Q1. The direction ratios of the line (x-5)/(3)=(y+4)/(7)=(2-z)/(6) are
- 3, 7, 6
- 5, -4, 2
- 3, 7, -6
- -5, 4, -2
NCERT · Class 12
NCERT Class 12 Mathematics: Chapter List and Official PDFs
All 13 chapters of the NCERT Class 12 Mathematics textbook(s), with the section headings of each chapter and a link to the official PDF on ncert.nic.in. Open a chapter to see what it covers.
13 chapters2 books
Mathematics Part-I (Textbook for Class XII)
Chapter 1: Relations and FunctionsUnit-I: Relations and Functions
- 1.1 Introduction
- 1.2 Types of Relations
- 1.3 Types of Functions
- 1.4 Composition of Functions and Invertible Function
- Miscellaneous Exercise
- Summary
- Historical Note
Chapter 2: Inverse Trigonometric FunctionsUnit-I: Relations and Functions
- 2.1 Introduction
- 2.2 Basic Concepts
- 2.3 Properties of Inverse Trigonometric Functions
- Miscellaneous Exercise
- Summary
- Historical Note
Chapter 3: MatricesUnit-II: Algebra
- 3.1 Introduction
- 3.2 Matrix
- 3.3 Types of Matrices
- 3.4 Operations on Matrices
- 3.5 Transpose of a Matrix
- 3.6 Symmetric and Skew Symmetric Matrices
- 3.7 Invertible Matrices
- Miscellaneous Exercise
- Summary
Chapter 4: DeterminantsUnit-II: Algebra
- 4.1 Introduction
- 4.2 Determinant
- 4.3 Area of a Triangle
- 4.4 Minors and Cofactors
- 4.5 Adjoint and Inverse of a Matrix
- 4.6 Applications of Determinants and Matrices
- Miscellaneous Exercise
- Summary
- Historical Note
Chapter 5: Continuity and DifferentiabilityUnit-III: Calculus
- 5.1 Introduction
- 5.2 Continuity
- 5.3 Differentiability
- 5.4 Exponential and Logarithmic Functions
- 5.5 Logarithmic Differentiation
- 5.6 Derivatives of Functions in Parametric Forms
- 5.7 Second Order Derivative
- Miscellaneous Exercise
- Summary
Chapter 6: Application of DerivativesUnit-III: Calculus
- 6.1 Introduction
- 6.2 Rate of Change of Quantities
- 6.3 Increasing and Decreasing Functions
- 6.4 Maxima and Minima
- Miscellaneous Exercise
- Summary
Mathematics Part-II (Textbook for Class XII)
Chapter 7: IntegralsUnit-III: Calculus
- 7.1 Introduction
- 7.2 Integration as an Inverse Process of Differentiation
- 7.3 Methods of Integration
- 7.4 Integrals of Some Particular Functions
- 7.5 Integration by Partial Fractions
- 7.6 Integration by Parts
- 7.7 Definite Integral
- 7.8 Fundamental Theorem of Calculus
- 7.9 Evaluation of Definite Integrals by Substitution
- 7.10 Some Properties of Definite Integrals
- Miscellaneous Exercise
- Summary
Chapter 8: Application of IntegralsUnit-III: Calculus
- 8.1 Introduction
- 8.2 Area under Simple Curves
- Miscellaneous Exercise
- Summary
- Historical Note
Chapter 9: Differential EquationsUnit-III: Calculus
- 9.1 Introduction
- 9.2 Basic Concepts
- 9.3 General and Particular Solutions of a Differential Equation
- 9.4 Methods of Solving First Order, First Degree Differential Equations
- Miscellaneous Exercise
- Summary
- Historical Note
Chapter 10: Vector AlgebraUnit-IV: Vectors and Three-Dimensional Geometry
- 10.1 Introduction
- 10.2 Some Basic Concepts
- 10.3 Types of Vectors
- 10.4 Addition of Vectors
- 10.5 Multiplication of a Vector by a Scalar
- 10.6 Product of Two Vectors
- Miscellaneous Exercise
- Summary
- Historical Note
Chapter 11: Three Dimensional GeometryUnit-IV: Vectors and Three-Dimensional Geometry
- 11.1 Introduction
- 11.2 Direction Cosines and Direction Ratios of a Line
- 11.3 Equation of a Line in Space
- 11.4 Angle between Two Lines
- 11.5 Shortest Distance between Two Lines
- Miscellaneous Exercise
- Summary
Chapter 12: Linear ProgrammingUnit-V: Linear Programming
- 12.1 Introduction
- 12.2 Linear Programming Problem and its Mathematical Formulation
- Summary
- Historical Note
Chapter 13: ProbabilityUnit-VI: Probability
- 13.1 Introduction
- 13.2 Conditional Probability
- 13.3 Multiplication Theorem on Probability
- 13.4 Independent Events
- 13.5 Bayes' Theorem
- Miscellaneous Exercise
- Summary
- Historical Note
Free sample questions
Three sample questions with answers. Full explanations — and the rest of the question bank — are free to read after you sign up.
Q2. Assertion (A): The rational function (x²+1)/(x²-5x+6) must be divided before it is decomposed into partial fractions. Reason (R): The degree of the numerator is not less than the degree of the denominator, so the function is improper.
- Both A and R are true and R is the correct explanation of A.
- Both A and R are true but R is not the correct explanation of A.
- A is true but R is false.
- A is false but R is true.
Show answer
Correct answer: A. Both A and R are true and R is the correct explanation of A.
🔒 The full explanation is free to read after you sign up →
Q3. If A is a non-singular square matrix of order 3 with |A|=-4, then |adjA| equals
- -16
- 16
- 4
- -64
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Chapter lists follow the NCERT textbooks as available to us; textbooks are revised from time to time, so confirm on ncert.nic.in.
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