# 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)….

# PHYSICS

**C H A P T E R 1**

**PHYSICAL WORLD**

1.1. What is physics ?

1.2. Scope and excitement of physics

1.3. Physics, technology and society

1.4. Fundamental forces in nature

1.5. Nature of physical laws

**C H A P T E R 2**

**UNITS AND MEASUREMENTS**

2.1. Introduction

2.2. The international system of units

2.3. Measurement of length

2.4. Measurement of mass

2.5. Measurement of time

2.6. Accuracy, precision of instruments and errors in measurement

2.7. Significant figures

2.8. Dimensions of physical quantities

2.9. Dimensional formulae and dimensional equations

2.10. Dimensional analysis and its applications

**C H A P T E R 3**

**MOTION IN A STRAIGHT LINE**

3.1. Introduction

3.2. Position, path length and displacement

3.3. Average velocity and average speed

3.4. Instantaneous velocity and speed

3.5. Acceleration

3.6. Kinematic equations for uniformly accelerated motion

3.7. Relative velocity

**C H A P T E R 4**

**MOTION IN A PLANE**

4.1. Introduction

4.2. Scalars and vectors

4.3. Multiplication of vectors by real numbers

4.4. Addition and subtraction of vectors – graphical method

4.5. Resolution of vectors

4.6. Vector addition – analytical method

4.7. Motion in a plane

4.8. Motion in a plane with constant acceleration

4.9. Relative velocity in two dimensions

4.10. Projectile motion

4.11. Uniform circular motion

**C H A P T E R 5**

**LAWS OF MOTION**

5.1. Introduction

5.2. Aristotle’s fallacy

5.3. The law of inertia

5.4. Newton’s first law of motion

5.5. Newton’s second law of motion

5.6. Newton’s third law of motion

5.7. Conservation of momentum

5.8. Equilibrium of a particle

5.9. Common forces in mechanics

5.10. Circular motion

5.11. Solving problems in mechanics

**C H A P T E R 6**

**WORK, ENERGY AND POWER**

6.1. Introduction

6.2. Notions of work and kinetic energy : The work-energy theorem

6.3. Work

6.4. Kinetic energy

6.5. Work done by a variable force

6.6. The work-energy theorem for a variable force

6.7. The concept of potential energy

6.8. The conservation of mechanical energy

6.9. The potential energy of a spring

6.10. Various forms of energy : the law of conservation of energy

6.11. Power

6.12. Collisions

**C H A P T E R 7**

**SYSTEM OF PARTICLES AND ROTATIONAL MOTION**

7.1. Introduction

7.2. Centre of mass

7.3. Motion of centre of mass

7.4. Linear momentum of a system of particles

7.5. Vector product of two vectors

7.6. Angular velocity and its relation with linear velocity

7.7. Torque and angular momentum

7.8. Equilibrium of a rigid body

7.9. Moment of inertia

7.10. Theorems of perpendicular and parallel axes

7.11. Kinematics of rotational motion about a fixed axis

7.12. Dynamics of rotational motion about a fixed axis

7.13. Angular momentum in case of rotations about a fixed axis

7.14. Rolling motion

**C H A P T E R 8**

**GRAVITATION**

8.1. Introduction

8.2. Kepler’s laws

8.3. Universal law of gravitation

8.4. The gravitational constant

8.5. Acceleration due to gravity of the earth

8.6. Acceleration due to gravity below and above the surface of earth

8.7. Gravitational potential energy

8.8. Escape speed

8.9. Earth satellite

8.10. Energy of an orbiting satellite

8.11. Geostationary and polar satellites

8.12. Weightlessness

**C H A P T E R 9**

**MECHANICAL PROPERTIES OF SOLIDS**

9.1. Introduction

9.2. Elastic behaviour of solids

9.3. Stress and strain

9.4. Hooke’s law

9.5. Stress-strain curve

9.6. Elastic moduli

9.7. Applications of elastic behaviour of materials

**C H A P T E R 10**

**MECHANICAL PROPERTIES OF FLUIDS**

10.1. Introduction

10.2. Pressure

10.3. Streamline flow

10.4. Bernoulli’s principle

10.5. Viscosity

10.6. Surface tension

**C H A P T E R 11**

**THERMAL PROPERTIES OF MATTER**

11.1. Introduction

11.2. Temperature and heat

11.3. Measurement of temperature

11.4. Ideal-gas equation and absolute temperature

11.5. Thermal expansion

11.6. Specific heat capacity

11.7. Calorimetry

11.8. Change of state

11.9. Heat transfer

11.10. Newton’s law of cooling

**C H A P T E R 12**

**THERMODYNAMICS**

12.1. Introduction

12.2. Thermal equilibrium

12.3. Zeroth law of thermodynamics

12.4. Heat, internal energy and work

12.5. First law of thermodynamics

12.6. Specific heat capacity

