NCERT Solutions For Class 11 Maths : Mathematics is a subject that is essential for students as it forms the foundation for various subjects in higher education such as engineering, science, and commerce. For students to excel in mathematics, it is important for them to have a solid understanding of the concepts and be able to apply them in solving problems. This is where NCERT solutions for Class 11 Maths come into play.
NCERT solutions for Class 11 Maths provide comprehensive and in-depth answers to all the questions given in the NCERT textbook for the subject. These solutions are designed to help students understand the concepts and develop the problem-solving skills required to excel in mathematics.
The NCERT solutions for Class 11 Maths cover a wide range of topics, including Sets and Functions, Algebra, Trigonometry, Three-Dimensional Geometry, Linear Programming, and more. The solutions are presented in a step-by-step format, making it easy for students to understand the thought process behind solving each problem.
Benefits Of Solving NCERT Solutions for Class 11 Maths
- One of the main benefits of using NCERT solutions for Class 11 Maths is that they provide a clear and concise explanation of the concepts.
- This helps students who may be struggling with the subject to grasp the material more easily and improves their overall understanding of the subject.
- Additionally, the NCERT solutions are prepared by experienced teachers and subject experts, ensuring that the information provided is accurate and up-to-date.
- Another advantage of NCERT solutions for Class 11 Maths is that they help students develop their problem-solving skills.
- The step-by-step explanations provided in the solutions help students to understand the process involved in solving each problem and apply the same techniques to solve similar problems on their own.
- This can be especially useful for students who find mathematics to be a challenging subject and may struggle to understand the concepts and solve problems on their own.
Name of Chapters in Class 11 Maths
Class 11 Maths Contain 16 Chapters. List of all the chapters of class 11 Maths are given below
- Chapter 1 Sets
- Chapter 2 Relations and Functions
- Chapter 3 Trigonometric Functions
- Chapter 4 Principle of Mathematical Induction
- Chapter 5 Complex Numbers and Quadratic Equations
- Chapter 6 Linear Inequalities
- Chapter 7 Permutations and Combinations
- Chapter 8 Binomial Theorem
- Chapter 9 Sequences and Series
- Chapter 10 Straight lines
- Chapter 11 Conic Sections
- Chapter 12 Introduction to Three Dimensional Geometry
- Chapter 13 Limits and Derivatives
- Chapter 14 Mathematical Reasoning
- Chapter 15 Statistics
- Chapter 16 Probability
Syllabus covered in Class 11 Maths
Syllabus of 11th Maths
| Chapter-1 Sets |
| Sets and their representations. Empty set. Finite and Infinite sets. Equal sets. Subsets. Subsets of the set of real numbers especially intervals (with notations). Power set. Universal set. Venn diagrams. Union and intersection of sets. Difference of sets. Complement of a set, Properties of Complement sets. |
| Chapter-2 : Relation and Function |
| Ordered pairs, Cartesian product of sets. Number of elements in the Cartesian product of two finite sets. Cartesian product of the reals with itself (upto R × R × R). Definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Function as a special kind of relation from one set to another. Pictorial representation of a function, domain, co-domain and range of a function. Real valued function of the real variable, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum and greatest integer functions with their graphs. Sum, difference, product and quotients of functions. |
| Chapter-3 : Trigonometric Functions |
| Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity sin2 x + cos2 x = 1, for all x. Signs of trigonometric functions and sketch of their graphs. Expressing sin (x+ y) and cos (x + y) in terms of sin x, sin y, cos x and cos y. Deducing the identities Identities related to sin2x, cos2x, tan2x, sin3x, cos3x and tan3x. General solution of trigonometric equations Proofs and simple applications of sine and cosine formulae. |
| Chapter-4 : Principle of Mathematical Induction |
| Process of the proof by induction, The principle of mathematical induction and simple applications. |
| Chapter-5 : Complex Number and Quadratic Equations |
| Need for complex numbers, especially −1, Brief description of algebraic properties of complex numbers. Argand plane and polar representation of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex number system, Square-root of a Complex number. |
| Chapter-6 : Linear Inequities |
| Linear inequalities, Algebraic solutions of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables. Solution of system of linear inequalities in two variables – graphially. |
| Chapter-7 : Permutations and combinations |
| Fundamental principle of counting. Factorial n. Permutations and combinations derivation of formulae and their connections, simple applications. |
| Chapter-8 : Binomial Theorem |
| History, statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle, general and middle term in binomial expansion, simple applications. |
| Chapter-9 : Sequence and Series |
| Sequence and Series. Arithmetic Progression (A.P.), Arithmetic Mean (A.M.), Geometric Progression (G.P.), general term of a G.P., sum of n terms of a G.P. Arithmetic and geometric series, infinite G.P. and its sum, geometric mean (G.M.). Relation between A.M. and G.M. Sum to n terms of the special series |
| Chapter-10 : Straight Lines |
| Brief recall of 2-D from earlier classes, shifting of origin. Slope of a line and angle between two lines. Various forms of equations of a line: parallel to axes, point-slope form, slope-intercept form, two-point form, intercepts form and normal form. General equation of a line. Equation of family of lines passing through the point of intersection of two lines. Distance of a point from a line. |
| Chapter-11 : Conic Section |
| Sections of a cone: Circles, ellipse, parabola, hyperbola, a point, a straight line and pair of intersecting lines Standard equations and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle. |
| Chapter-12 : Introduction to Three Dimensional Geometry |
| Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula. |
| Chapter-13 : Limits and Derivatives |
| Derivative introduced as rate of change both as that of distance function and geometrically, Definition of derivative, relate it to slope of tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions. |
| Chapter-14 : Mathematical Reasoning |
| Mathematically acceptable statements. Connecting words/phrases – consolidating the understanding of “if and only if (necessary and sufficient) condition”, “implies”, “and/or”, “implied by”, “and”, “or”, “there exists” and their use through variety of examples related to real life and Mathematics. Validating the statements involving the connecting words – difference between contradiction, converse and contrapositive. |
| Chapter-15 : Statistics |
| Measure of dispersion; mean deviation, variance and standard deviation of ungrouped/grouped data. Analysis of frequency distributions with equal means but different variances. |
| Chapter-16 : Probability |
| Random experiments: outcomes, sample spaces (set representation). Events: Occurrence of events, ‘not’, ‘and’ & ‘or’ events, exhaustive events, mutually exclusive events. Probability of an event, probability of ‘not’, ‘and’, & ‘or’ events. |
NCERT Solutions For Class 11 Maths Free PDF Download
Chapter 1 Set
Chapter 2 Relations And Functions
Chapter 3 Trigonometric Functions
Chapter 4 Principle of Mathematical Induction
Chapter 5 Complex Number And Quadratic Equations
Chapter 6 Linear Inequalities
Chapter 7 Permutation And Combination
Chapter 8 Binomial Theorem
Chapter 9 Sequences And Series
Chapter 10 Straight Lines
Chapter 11 Conic Sections
Chapter 12 Introduction to Three Dimensional Geometry
Chapter 13 Limits and Derivatives
Chapter 14 Mathematical Reasoning
Chapter 15 Statistics
Chapter 16 Probability
Final Words
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