# NCERT Solutions for class 11 Maths

NCERT Solutions for class 11 maths in PDF form to free download. The NCERT solutions for CBSE board and UP board (High School and Intermediate students 2018-19 onward) students are prepared for 10 + 2 level (11th and 12th class) in accordance with NCERT Syllabus 2018-19. In class 11th maths solutions, the chapter mathematical reasoning is based on logical thinking which is to be applied further in development.

## 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.

- Exercise 1.1
- Exercise 1.2
- Exercise 1.3
- Exercise 1.4
- Exercise 1.5
- Exercise 1.6
- Miscellaneous Exercise 1
- NCERT Book Chapter 1
- Revision Books for all Chapters

#### 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.

- Exercise 3.1
- Exercise 3.2
- Exercise 3.3
- Exercise 3.4
- Miscellaneous Exercise 3
- NCERT Book Chapter 3
- Level 1 Test 1

#### Chapter 4: Principle of Mathematical Induction

The early traces of mathematical induction can be found in Euclid’s proof that 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.

- Exercise 9.1
- Exercise 9.2
- Exercise 9.3
- Exercise 9.4
- Miscellaneous Exercise 9
- Supplementary Exercise 9.4
- NCERT Book Chapter 9

#### 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 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).

- Exercise 11.1
- Exercise 11.2
- Exercise 11.3
- Exercise 11.4
- Miscellaneous Exercise 11
- NCERT Book Chapter 11

#### 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 in 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.

- Exercise 13.1
- Exercise 13.2
- Miscellaneous Exercise 13
- Supplementary Exercise 13.2
- NCERT Book Chapter 12

#### 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.

- Exercise 14.1
- Exercise 14.2
- Exercise 14.3
- Exercise 14.4
- Exercise 14.5
- Miscellaneous Exercise 14
- NCERT Book Chapter 14

#### Chapter 15: Statistics

We know that the statistics deals with data collection for specific purposes. We will do the next level of statistics in 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.

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