## NCERT Solutions for class 11 Maths

Download NCERT Solutions for class 11 Maths in PDF form – all chapters. Along with the NCERT book, a revision book is also given, based on CBSE syllabus, providing ample practice of questions.

### 11th Maths – NCERT Solutions

#### Chapter 1: Sets

In this chapter logical approach to set theory is discussed. The term set falls in the category of undefined terms in mathematics. Also to be an element of a set is also undefined term. However, a set means a well-defined collection of objects.

#### Chapter 2: Relations and Functions

The concept of functions is very fundamental in modern mathematics. French mathematician Descartes used the word FUNCTION in the year 1637 and James Gregory gave the definition of a function in 1667.

#### Chapter 3: Trigonometric Functions

The study of trigonometry initially started in India. The ancient Indian mathematicians Aryabhatta (476 AD), Brahmagupta (598 AD), Bhaskara I (600 AD) and Bhaskara II (1114 AD) got important results.

#### Chapter 4: Principle of Mathematical Induction

The early traces of mathematical induction can be found in Euclid’s proof that the number of primes is infinite. Bhaskara II’s cyclic method (Chakravala) also introduces mathematical induction.

#### Chapter 5: Complex Numbers and Quadratic Equations

To allow the square root of negative numbers, the real number system is extended to complex numbers. In fact, Greeks were the first to recognize the fact that square root of a negative number does not exist in the real number system. It is also mentioned in ‘GANITASARA SANGRAHA’ by Indian mathematician Mahaviracharya (850 AD).

#### Chapter 6: Linear Inequalities

In this chapter, we will study how the inequalities arise in day to day practice. Whenever we compare two quantities, they are more likely to be unequal than equal.

#### Chapter 7: Permutations and Combinations

Permutation – A permutation is an arrangement in a definite order of a number of distinct of n different objects taking r at a time. Combinations – The number of ways of selecting r things out of n different things is called r combination number of n things.

#### Chapter 8: Binomial Theorem

It is believed that in the eleventh century, Persian poet and mathematician Omar Khayyam gave the general formula for (a + b)^n, where n is a positive integer. This formula or expansion is called Binomial theorem.

#### Chapter 9: Sequences and Series

Historically, Aryabhata was the first mathematician to give the formula for the sum of the square of the first n natural numbers, the sum of cubes of first n natural numbers, etc. This is given in his work ARYABHATIYAM.

#### Chapter 10: Straight Lines

French mathematician Rene Descartes was the first mathematician who used algebra for the study of geometry. Using Cartesian coordinates, he represented lines and curves by the algebraic equation.

#### Chapter 11: Conic Sections

The special curves like circles, ellipse, parabolas, and hyperbolas are called conic sections or more commonly conics. The names PARABOLA and HYPERBOLA are given by Apollonius (262 BC – 19 BC).

#### Chapter 12: Introduction to Three Dimensional Geometry

Earlier the concepts of plane coordinate geometry were initiated by French mathematician Rene Descartes and also by Fermat at the beginning of 17th century. In this chapter, we will study the coordinate geometry in the 3 – D space.

#### Chapter 13: Limits and Derivatives

BRAHMAGUPTA’S YUKTIBHASHA is considered to be the first book on calculus. BHASKAR’S work on calculus precedes much before the time of LEIBJITZ and NEWTON. BHASKARA – II used principles of differential calculus in problems on Astronomy.

#### Chapter 14: Mathematical Reasoning

In mathematics, mainly two kinds of reasoning occur. One is inductive reasoning which is studied in chapter 4 – mathematical induction and the other is deductive reasoning which we intend to study in this chapter.

#### Chapter 15: Statistics

We know that the statistics deal with data collection for specific purposes. We will do the next level of statistics in the chapter than whatever we have studied in classes 8, 9 and 10.

#### Chapter 16: Probability

Probability is the word we use calculating the degree of the certainty of events in ideal conditions. An experiment means an operation which can produce some well-defined outcomes. The classical approach is given by Blaise Pascal and the axiomatic approach is given by a Russian mathematician A Kolmogorov in 1937.

The link for the solutions to the exercises mentioned at the end of the chapters is :

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