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Latest Class 11 Mathematics NCERT Solutions
Chapter 1 – Sets
Sets form the foundation of modern mathematics. In this chapter, students explore the idea of a collection of well-defined objects called a set. Learn about types of sets such as finite, infinite, empty, equal, and universal sets. Understand subsets, power sets, and Venn diagrams in detail. The chapter also introduces operations on sets — union, intersection, and complement — along with their properties and real-life applications in representing data and solving problems involving overlapping groups.
Chapter 2 – Relations and Functions
This chapter builds on set theory by defining relations between pairs of elements and their domain, co-domain, and range. Learn to identify and classify different types of relations such as reflexive, symmetric, transitive, and equivalence relations. Later, understand functions as special types of relations and explore one-one, onto, into, and constant functions. The chapter also covers real-life mappings and introduces the concept of inverse functions with practical examples.
Chapter 3 – Trigonometric Functions
Trigonometric Functions expand the traditional study of triangles into a more general framework. This chapter explains radian and degree measures of angles, trigonometric ratios for all real numbers, and their graphical representations. Students also learn about trigonometric identities, transformations, and how these functions behave over intervals. Applications include solving trigonometric equations and modeling periodic phenomena found in science and engineering.
Chapter 4 – Complex Numbers and Quadratic Equations
This chapter extends the concept of real numbers to the complex number system, where numbers take the form a + bi. Understand the algebra of complex numbers, modulus and argument, and their geometric representation in the Argand plane. Students also explore quadratic equations with complex roots and how to express them in polar form. The chapter strengthens algebraic manipulation skills and introduces the use of De Moivre’s Theorem in problem-solving.
Chapter 5 – Linear Inequalities
Learn how to express inequalities algebraically and graphically. The chapter covers inequalities involving one and two variables, and students understand how to represent solution sets on number lines and coordinate planes. Explore practical applications such as optimization and feasible regions, forming a foundation for higher-level topics like linear programming in Class 12.
Chapter 6 – Permutations and Combinations
This chapter introduces counting principles — the Fundamental Principle of Counting — followed by permutations (arrangements) and combinations (selections). Students learn how to compute different arrangements of objects, handle repetition, and solve real-life problems involving probability, seating arrangements, and password generation. A strong conceptual understanding of this chapter is essential for probability and combinatorics in advanced studies.
Chapter 7 – Binomial Theorem
Discover the power of binomial expansion through the Binomial Theorem. This chapter explains how to expand expressions like (a + b)n, find specific terms, and compute binomial coefficients using Pascal’s Triangle. Learn how the theorem simplifies complex algebraic calculations and how it’s used in probability, approximation, and algebraic proofs.
Chapter 8 – Sequences and Series
Understand how numbers progress through arithmetic and geometric sequences. Learn formulas for the nth term and sum of series along with concepts like mean values, harmonic progression, and sum to infinity. The chapter emphasizes pattern recognition and practical use cases in finance, data analysis, and natural patterns.
Chapter 9 – Straight Lines
This chapter explores the Cartesian system and the equations of straight lines in various forms: slope-intercept, point-slope, two-point, intercept, and normal forms. Learn about angles between lines, parallelism, perpendicularity, and the concept of distance of a point from a line. These ideas serve as a foundation for coordinate geometry and 3D space.
Chapter 10 – Conic Sections
Study circles, parabolas, ellipses, and hyperbolas — collectively known as conic sections. Learn their standard equations, focal properties, and latus rectum. Visualize these shapes and understand their applications in physics, astronomy, and engineering. The chapter strengthens spatial and analytical understanding of curves.
Chapter 11 – Introduction to Three Dimensional Geometry
Transition from 2D to 3D by studying coordinate geometry in space. Learn to locate points using (x, y, z) coordinates, calculate distance between points, section formula, and midpoint formula. This chapter lays the groundwork for vector geometry and 3D equations of lines and planes introduced in Class 12.
Chapter 12 – Limits and Derivatives
This chapter marks the beginning of Calculus. Learn about the limit of a function, its graphical interpretation, and the derivative as the rate of change. Explore the rules of differentiation and understand how derivatives are applied in motion, growth, optimization, and economics. A crucial introduction to the world of continuous change.
Chapter 13 – Statistics
Statistics helps interpret data meaningfully. In this chapter, study measures of dispersion such as range, mean deviation, variance, and standard deviation. Learn how to compare data sets and understand coefficient of variation. These tools are vital in economics, research, and real-life data analysis.
Chapter 14 – Probability
The final chapter deepens your understanding of chance and uncertainty. Learn about random experiments, sample space, events, and their probabilities. Advance into conditional probability, independent events, and Bayes’ Theorem. Applications include risk analysis, statistics, and everyday decision-making.