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JEE 2028 Syllabus
2028 ( Online Exam : 3 hr 15 mins )
Number of Question : 25 | Total Marks : 100 Number of Question : 25 | Total Marks : 100 Number of Question : 25 | Total Marks : 100
Physics Chemistry Mathematics
Class 11 Class 12 Class 11 Class 12 Class 11 Class 12
Physical World and Measurement Electrostatics Some Basic Concepts of Chemistry Solutions Diversity of Living Organisms Reproduction
Kinematics Current Electricity Structure of Atom Electrochemistry Structural Organisation Genetics & Evolution
Laws of Motion Magnetic Effects of Current & Magnetism Classification of Elements and Periodicity in Properties Chemical Kinetics Cell Biology Biology in Human Welfare
Work, Energy and Power EMI and Alternating Current Chemical Bonding & Molecular Structure p Block Elements Plant Physiology Biotechnology
Motion of System of Particles and Rigid Body Electromagnetic Waves Chemical Thermodynamics d and f Block Elements Human Physiology Ecology
Gravitation Optics Chemical & Ionic Equilibrium Coordination Compounds    
Properties of Bulk Matter Dual Nature of Radiation & Matter Redox Reactions Haloalkanes and Haloarenes    
Thermodynamics Atoms and Nuclei Organic Chemistry: Basic Principles Alcohols, Phenols, and Ethers    
Behaviour of Perfect Gas and Kinetic Theory Electronic Devices Hydrocarbons Aldehydes, Ketones & Carboxylic Acids    
Oscillations and Waves     Organic Compounds Containing Nitrogen    
      Biomolecules    


Physics

Class XI :



1. Physical World and Measurement
  • 1. Units and Measurements.
  • 2. Need for measuremen.
  • 3. Units of measurement.
  • 4. Systems of Units.
  • 5. SI Units.
  • 6. Fundamental and Derived Units.
  • 7. Significant Figures.
  • 8. Dimensions of Physical Quantities.
  • 9. Dimensional Analysis and its Applications.
2. Kinematics
  • 1. Frame of Reference.
  • 2. Motion in Straight Line.
  • 3. Elementary Concepts of Differentiation and Integration for Describing Motion.
  • 4. Uniform and Non-Uniform Motion.
  • 5. Average Speed and Instantaneous Velocity.
  • 6. Uniformly Accelerated Motion.
  • 7. Velocity Time Graph and Position Time Graph.
  • 8. Scalar Quantities and Vector Quantities.
  • 9. Axial and Polar Vectors.
  • 10. Addition and Subtraction of Vectors.
  • 11. Relative Velocity.
  • 12. Unit Vector.
  • 13. Resolution of a Vector In a Plane.
  • 14. Scalar and Vector Product of Vector.
  • 15. Motion in a plane.
  • 16. Cases of Uniform Velocity and Uniform Acceleration-Projectile Motion.
  • 17. Uniform Circular Motion.
3. Laws of Motion
  • 1. Intuitive Concept of Force.
  • 2. Inertia.
  • 3. Newton's First Law of Motion.
  • 4. Momentum and Newton's Second Law of Motion.
  • 5. Impulse.
  • 6. Newton's Third Law of Motion.
  • 7. Law of Conservation of Linear Momentum and its Applications.
  • 8. Equilibrium of Concurrent Forces.
  • 9. Static and Kinetic Friction.
  • 10. Laws of Friction.
  • 11. Rolling Friction.
  • 12. Lubrication.
  • 13. Dynamics of Uniform Circular Motion.
  • 14. Centripetal Force.
  • 15. Examples of Circular Motion ( Vehicle on a Level Circular Road,Vehicle on a Banked Road ).
4. Work Energy and Power
  • 1. Work Done by a Constant Force and a Variable Force.
  • 2. Kinetic Energy.
  • 3. Work-Energy Theorem.
  • 4. Power.
  • 5. Notion of Potential Energy.
  • 6. Potential Energy of a Spring.
  • 7. Conservative Forces..
  • 8. Conservation of Mechanical Energy ( Kinetic Energy and Potential Energy ).
  • 9. Non-Conservative Forces.
  • 10. Motion in a Vertical Circle.
  • 11. Elastic and Inelastic Collisions in One and Two Dimension.
5. Motion of System of Particles and Rigid Body
  • 1. Centre of Mass of a Two-Particle System.
  • 2. Momentum Conservation and Centre of Mass Motion.
  • 3. Centre of Mass of a Rigid Body.
  • 4. Centre of Mass of a Uniform Rod.
  • 5. Moment of a Force.
  • 6. Torque.
  • 7. Angular Momentum.
  • 8. Law of Conservation of Angular Momentum and its Applications.
  • 9. Equilibrium of Rigid Bodies.
