# Hi, I'm Rahul, I study in Class 11

And I Learn My Subjects Easily With Vikrant Academy®

## Hi, I'm Rahul, I study in Class 11

And I Learn My Subjects Easily With Vikrant Academy®

# MATHEMATICS

**Chapter 1**

**Sets**

1.1 Introduction

1.2 Sets and their Representations

1.3 The Empty Set

1.4 Finite and Infinite Sets

1.5 Equal Sets

1.6 Subsets

1.7 Power Set

1.8 Universal Set

1.9 Venn Diagrams

1.10 Operations on Sets

1.11 Complement of a Set

1.12 Practical Problems on Union and Intersection of Two Sets

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2.1 Introduction

2.2 Cartesian Product of Sets

2.3 Relations

2.4 Functions

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3.1 Introduction

3.2 Angles

3.3 Trigonometric Functions

3.4 Trigonometric Functions of Sum and Difference of Two Angles

3.5 Trigonometric Equations

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4.1 Introduction

4.2 Motivation

4.3 The Principle of Mathematical Induction

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5.1 Introduction

5.2 Complex Numbers

5.3 Algebra of Complex Numbers

5.4 The Modulus and the Conjugate of a Complex Number

5.5 Argand Plane and Polar Representation

5.6 Quadratic Equations

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6.1 Introduction

6.2 Inequalities

6.3 Algebraic Solutions of Linear Inequalities in One Variable

and their Graphical Representation

6.4 Graphical Solution of Linear Inequalities in Two Variables

6.5 Solution of System of Linear Inequalities in Two Variables

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7.1 Introduction

7.2 Fundamental Principle of Counting

7.3 Permutations

7.4 Combinations

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8.1 Introduction

8.2 Binomial Theorem for Positive Integral Indices

8.3 General and Middle Terms

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9.1 Introduction

9.2 Sequences

9.3 Series

9.4 Arithmetic Progression (A.P.)

9.5 Geometric Progression (G.P.)

9.6 Relationship Between A.M. and G.M.

9.7 Sum to n terms of Special Series

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10.1 Introduction

10.2 Slope of a Line

10.3 Various Forms of the Equation of a Line

10.4 General Equation of a Line

10.5 Distance of a Point from a Line

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11.1 Introduction

11.2 Sections of a Cone

11.3 Circle

11.4 Parabola

11.5 Ellipse

11.6 Hyperbola

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12.1 Introduction

12.2 Coordinate Axes and Coordinate Planes in

Three-Dimensional Space

12.3 Coordinates of a Point in Space

12.4 Distance between Two Points

12.5 Section Formula

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13.1 Introduction

13.2 Intuitive Idea of Derivatives

13.3 Limits

13.4 Limits of Trigonometric Functions

13.5 Derivatives

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14.1 Introduction

14.2 Statements

14.3 New Statements from Old

14.4 Special Words/Phrases

14.5 Implications

14.6 Validating Statements

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15.1 Introduction

15.2 Measures of Dispersion

15.3 Range

15.4 Mean Deviation

15.5 Variance and Standard Deviation

15.6 Analysis of Frequency Distributions

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16.1 Introduction

16.2 Random Experiments

16.3 Event

16.4 Axiomatic Approach to Probability

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# Question & Answers (Solved)

## Chapter – 3: Trigonometric Functions

Exercise 3.1 1. Find the radian measures corresponding to the following degree measures: (i) 25° (ii) – 47° 30′ (iii) 240° (iv) 520° Solution: – (iv) 520° 2. Find the degree measures corresponding to the following radian…

## Chapter – 1: Sets

Exercise 1.1 1. Which of the following are sets? Justify our answer. (i) The collection of all months of a year beginning with the letter J. (ii) The collection of ten most talented writers of India. (iii) A team of…

## Chapter – 2: Relations and Function

Exercise 2.1 1. If , find the values of x and y. Solution: – Given, As the ordered pairs are equal, the corresponding elements should also be equal. Thus, x/3 + 1 = 5/3 and y – 2/3 = 1/3…

## Chapter – 4: Principle of Mathematical Induction

Exercise 4.1 Prove the following by using the principle of mathematical induction for all n ∈ N: 1. Solution: – P (k + 1) is true whenever P (k) is true. Therefore, by the principle of mathematical…

## Chapter – 5: Complex Numbers and Quadratic Equations

Exercise 5.1 Express each of the complex number given in the Exercises 1 to 10 in the form a + ib. 1. (5i) (-3/5i) Solution: – (5i) (-3/5i) = 5 x (-3/5) x i2 = -3 x…

## Chapter – 7: Permutations and Combinations

Exercise 7.1 1. How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that (i) Repetition of the digits is allowed? (ii) Repetition of the digits is not allowed? Solution:…

## Chapter – 8: Binomial Theorem

Exercise 8.1 Expand each of the expressions in Exercises 1 to 5. 1. (1 – 2x)5 Solution: – From binomial theorem expansion we can write as (1 – 2x)5 = 5Co (1)5 – 5C1 (1)4 (2x) + 5C2 (1)3 (2x)2 – 5C3 (1)2 (2x)3 + 5C4 (1)1 (2x)4 – 5C5 (2x)5 = 1 – 5 (2x) +…

## Chapter – 9: Sequences and Series

Exercise 9.1 Write the first five terms of each of the sequences in Exercises 1 to 6 whose nth terms are: 1. an = n (n + 2) Solution: – Given, nth term of a sequence an = n (n…

## Chapter – 10: Straight Lines

EXERCISE 10.1 1. Draw a quadrilateral in the Cartesian plane, whose vertices are (– 4, 5), (0, 7), (5, – 5) and (– 4, –2). Also, find its area. Solution: – Let ABCD be the given quadrilateral…

## Chapter – 11: Conic Sections

EXERCISE 11.1 In each of the following Exercise 1 to 5, find the equation of the circle with1. Centre (0, 2) and radius 2 Solution: – Given: Centre (0, 2) and radius 2 Let us consider the…

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

EXERCISE 12.1 1. A point is on the x-axis. What are its y coordinate and z-coordinates? Solution: – If a point is on the x-axis, then the coordinates of y and z are 0. So the point is (x, 0, 0)….