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, ∆rH 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