  • 10. Rigid Body Rotation.
  • 11. Equations of Rotational Motion.
  • 12. Comparison of Linear and Rotational Motion.
  • 13. Moment of Inertia.
  • 14. Radius of Gyration.
  • 15. Values of Moments of Inertia for Simple Geometrical Objects (No Derivation).
6. Gravitation
  • 1. Kepler's Laws of Planetary Motion.
  • 2. Universal Law of Gravitation.
  • 3. Acceleration Due to Gravity and its Variation with Altitude and Depth.
  • 4. Gravitational Potential Energy AND Gravitational Potential.
  • 5. Escape Velocity.
  • 6. Orbital Velocity of a Satellite.
7. Properties of Bulk Matter
  • 1. Elastic Behaviour.
  • 2. Stress-Strain Relationship.
  • 3. Hooke's Law.
  • 4. Young's Modulus.
  • 5. Bulk Modulus.
  • 6. Shear Modulus of Rigidity.
  • 7. Poisson's Ratio.
  • 8. Elastic Energy.
  • 9. Pressure Due to a Fluid Column.
  • 10. Pascal's Law and its Applications ( Hydraulic Lift and Hydraulic Brakes ).
  • 11. Effect of Gravity on Fluid Pressure.
  • 12. Viscosity.
  • 13. Stokes' Law.
  • 14. Terminal Velocity.
  • 15. Streamline and Turbulent Flow.
  • 16. Critical Velocity.
  • 17. Bernoulli's Theorem and its Applications.
  • 18. Surface Energy and Surface Tension.
  • 19. Angle of Contact.
  • 20. Excess Pressure Across a Curved Surface.
  • 21. Applications of Surface Tension ideas to drops.
  • 22. Bubbles and Capillary Rise.
  • 23. Heat.
  • 24. Temperature.
  • 25. Thermal Expansion.
  • 26. Thermal Expansion of Solids.
  • 27. Thermal Expansion of Liquids.
  • 28. Thermal Expansion of Gases.
  • 29. Anomalous Expansion of Water.
  • 30. Specific Heat Capacity.
  • 31. Cp - Cv Calorimetry.
  • 32. Change of State - Latent Heat Capacity.
  • 33. Heat Transfer - Conduction,Conduction,Convection and Radiation.
  • 34. Thermal Conductivity.
  • 35. Qualitative Ideas of Blackbody Radiation.
  • 36. Wien's Displacement Law.
  • 37. Stefan's Law.
8. Thermodynamics
  • 1. Thermal Equilibrium and Definition of Temperature ( Zeroth Law of Thermodynamics ).
  • 2. Heat.
  • 3. Work and Internal Energy.
  • 4. First Law of Thermodynamics.
  • 5. Isothermal and Adiabatic Process.
  • 6. Second Law of Thermodynamics.
  • 7. Reversible and Irreversible Processes.
9. Behaviour of Perfect Gas and Kinetic Theory
  • 1. Equation of State of a Perfect Gas.
  • 2. Work Done in Compressing a Gas.
  • 3. Kinetic Theory of Gases - Assumptions.
  • 4. Concept of Pressure.
  • 5. Kinetic Interpretation of Temperature.
  • 6. RMS Speed of Gas Molecules.
  • 7. Degrees of Freedom.
  • 8. Law of Equipartition of Energy ( Statement Only ) and Applications to Specific Heat Capacities of Gases.
  • 9. Concept of Mean Free Path.
  • 10. Avogadro's Number.
10. Oscillations and Waves
  • 1. Periodic Motion - Time Period.
  • 2. Frequency.
  • 3. Displacement as a Function of Time.
  • 4. Periodic Functions.
  • 5. Simple Harmonic Motion (SHM)and its Equation.
  • 6. Phase.
  • 7. Oscillations of a Loaded Spring : Restoring Force and Force Constant.
  • 8. Energy in Simple Harmonic Motion.
  • 9 . Kinetic Energy and Potential Energy.
  • 10. Simple Pendulum derivation of expression for its time period.
  • 11. Free Oscillations.
  • 12. Forced , Forced and Damped Oscillations(qualitative ideas only).
  • 13. Resonance.
  • 14. Wave Motion.
  • 15. Transverse and Longitudinal Waves.
  • 16. Speed of Wave Motion.
  • 17. Displacement Relation for a Progressive Wave.
  • 18. Principle of Superposition of Waves.
  • 19. Reflection of Waves.
  • 20. Standing Waves in Strings and Organ Pipes.
  • 21. Fundamental Mode and Harmonics.
  • 22. Beats.


Class XII :



1. Electrostatics
  • 1. Electric Charges.
  • 2. Conservation of Charge.
  • 3. Coulomb's Law.
  • 4. Force Between Two Point Charges.