12.7. Thermodynamic state variables and equation of state

12.8. Thermodynamic processes

12.9. Heat engines

12.10. Refrigerators and heat pumps

12.11. Second law of thermodynamics

12.12. Reversible and irreversible processes

12.13. Carnot engine

**C H A P T E R 13**

**KINETIC THEORY**

13.1. Introduction

13.2. Molecular nature of matter

13.3. Behaviour of gases

13.4. Kinetic theory of an ideal gas

13.5. Law of equipartition of energy

13.6. Specific heat capacity

13.7. Mean free path

**C H A P T E R 14**

**OSCILLATIONS**

14.1. Introduction

14.2. Periodic and oscilatory motions

14.3. Simple harmonic motion

14.4. Simple harmonic motion and uniform circular motion

14.5. Velocity and acceleration in simple harmonic motion

14.6. Force law for simple harmonic motion

14.7. Energy in simple harmonic motion

14.8. Some systems executing Simple Harmonic Motion

14.9. Damped simple harmonic motion

14.10. Forced oscillations and resonance

**C H A P T E R 15**

**WAVES**

15.1. Introduction

15.2. Transverse and longitudinal waves

15.3. Displacement relation in a progressive wave

15.4. The speed of a travelling wave

15.5. The principle of superposition of waves

15.6. Reflection of waves

15.7. Beats

15.8. Doppler effect

# Question & Answers (Solved)

## Class 11 Physics Chapter 1 Physical World

## Chapter 2: Units and Measurements

## Chapter 3: Motion in a Straight Line

## Chapter 4: Motion in a Plane

## Chapter 5: Laws of Motion

## Chapter 6: Work Energy and Power

## Chapter 7: System of Particles and Rotational Motion

## Chapter 8: Gravitation

## Chapter 9: Mechanical Properties of Solids

## Chapter 10: Mechanical Properties of Fluids

## Chapter 11: Thermal Properties of matter

## Chapter 12: Thermodynamics

## Chapter 13: Kinetic Theory

## Chapter 14: Oscillations

## Chapter 15: Waves

# CHEMISTRY

**Unit 1**

**Some Basic Concepts of Chemistry**

1.1. Importance of Chemistry

1.2. Nature of Matter

1.3. Properties of Matter and their Measurement

1.4. Uncertainty in Measurement

1.5. Laws of Chemical Combinations

1.6. Dalton’s Atomic Theory

1.7. Atomic and Molecular Masses

1.8. Mole Concept and Molar Masses

1.9. Percentage Composition

1.10. Stoichiometry and Stoichiometric Calculations

**Unit 2**

**Structure of Atom**

2.1. Discovery of Sub-atomic Particles

2.2. Atomic Models

2.3. Developments Leading to the Bohr’s Model of Atom

2.4. Bohr’s Model for Hydrogen Atom

2.5. Towards Quantum Mechanical Model of the Atom

2.6. Quantum Mechanical Model of Atom

**Unit 3**

**Classification of Elements and Periodicity in Properties**

3.1. Why do we Need to Classify Elements ?

3.2. Genesis of Periodic Classification

3.3. Modern Periodic Law and the present form of the Periodic Table

3.4. Nomenclature of Elements with Atomic Numbers > 100

3.5. Electronic Configurations of Elements and the Periodic Table

3.6. Electronic Configurations and Types of Elements:

s-, p-, d-, f- Blocks

3.7. Periodic Trends in Properties of Elements

**Unit 4**

**Chemical Bonding and Molecular Structure**

4.1. Kössel-Lewis Approach to Chemical Bonding

4.2. Ionic or Electrovalent Bond

4.3. Bond Parameters

4.4. The Valence Shell Electron Pair Repulsion (VSEPR) Theory

4.5. Valence Bond Theory

4.6. Hybridisatio

4.7. Molecular Orbital Theory

4.8. Bonding in Some Homonuclear Diatomic Molecules

4.9. Hydrogen Bonding

**Unit 5**

**States of Matter**

5.1. Intermolecular Forces

5.2. Thermal Energy

5.3. Intermolecular Forces vs Thermal Interactions

5.4. The Gaseous State

5.5. The Gas Laws

5.6. Ideal Gas Equation

5.7. Kinetic Energy and Molecular Speeds

5.8. Kinetic Molecular Theory of Gases

5.9. Behaviour of Real Gases: Deviation from Ideal Gas Behaviour

5.10. Liquefaction of Gases

5.11. Liquid State

**Unit 6**

**Thermodynamics**

6.1. Thermodynamic Terms

6.2. Applications

6.3. Measurement of ∆U and ∆H: Calorimetry

6.4. Enthalpy Change, ∆_{r}H of a Reaction – Reaction Enthalpy

6.5. Enthalpies for Different Types of Reactions

6.6. Spontaneity

6.7. Gibbs Energy Change and Equilibrium186

**Unit 7**

**Equilibrium**

7.1. Equilibrium in Physical Processes

7.2. Equilibrium in Chemical Processes – Dynamic Equilibrium

7.3. Law of Chemical Equilibrium and Equilibrium Constant

7.4. Homogeneous Equilibria

7.5. Heterogeneous Equilibria

