Chapter 06 Matrices ISC Solutions Exercise 6 (A)
Chapter 06 Matrices ISC Solutions Exercise 6 (G)
Chapter 06 Matrices ISC Solutions Exercise 6 (F)
Chapter 8 Differentiation
Chapter 08 Differentiation ISC Solutions Exercise 8 (A)
Chapter 08 Differentiation ISC Solutions Exercise 8 (G)
Chapter 08 Differentiation ISC Solutions
Chapter 08 Differentiation ISC Solutions Exercise 8 (F)
Chapter 08 Differentiation ISC Solutions Exercise 8 (L)
Chapter 08 Differentiation ISC Solutions Exercise 8 (E)
Chapter 08 Differentiation ISC Solutions Exercise 8 (K)
Chapter 08 Differentiation ISC Solutions Exercise 8 (D)
Chapter 08 Differentiation ISC Solutions Exercise 8 (J)
Chapter 08 Differentiation ISC Solutions Exercise 8 (C)
Chapter 08 Differentiation ISC Solutions Exercise 8 (I)
Chapter 08 Differentiation ISC Solutions Exercise 8 (B)
Chapter 08 Differentiation ISC Solutions Exercise 8 (H)
Chapter 9 Indeterminate Forms of Limits
Chapter 09 Indeterminate Forms of Limits ISC Solutions Exercise 9 (A)
Chapter 09 Indeterminate Forms of Limits ISC Solutions Chapter Test
Chapter 09 Indeterminate Forms of Limits ISC Solutions Exercise 9 (B)

Explore more Useful Resources for Class 12

Mathematics

Free study material for Mathematics

Class 12 Mathematics ISC Solutions, Chapter by Chapter (2026-27)

Comprehensive chapter-wise solutions for the 2026-27 ISC Class 12 Mathematics textbook provide verified, step-by-step answers across all exercise sets. Authored by experienced educators, these detailed explanations establish a reliable academic foundation for formal school evaluations.

ISC Mathematics Solutions for Class 12

Curriculum-matched solution frameworks provide authoritative guidance for mastering complex textbook exercises, ensuring complete preparation for formal academic evaluations throughout the 2026-27 term.

Utilizing official solution sets enables students to:

  • Verifying computational and theoretical accuracy following independent exercise completion.
  • Mastering proper step-by-step derivations and structured answer presentation.
  • Reinforcing core competencies ahead of official ISC class evaluations and examinations.

Download Links for Class 12 Mathematics Solutions

Digital editions of verified textbook solutions are provided free of charge, enabling students to review complex problem sets offline at any time while maintaining a structured preparation workflow.

More Free Mathematics Downloads for Class 12

Complement your textbook review by exploring our comprehensive repository of solved sample papers, previous year examination archives, printable worksheets, and revision notes tailored for ISC Class 12 Mathematics.

📐 Strategic Insights for Class 12 ISC Mathematics Board Excellence

Class 12 board examinations require flawless execution, deep calculus mastery, and precise formula application. OP Malhotra's textbook offers a rigorous collection of challenging problems that thoroughly prepare senior-secondary students for the high-difficulty standards of the ISC board paper.

Key Focus Areas for Board Aspirants:

  • Calculus Fluency: Practicing complex integration techniques and application of derivatives regularly to secure full marks in Section B/C.
  • Vector & 3D Precision: Mastering line-plane intersections and shortest distance formulas without vector sign errors.
  • Probability Logic: Developing clear logical steps when solving conditional probability and Bayes' theorem word problems.

Recommended Revision Methodology:

  1. Verify Working Steps: Use detailed chapter solutions to cross-check integration methods and matrix determinant properties.
  2. Simulate Board Pacing: Practice full-length past papers under strict time constraints to master paper management across all sections.
  3. Maintain a Formula Log: Compile all inverse trigonometric identities, vector formulas, and differential equation forms for fast pre-exam reviews.

FAQs

How can I download the latest ISC solutions for Class 12 in PDF?

You can download chapter-wise ISC solutions for all Class 12 subjects for free from StudiesToday. All files are provided in high-quality, mobile-friendly PDF formats for easy offline viewing

Are these Class 12 solutions based on the rationalized syllabus for 2026-27?

Yes, all solutions for Class 12 are strictly aligned with the latest rationalized ISC syllabus. Deleted chapters have been removed, and answers for new question patterns have been updated for the current academic session.

Do the Class 12 solutions include step-by-step explanations?

Yes, our subject teachers provide detailed, step-by-step solutions for textbook exercises. This includes comprehensive answers for theoretical questions, solved numericals, and labeled diagrams wherever applicable.

How does practicing ISC textbook solutions help in exams?

Most ISC school tests and board exam questions are drawn directly from official textbook exercises. Practicing these solutions helps Class 12 students understand the marking scheme and structure clear, high-scoring answers.

Is it completely free to access Class 12 solutions on StudiesToday?

Yes, access to all ISC solutions, practice worksheets, and revision notes for Class 12 is 100% free. Students and teachers can view or download any chapter without registration or hidden fees.

Are ISC solutions available in both English and Hindi medium?

Yes, to assist students across different mediums, we provide Class 12 ISC solutions in multiple languages, including English Medium and Hindi Medium (हिंदी माध्यम).