  • 5. Forces Between Multiple Charges.
  • 6. Superposition Principle and Continuous Charge Distribution.
  • 7. Electric Field.
  • 8. Electric Field Lines.
  • 9. Electric Dipole.
  • 10. Electric Field Due to an Electric Dipole.
  • 11. Torque on a Dipole in a Uniform Electric Field.
  • 12. Electric Flux.
  • 13. Gauss's Theorem.
  • 14. Applications of Gauss's Theorem.
  • 15. Electric Field Due to an Infinitely Long Straight Wire.
  • 16. Electric Field Due to a Uniformly Charged Infinite Plane Sheet.
  • 17. Electric Field Due to a Uniformly Charged Thin Spherical Shell.
  • 18. Electric Potential.
  • 19. Potential Difference.
  • 20. Electric Potential Due to a Point Charge.
  • 21. Electric Potential Due to an Electric Dipole.
  • 22. Electric Potential Due to a System of Charges.
  • 23. Equipotential Surfaces.
  • 24. Electrical Potential Energy of a System of Two Point Charges.
  • 25. Electrical Potential Energy of an Electric Dipole in an Electrostatic Field.
  • 26. Conductors.
  • 27. Insulators.
  • 28. Free Charges Inside a Conductor.
  • 29. Bound Charges Inside a Conductor.
  • 30. Dielectrics.
  • 31. Electric Polarisation.
  • 32. Capacitors.
  • 33. Capacitance.
  • 34. Combination of Capacitors in Series.
  • 35. Combination of Capacitors in Parallel.
  • 36. Capacitance of a Parallel Plate Capacitor.
  • 37. Capacitance of a Parallel Plate Capacitor with Dielectric Medium.
  • 38. Energy Stored in a Capacitor.
2. Current Electricity
  • 1. Electric Current.
  • 2. Flow of Electric Charges in a Metallic Conductor.
  • 3. Drift Velocity.
  • 4. Mobility.
  • 5. Relation Between Drift Velocity and Electric Current.
  • 6. Ohm's Law.
  • 7. Electrical Resistance.
  • 8. V-I Characteristics.
  • 9. Linear V-I Characteristics.
  • 10. Non-Linear V-I Characteristics.
  • 11. Electrical Energy.
  • 12. Electrical Power.
  • 13. Electrical Resistivity.
  • 14. Electrical Conductivity.
  • 15. Carbon Resistors.
  • 16. Colour Code for Carbon Resistors.
  • 17. Series Combination of Resistors.
  • 18. Parallel Combination of Resistors.
  • 19. Temperature Dependence of Resistance.
  • 20. Internal Resistance of a Cell.
  • 21. Potential Difference of a Cell.
  • 22. Electromotive Force (EMF) of a Cell.
  • 23. Combination of Cells in Series.
  • 24. Combination of Cells in Parallel.
  • 25. Kirchhoff's Laws.
  • 26. Applications of Kirchhoff's Laws.
  • 27. Wheatstone Bridge.
  • 28. Metre Bridge.
  • 29. Potentiometer.
  • 30. Principle of Potentiometer.
  • 31. Measurement of Potential Difference Using Potentiometer.
  • 32. Comparison of EMF of Two Cells.
  • 33. Measurement of Internal Resistance of a Cell.
3. Magnetic Effects of Current and Magnetism
  • 1. Concept of Magnetic Field.
  • 2. Oersted's Experiment.
  • 3. Biot-Savart Law.
  • 4. Application of Biot-Savart Law to a Current Carrying Circular Loop.
  • 5. Ampere's Circuital Law.
  • 6. Applications of Ampere's Law.
  • 7. Magnetic Field Due to an Infinitely Long Straight Wire.
  • 8. Straight Solenoid.
  • 9. Toroidal Solenoid.
  • 10. Force on a Moving Charge in a Uniform Magnetic Field.
  • 11. Force on a Moving Charge in a Uniform Electric Field.
  • 12. Cyclotron.
  • 13. Force on a Current-Carrying Conductor in a Uniform Magnetic Field.
  • 14. Force Between Two Parallel Current-Carrying Conductors.
  • 15. Definition of Ampere.
  • 16. Torque on a Current Loop in a Uniform Magnetic Field.
  • 17. Moving Coil Galvanometer.
  • 18. Current Sensitivity of a Moving Coil Galvanometer.
  • 19. Conversion of Galvanometer into Ammeter.
  • 20. Conversion of Galvanometer into Voltmeter.
  • 21. Current Loop as a Magnetic Dipole.
  • 22. Magnetic Dipole Moment of a Current Loop.
  • 23. Magnetic Dipole Moment of a Revolving Electron.
  • 24. Magnetic Field Intensity Due to a Magnetic Dipole.