7.6. Applications of Equilibrium Constants

7.7. Relationship between Equilibrium Constant K,

Reaction Quotient Q and Gibbs Energy G

7.8. Factors Affecting Equilibria

7.9. Ionic Equilibrium in Solution

7.10. Acids, Bases and Salts

7.11. Ionization of Acids and Bases216

7.12. Buffer Solutions226

7.13. Solubility Equilibria of Sparingly Soluble Salts

**Unit 8**

**Redox Reactions**

8.1. Classical Idea of Redox Reactions-Oxidation and Reduction Reactions

8.2. Redox Reactions in Terms of Electron Transfer Reactions

8.3. Oxidation Number

8.4. Redox Reactions and Electrode Processes

**Unit 9**

**Hydrogen**

9.1. Position of Hydrogen in the Periodic Table

9.2. Dihydrogen, H2

9.3. Preparation of Dihydrogen, H2

9.4. Properties of Dihydrogen

9.5. Hydrides

9.6. Water

9.7. Hydrogen Peroxide (H2O2)

9.8. Heavy Water, D2O

9.9. Dihydrogen as a Fuel

**Unit 10**

**The s-Block Elements**

10.1. Group 1 Elements: Alkali Metals

10.2. General Characteristics of the Compounds of the Alkali Metals

10.3. Anomalous Properties of Lithium

10.4. Some Important Compounds of Sodium

10.5. Biological Importance of Sodium and Potassium

10.6. Group 2 Elements : Alkaline Earth Metals

10.7. General Characteristics of Compounds of the Alkaline Earth Metals

10.8. Anomalous Behaviour of Beryllium

10.9. Some Important Compounds of Calcium

10.10. Biological Importance of Magnesium and Calcium

**Unit 11**

**The p-Block Elements**

11.1. Group 13 Elements: The Boron Family

11.2. Important Trends and Anomalous Properties of Boron

11.3. Some Important Compounds of Boron

11.4. Uses of Boron and Aluminium and their Compounds

11.5. Group 14 Elements: The Carbon Family

11.6. Important Trends and Anomalous Behaviour of Carbon

11.7. Allotropes of Carbon

11.8. Some Important Compounds of Carbon and Silicon

**Unit 12**

**Organic Chemistry – Some Basic Principles and Techniques**

12.1. General Introduction

12.2. Tetravalence of Carbon: Shapes of Organic Compounds

12.3. Structural Representations of Organic Compounds

12.4. Classification of Organic Compounds

12.5. Nomenclature of Organic Compounds

12.6. Isomerism

12.7. Fundamental Concepts in Organic Reaction Mechanism

12.8. Methods of Purification of Organic Compounds

12.9. Qualitative Analysis of Organic Compounds

12.10 Quantitative Analysis

**Unit 13**

**Hydrocarbons**

13.1. Classification

13.2. Alkanes

13.3. Alkenes

13.4. Alkynes

13.5. Aromatic Hydrocarbon

13.6. Carcinogenicity and Toxicity

**Unit 14**

**Environmental Chemistry**

14.1. Environmental Pollution

14.2. Atmospheric Pollution

14.3. Water Pollution

14.4. Soil Pollution

14.5. Industrial Waste

14.6. Strategies to control Environmental Pollution

14.7. Green Chemistry

# Question & Answers (Solved)

## How many seconds are there in 2 days?

## Chapter 2: Structure of Atom

## Chapter 3: Periodicity in Properties and Classification of Elements

## Chapter 4: Chemistry Chemical Bonding and Molecular Structure

## Chapter 5: States of Matter

## Chapter 6: Thermodynamics

## Chapter 7: Equilibrium

## Chapter 8: Redox Reaction

## Chapter 9: Hydrogen

## Chapter 10: The s-Block Elements

## Chapter 11: The p-Block Elements

## Chapter 12: Organic Chemistry Some Basic Principles and Techniques

## Chapter 13: Hydrocarbons

## Chapter 14: Environmental Chemistry

# BIOLOGY

**UNIT I**

**DIVERSITY IN THE LIVING WORLD**

**Chapter 1 :** The Living World

**Chapter 2 :** Biological Classification

**Chapter 3 :** Plant Kingdom

**Chapter 4 :** Animal Kingdom

**Chapter 5 :** Morphology of Flowering Plants

**Chapter 6 :** Anatomy of Flowering Plants

**Chapter 7 :** Structural Organisation in Animals

**Chapter 8 :** Cell : The Unit of Life

**Chapter 9 :** Biomolecules

**Chapter 10 :** Cell Cycle and Cell Division

**Chapter 11 :** Transport in Plants

**Chapter 12 :** Mineral Nutrition

**Chapter 13 :** Photosynthesis in Higher Plants

**Chapter 14 :** Respiration in Plants

**Chapter 15 :** Plant Growth and Development

**Chapter 16 :** Digestion and Absorption

**Chapter 17 :** Breathing and Exchange of Gases

**Chapter 18 :** Body Fluids and Circulation

**Chapter 19 :** Excretory Products and their Elimination

**Chapter 20 :** Locomotion and Movement

**Chapter 21 :** Neural Control and Coordination

**Chapter 22 :** Chemical Coordination and Integration