NCERT Solutions for Class 11 Maths: Class 11 Maths from NCERT Solutions has solved answers for every chapters and at the end of the chapter, the student will find exercise questions to practice on. This makes it best material for students that are getting ready to sit for exams. Remember that the solutions offered here suits NCERT syllabus & curriculum.
NCERT solutions for class 11 Maths chapter wise
Chapter 1: Sets
Chapter 1 explains sets concept along with it’s representation. Topics in this chapter includes Empty set, Infinite & Finite sets, Subsets, Equal sets, Power set & Universal set. This chapter helps the students know how they can draw Venn diagrams and be conversant with concepts of Intersection & Union of sets. Moreover, other concept covered in this covered in this chapter includes Difference of sets & Complement of sets, with its properties.
Chapter 2: Relations & Functions
Chapter 2 includes an introduction, relations, Cartesian-product of sets, domain & range of a relation, domain & range of a function, inverse of a relation & functions, rules for getting domain & range, types of functions, ways of checking one-one mapping, algebra of real-functions, periodic function, and standard real functions & their graphs.
Chapter 3: Trigonometric Functions
This chapter explains the positive & negative angles, ways of measuring angles at radians and in degrees & conversion to different measures. Furthermore, this chapter also explains Trigonometric Functions definition with the assistance of unit circle, signs, general-solution of trigonometric equations, domain & range of Functions of Trigonometric & graphs.
Chapter 4: Principle of Mathematical Induction
Chapter Four includes topics like deduction, induction, process of principle of mathematical-induction, & examples for showing these principles. The student will get questions which are related to Principle of Mathematical Induction with its applications.
Chapter 5: Complex Numbers & Quadratic Equations
Chapter five explains in detail why one needs complex numbers, particularly √−1, which is motivated by inability in solving some of quadratic equations. Chapter five also allows students learn about algebraic properties for complex numbers, polar representation and argand plane of complex numbers. Other topics includes statement of fundamental-theorem of algebra, quadratic equations solutions in complex number-system & square root of complex number.
Chapter 6: Linear Inequalities
This chapter’s topics includes introduction to linear-inequalities, inequality examples in our everyday life, inequalities types, notations, rules of inequality, linear inequality solution in one-variable solution & solution set, graphical solution of linear-inequalities in two variables. The student will also learn about linear-inequalities in one variable, quadratic inequalities and linear-inequalities in two-variables.
Chapter 7: Permutations & Combinations
This chapter introduces the students to advanced permutation & combinations. This is a crucial part when learning mathematics as its applications is at numerous fields. Other concepts in this chapter includes principles of counting, basic arrangements & selections, geometric nCr applications, permutations in certain conditions, division of objects to groups of same sizes, distribution of similar objects, division of objects to groups, permutations of similar objects, number of integral-solutions of linear equations & inequations, selection of one-or-more objects, circular permutations, number of divisors & sum of divisors of natural number, & rearrangements.
Chapter 8: Binomial Theorem
Here, the students will learn about Binomial-Theorem for positive integers. Binomial theorem is used in solving complex calculations which are hard to solve utilizing repeated multiplication. Additionally, this chapter explains the history, statement & proof of Binomial-Theorem for positive integral-indices.
Chapter 9: Sequences & Series
Topics covered in this chapter discusses includes Sequence & Series, Arithmetic Progression, Arithmetic Mean, Geometric Progression, term of a Geometric Progression, sum of first n-terms of a Geometric Progression, infinite Geometric Progression & its sum, geometric mean, relation between Arithmetic Mean and Geometric Progression, formulae for special series sums etc.
Chapter 10: Straight Lines
In chapter 10, topics which are covered includes slope of line, Collinearity between 2-points, angle between two-lines, horizontal & vertical lines etc. Other concepts covered here include equation of a line, equation of lines passing via a point of intersection of two-lines, distance of a line from a point etc.
Chapter 11: Conic Sections
This chapter explains the concept of Conic-Sections in depth. The topics which are covered here includes cone, circle, parabola, ellipse, hyperbola, a straight line, a point & a pair of intersecting-lines as a degenerate-case of conic section. Furthermore, standard equations & simple properties of parabola, circle, ellipse & hyperbola are present here.
Chapter 12: Introduction to 3D Geometry
Chapter 12 explains concept of coordinate-axes & coordinate planes at three dimensions, distance between 2 points & section formula, coordinates of a point all in depth. In this chapter, the student will find 3 practice exercises.
Chapter 13: Limits and Derivatives
Chapter 13 talks about Limits & Derivatives which offers a Calculus introduction. Here, the student will first get an intuitive concept of derivative. Moreover, this chapter offers definition of a limit & algebra of limits. Here, the student will have two exercises for practicing.
Chapter 14: Mathematical Reasoning
This chapter concentrates with deductive reasoning & the student needs to be very engaging as they are needed to deduce solutions to questions depending on the scenarios given. Additionally topics here are basics of mathematical-reasoning, statement, logic, open & compound statement, disjunction, basic operation of logic, conditional sentence, biconditional sentence, truth value & truth table, table for basic-logical, tautology & contradiction, validating statements, quantified and quantifiers statements, contrapositive & converse, implications, and by contradiction.
Chapter 15: Statistics
Topics covered in this chapter includes range, Measures of dispersion, mean deviation, Standard deviation, ungrouped data Mean deviation, etc. Moreover, terminologies including statistics, limit of class, primary & secondary data, class interval, variate or variable, cumulative frequency distribution, discrete frequency distribution, frequency, and continuous frequency-distribution will be explained.
Chapter 16: Probability
Chapter sixteen explains probability concept as a measure of various phenomena uncertainty or chances of an event happening. Here the students will learn random experiments, types of event, simple event, algebra of events, compound event, mutually exclusive events, exhaustive events, etc.