  • 25. Magnetic Field Along the Axis of a Bar Magnet.
  • 26. Magnetic Field Perpendicular to the Axis of a Bar Magnet.
  • 27. Torque on a Magnetic Dipole in a Uniform Magnetic Field.
  • 28. Bar Magnet as an Equivalent Solenoid.
  • 29. Magnetic Field Lines.
  • 30. Earth's Magnetic Field.
  • 31. Magnetic Elements of Earth.
  • 32. Paramagnetic Substances.
  • 33. Diamagnetic Substances.
  • 34. Ferromagnetic Substances.
  • 35. Examples of Paramagnetic Substances.
  • 36. Examples of Diamagnetic Substances.
  • 37. Examples of Ferromagnetic Substances.
  • 38. Electromagnets.
  • 39. Factors Affecting the Strength of Electromagnets.
  • 40. Permanent Magnets.
4. Electromagnetic Induction and Alternating Current
  • 1. Electromagnetic Induction.
  • 2. Faraday's Laws of Electromagnetic Induction.
  • 3. Induced EMF.
  • 4. Induced Current.
  • 5. Lenz's Law.
  • 6. Eddy Currents.
  • 7. Self Induction.
  • 8. Mutual Induction.
  • 9. Alternating Current (AC).
  • 10. Peak Value of Alternating Current.
  • 11. Peak Value of Alternating Voltage.
  • 12. RMS Value of Alternating Current.
  • 13. RMS Value of Alternating Voltage.
  • 14. Reactance.
  • 15. Impedance.
  • 16. LC Oscillations.
  • 17. LCR Series Circuit.
  • 18. Resonance in LCR Circuit.
  • 19. Power in AC Circuits.
  • 20. Wattless Current.
  • 21. AC Generator.
  • 22. Transformer.
5. Electromagnetic Waves
  • 1. Need for Displacement Current.
  • 2. Electromagnetic Waves.
  • 3. Characteristics of Electromagnetic Waves.
  • 4. Transverse Nature of Electromagnetic Waves.
  • 5. Electromagnetic Spectrum.
  • 6. Radio Waves.
  • 7. Uses of Radio Waves.
  • 8. Microwaves.
  • 9. Uses of Microwaves.
  • 10. Infrared Rays.
  • 11. Uses of Infrared Rays.
  • 12. Visible Light.
  • 13. Uses of Visible Light.
  • 14. Ultraviolet Rays.
  • 15. Uses of Ultraviolet Rays.
  • 16. X-Rays.
  • 17. Uses of X-Rays.
  • 18. Gamma Rays.
  • 19. Uses of Gamma Rays.
6. Optics
  • 1. Reflection of Light.
  • 2. Spherical Mirrors.
  • 3. Mirror Formula.
  • 4. Refraction of Light.
  • 5. Total Internal Reflection.
  • 6. Applications of Total Internal Reflection.
  • 7. Optical Fibres.
  • 8. Refraction at Spherical Surfaces.
  • 9. Lenses.
  • 10. Thin Lens Formula.
  • 11. Lensmaker's Formula.
  • 12. Magnification.
  • 13. Power of a Lens.
  • 14. Combination of Thin Lenses in Contact.
  • 15. Combination of a Lens and a Mirror.
  • 16. Refraction Through a Prism.
  • 17. Dispersion of Light Through a Prism.
  • 18. Scattering of Light.
  • 19. Blue Colour of the Sky.
  • 20. Reddish Appearance of the Sun at Sunrise.
  • 21. Reddish Appearance of the Sun at Sunset.
  • 22. Optical Instruments.
  • 23. Microscopes.
  • 24. Magnifying Power of a Microscope.
  • 25. Astronomical Telescopes.
  • 26. Reflecting Telescope.
  • 27. Refracting Telescope.
  • 28. Magnifying Power of an Astronomical Telescope.
  • 29. Wave Optics.
  • 30. Wavefront.
  • 31. Huygens' Principle.
  • 32. Reflection of Plane Wavefront at a Plane Surface.
  • 33. Refraction of Plane Wavefront at a Plane Surface.
  • 34. Laws of Reflection Using Huygens' Principle.
  • 35. Laws of Refraction Using Huygens' Principle.
  • 36. Interference of Light.
  • 37. Young's Double Slit Experiment.
  • 38. Fringe Width.
  • 39. Expression for Fringe Width.
  • 40. Coherent Sources.
  • 41. Sustained Interference of Light.
  • 42. Diffraction.
  • 43. Diffraction Due to a Single Slit.
  • 44. Width of Central Maximum.
  • 45. Resolving Power of a Microscope.
  • 46. Resolving Power of an Astronomical Telescope.
  • 47. Polarisation.
  • 48. Plane Polarised Light.
  • 49. Brewster's Law.
  • 50. Uses of Plane Polarised Light.
  • 51. Polaroids.
  • 52. Uses of Polaroids.
7. Dual Nature of Matter and Radiation
  • 1. Dual Nature of Radiation.
  • 2. Photoelectric Effect.
  • 3. Hertz's Observations on Photoelectric Effect.
  • 4. Lenard's Observations on Photoelectric Effect.
  • 5. Einstein's Photoelectric Equation.
  • 6. Particle Nature of Light.
  • 7. Matter Waves.
  • 8. Wave Nature of Particles.
  • 9. de Broglie Relation.
  • 10. Davisson-Germer Experiment.
  • 11. Conclusion of Davisson-Germer Experiment.
8. Atoms and Nuclei
  • 1. Alpha-Particle Scattering Experiment.
  • 2. Rutherford's Model of Atom.
  • 3. Bohr Model of Atom.
  • 4. Energy Levels in an Atom.
  • 5. Hydrogen Spectrum.
  • 6. Composition of Nucleus.
  • 7. Size of Nucleus.
  • 8. Atomic Masses.
  • 9. Isotopes.
  • 10. Isobars.
  • 11. Isotones.
  • 12. Radioactivity.
  • 13. Alpha Particles and Their Properties.
  • 14. Beta Particles and Their Properties.
  • 15. Gamma Rays and Their Properties.
  • 16. Radioactive Decay Law.
  • 17. Mass-Energy Relation.
  • 18. Mass Defect.
  • 19. Binding Energy per Nucleon.
  • 20. Variation of Binding Energy with Mass Number.
  • 21. Nuclear Fission.
  • 22. Nuclear Fusion.
9. Electronic Devices
  • 1. Energy Bands in Solids.
  • 2. Metals.
  • 3. Insulators.
  • 4. Semiconductors.
  • 5. Semiconductor Diode.
  • 6. I-V Characteristics of a Semiconductor Diode.
  • 7. Forward Bias of a Diode.
  • 8. Reverse Bias of a Diode.
  • 9. Diode as a Rectifier.
  • 10. Light Emitting Diode (LED).
  • 11. I-V Characteristics of LED.
  • 12. Photodiode.
  • 13. I-V Characteristics of Photodiode.
  • 14. Solar Cell.
  • 15. I-V Characteristics of Solar Cell.
  • 16. Zener Diode.
  • 17. I-V Characteristics of Zener Diode.
  • 18. Zener Diode as a Voltage Regulator.
  • 19. Junction Transistor.
  • 20. Transistor Action.
  • 21. Characteristics of a Transistor.
  • 22. Transistor as an Amplifier.
  • 23. Common Emitter Configuration.
  • 24. Transistor as an Oscillator.
  • 25. Logic Gates.
  • 26. OR Gate.
  • 27. AND Gate.
  • 28. NOT Gate.
  • 29. NAND Gate.
  • 30. NOR Gate.



Chemistry

Class XI :



1. Some Basic Concepts of Chemistry
  • 1. General Introduction to Chemistry.
  • 2. Importance of Chemistry.
  • 3. Scope of Chemistry.
  • 4. Nature of Matter.
  • 5. Laws of Chemical Combination.
  • 6. Dalton's Atomic Theory.
  • 7. Elements.
  • 8. Atoms.
  • 9. Molecules.
  • 10. Atomic Mass.
  • 11. Molecular Mass.
  • 12. Mole Concept.
  • 13. Molar Mass.
  • 14. Percentage Composition.
  • 15. Empirical Formula.
  • 16. Molecular Formula.
  • 17. Chemical Reactions.
  • 18. Stoichiometry.
  • 19. Stoichiometric Calculations.
2. Structure of Atom
  • 1. Atomic Number.
  • 2. Isotopes.
  • 3. Isobars.
  • 4. Shells.
  • 5. Subshells.
  • 6. Dual Nature of Light and Matter.
  • 7. de Broglie's Relationship.
  • 8. Heisenberg Uncertainty Principle.
  • 9. s-Orbitals.
  • 10. p-Orbitals.
  • 11. d-Orbitals.
  • 12. Shapes of s-Orbitals.
  • 13. Shapes of p-Orbitals.
  • 14. Shapes of d-Orbitals.
  • 15. Quantum Numbers.
  • 16. Principal Quantum Number.
  • 17. Azimuthal Quantum Number.
  • 18. Magnetic Quantum Number.
  • 19. Spin Quantum Number.
  • 20. Aufbau Principle.
  • 21. Pauli's Exclusion Principle.
  • 22. Hund's Rule of Maximum Multiplicity.
  • 23. Electronic Configuration.
  • 24. Stability of Half-Filled Orbitals.
  • 25. Stability of Completely Filled Orbitals.
3. Classification of Elements and Periodicity
  • 1. Modern Periodic Law.
  • 2. Present Form of the Periodic Table.
  • 3. Periodic Trends in Properties of Elements.
  • 4. Atomic Radii.
  • 5. Ionic Radii.
  • 6. Inert Gas Radii.
  • 7. Ionization Enthalpy.
  • 8. Electron Gain Enthalpy.
  • 9. Electronegativity.
  • 10. Valence.
4. Chemical Bonding and Molecular Structure
  • 1. Valence Electrons.
  • 2. Ionic Bond.
  • 3. Covalent Bond.
  • 4. Bond Parameters.
  • 5. Lewis Structure.
  • 6. Polar Character of Covalent Bond.
  • 7. Valence Bond Theory.
  • 8. Resonance.
  • 9. Geometry of Molecules.
  • 10. VSEPR Theory.
  • 11. Hybridization.
  • 12. Hybridization Involving s Orbitals.
  • 13. Hybridization Involving p Orbitals.
  • 14. Hybridization Involving d Orbitals.
  • 15. Shapes of Simple Molecules.
  • 16. Molecular Orbital Theory.
  • 17. Homonuclear Diatomic Molecules.
  • 18. Hydrogen Bond.
5. Chemical Thermodynamics
  • 1. System and Surroundings.
  • 2. Types of Systems.
  • 3. Work.
  • 4. Heat.
  • 5. Energy.
  • 6. State Functions.
  • 7. Internal Energy.
  • 8. First Law of Thermodynamics.
  • 9. Enthalpy.
  • 10. Heat Capacity.
  • 11. Hess's Law of Constant Heat Summation.
  • 12. Enthalpy of Combustion.
  • 13. Enthalpy of Formation.
  • 14. Enthalpy of Atomization.
  • 15. Enthalpy Change.
  • 16. Second Law of Thermodynamics.
  • 17. Third Law of Thermodynamics.
  • 18. Entropy.
  • 19. Gibbs Energy Change.
  • 20. Spontaneity of a Process.
  • 21. Criteria for Spontaneity.
  • 22. Chemical Equilibrium.
  • 23. Criteria for Equilibrium.
6. Chemical & Ionic Equilibrium
  • 1. Equilibrium.
  • 2. Equilibrium in Physical Processes.
  • 3. Equilibrium in Chemical Processes.
  • 4. Law of Mass Action.
  • 5. Le Chatelier's Principle.
  • 6. Ionic Equilibrium.
  • 7. Ionization of Acids.
  • 8. Ionization of Bases.
  • 9. Degree of Ionization.
  • 10. pH Concept.
  • 11. Henderson Equation.
  • 12. Salt Hydrolysis.
  • 13. Buffer Solutions.
  • 14. Solubility Product (Ksp).
  • 15. Common Ion Effect.
7. Redox Reactions
  • 1. Oxidation.
  • 2. Reduction.
  • 3. Redox Reactions.
  • 4. Identification of Redox Reactions.
  • 5. Oxidation Number.
  • 6. Rules for Calculating Oxidation Numbers.
  • 7. Calculation of Oxidation Numbers.
  • 8. Balancing Redox Reactions.
  • 9. Electron Loss Method.
  • 10. Electron Gain Method.
  • 11. Oxidation Number Change Method.
  • 12. Oxidizing Agents.
  • 13. Reducing Agents.
8. Organic Chemistry - Some Basic Principles and Techniques
  • 1. General Introduction to Organic Chemistry.
  • 2. Methods of Purification of Organic Compounds.
  • 3. Qualitative Analysis.
  • 4. Quantitative Analysis.
  • 5. Classification of Organic Compounds.
  • 6. IUPAC Nomenclature of Organic Compounds.
  • 7. Electronic Displacement in a Covalent Bond.
  • 8. Inductive Effect.
  • 9. Electromeric Effect.
  • 10. Resonance.
  • 11. Hyperconjugation.
  • 12. Homolytic Fission of a Covalent Bond.
  • 13. Heterolytic Fission of a Covalent Bond.
  • 14. Free Radicals.
  • 15. Carbocations.
  • 16. Carbanions.
  • 17. Electrophiles.
  • 18. Nucleophiles.
  • 19. Types of Organic Reactions.
  • 20. Addition Reactions.
  • 21. Substitution Reactions.
  • 22. Elimination Reactions.
  • 23. Rearrangement Reactions.
9. Hydrocarbons
  • 1. Classification of Hydrocarbons.
  • 2. Alkanes.
  • 3. Nomenclature of Alkanes.
  • 4. Isomerism in Alkanes.
  • 5. Conformations of Ethane.
  • 6. Physical Properties of Alkanes.
  • 7. Chemical Reactions of Alkanes.
  • 8. Free Radical Mechanism of Halogenation.
  • 9. Halogenation of Alkanes.
  • 10. Combustion of Alkanes.
  • 11. Pyrolysis of Alkanes.
  • 12. Alkenes.
  • 13. Nomenclature of Alkenes.
  • 14. Structure of Double Bond in Ethene.
  • 15. Geometrical Isomerism.
  • 16. Physical Properties of Alkenes.
  • 17. Methods of Preparation of Alkenes.
  • 18. Addition of Hydrogen to Alkenes.
  • 19. Addition of Halogens to Alkenes.
  • 20. Addition of Water to Alkenes.
  • 21. Addition of Hydrogen Halides to Alkenes.
  • 22. Markovnikov's Rule.
  • 23. Peroxide Effect.
  • 24. Ozonolysis.
  • 25. Oxidation of Alkenes.
  • 26. Mechanism of Electrophilic Addition.
  • 27. Alkynes.
  • 28. Nomenclature of Alkynes.
  • 29. Structure of Triple Bond in Ethyne.
  • 30. Physical Properties of Alkynes.
  • 31. Methods of Preparation of Alkynes.
  • 32. Acidic Character of Alkynes.
  • 33. Addition of Hydrogen to Alkynes.
  • 34. Addition of Halogens to Alkynes.
  • 35. Addition of Hydrogen Halides to Alkynes.
  • 36. Addition of Water to Alkynes.
  • 37. Aromatic Hydrocarbons.
  • 38. Introduction to Aromatic Hydrocarbons.
  • 39. IUPAC Nomenclature of Aromatic Hydrocarbons.
  • 40. Benzene.
  • 41. Resonance in Benzene.
  • 42. Aromaticity.
  • 43. Chemical Properties of Benzene.
  • 44. Mechanism of Electrophilic Substitution.
  • 45. Nitration of Benzene.
  • 46. Sulphonation of Benzene.
  • 47. Halogenation of Benzene.
  • 48. Friedel-Crafts Alkylation.
  • 49. Friedel-Crafts Acylation.
  • 50. Directive Influence of Functional Groups.
  • 51. Mono-Substituted Benzene.


Class XII :



1. Solutions
  • 1. Types of Solutions.
  • 2. Solutions of Solids in Liquids.
  • 3. Concentration Expressions.
  • 4. Mass Percentage.
  • 5. Volume Percentage.
  • 6. Parts Per Million (PPM).
  • 7. Mole Fraction.
  • 8. Molarity.
  • 9. Molality.
  • 10. Solubility.
  • 11. Gas Solubility in Liquids.
  • 12. Henry's Law.
  • 13. Raoult's Law.
  • 14. Vapour Pressure of Solutions.
  • 15. Relative Lowering of Vapour Pressure.
  • 16. Colligative Properties.
  • 17. Elevation of Boiling Point.
  • 18. Depression of Freezing Point.
  • 19. Osmotic Pressure.
  • 20. Abnormal Molecular Masses.
  • 21. Van't Hoff Factor.
2. Electrochemistry
  • 1. Electrolytic Solutions.
  • 2. Conductance in Electrolytic Solutions.
  • 3. Specific Conductance (Conductivity).
  • 4. Molar Conductivity.
  • 5. Variation of Conductivity with Concentration.
  • 6. Kohlrausch's Law.
  • 7. Applications of Kohlrausch's Law.
  • 8. Electrolysis.
  • 9. Faraday's Laws of Electrolysis.
  • 10. Electrochemical Cells.
  • 11. Electromotive Force (EMF) of a Cell.
  • 12. Standard Electrode Potential.
  • 13. Nernst Equation.
  • 14. Gibbs Energy Change.
  • 15. Relationship Between Gibbs Energy and EMF.
  • 16. Cell Reactions.
  • 17. Galvanic Cells.
  • 18. Dry Cell.
  • 19. Lead Accumulator.
  • 20. Fuel Cells.
  • 21. Corrosion.
  • 22. Prevention of Corrosion.
3. Chemical Kinetics
  • 1. Rate of Reaction.
  • 2. Average Rate of Reaction.
  • 3. Instantaneous Rate of Reaction.
  • 4. Factors Affecting Rate of Reaction.
  • 5. Effect of Concentration on Reaction Rate.
  • 6. Effect of Temperature on Reaction Rate.
  • 7. Effect of Catalysts on Reaction Rate.
  • 8. Order of Reaction.
  • 9. Molecularity of Reaction.
  • 10. Rate Law.
  • 11. Rate Constant.
  • 12. Integrated Rate Equation.
  • 13. Zero Order Reactions.
  • 14. Integrated Rate Equation for Zero Order Reactions.
  • 15. Half-Life of Zero Order Reactions.
  • 16. First Order Reactions.
  • 17. Integrated Rate Equation for First Order Reactions.
  • 18. Half-Life of First Order Reactions.
  • 19. Activation Energy.
  • 20. Arrhenius Equation.
  • 21. Collision Theory of Chemical Reactions.
  • 22. Effective Collisions.
  • 23. Collision Frequency.
  • 24. Orientation Factor.
4. p-Block Elements
  • 1. Group 15 Elements (Nitrogen Family).
  • 2. Group 16 Elements (Oxygen Family).
  • 3. Group 17 Elements (Halogen Family).
  • 4. Group 18 Elements (Noble Gases).
  • 5. General Introduction to p-Block Elements.
  • 6. Electronic Configuration of Group 15 Elements.
  • 7. Electronic Configuration of Group 16 Elements.
  • 8. Electronic Configuration of Group 17 Elements.
  • 9. Electronic Configuration of Group 18 Elements.
  • 10. Physical Properties of Group 15 Elements.
  • 11. Chemical Properties of Group 15 Elements.
  • 12. Physical Properties of Group 16 Elements.
  • 13. Chemical Properties of Group 16 Elements.
  • 14. Physical Properties of Group 17 Elements.
  • 15. Chemical Properties of Group 17 Elements.
  • 16. Physical Properties of Group 18 Elements.
  • 17. Chemical Properties of Group 18 Elements.
  • 18. Periodic Trends Across Periods.
  • 19. Periodic Trends Down the Groups.
  • 20. Unique Behaviour of Nitrogen.
  • 21. Unique Behaviour of Oxygen.
  • 22. Unique Behaviour of Fluorine.
  • 23. Unique Behaviour of Helium.
5. d and f Block Elements
  • 1. General Introduction to d-Block and f-Block Elements.
  • 2. Electronic Configuration of Transition Elements.
  • 3. Occurrence of Transition Metals.
  • 4. Characteristics of Transition Metals.
  • 5. First Row Transition Elements.
  • 6. Metallic Character of Transition Metals.
  • 7. Ionization Enthalpy of Transition Metals.
  • 8. Oxidation States of Transition Metals.
  • 9. Ionic Radii of Transition Metals.
  • 10. Colour of Transition Metal Compounds.
  • 11. Catalytic Properties of Transition Metals.
  • 12. Magnetic Properties of Transition Metals.
  • 13. Interstitial Compounds.
  • 14. Alloy Formation.
  • 15. Potassium Dichromate (K₂Cr₂O₇).
  • 16. Preparation of Potassium Dichromate (K₂Cr₂O₇).
  • 17. Properties of Potassium Dichromate (K₂Cr₂O₇).
  • 18. Potassium Permanganate (KMnO₄).
  • 19. Preparation of Potassium Permanganate (KMnO₄).
  • 20. Properties of Potassium Permanganate (KMnO₄).
  • 21. Lanthanoids.
  • 22. Electronic Configuration of Lanthanoids.
  • 23. Oxidation States of Lanthanoids.
  • 24. Chemical Reactivity of Lanthanoids.
  • 25. Lanthanoid Contraction.
  • 26. Consequences of Lanthanoid Contraction.
  • 27. Actinoids.
  • 28. Electronic Configuration of Actinoids.
  • 29. Oxidation States of Actinoids.
  • 30. Comparison Between Actinoids and Lanthanoids.
6. Coordination Compounds
  • 1. Introduction to Coordination Compounds.
  • 2. Ligands.
  • 3. Types of Ligands.
  • 4. Coordination Number.
  • 5. Colour of Coordination Compounds.
  • 6. Magnetic Properties of Coordination Compounds.
  • 7. Shapes of Coordination Compounds.
  • 8. IUPAC Nomenclature of Mononuclear Coordination Compounds.
  • 9. Isomerism in Coordination Compounds.
  • 10. Structural Isomerism.
  • 11. Stereo Isomerism.
  • 12. Bonding in Coordination Compounds.
  • 13. Werner's Theory of Coordination Compounds.
  • 14. Valence Bond Theory (VBT).
  • 15. Crystal Field Theory (CFT).
  • 16. Importance of Coordination Compounds.
  • 17. Coordination Compounds in Qualitative Analysis.
  • 18. Coordination Compounds in Extraction of Metals.
  • 19. Coordination Compounds in Biological Systems.
7. Haloalkanes and Haloarenes
  • 1. Haloalkanes.
  • 2. Nomenclature of Haloalkanes.
  • 3. Nature of C–X Bond in Haloalkanes.
  • 4. Physical Properties of Haloalkanes.
  • 5. Chemical Properties of Haloalkanes.
  • 6. Substitution Reactions of Haloalkanes.
  • 7. Mechanism of Substitution Reactions.
  • 8. Optical Rotation.
  • 9. Haloarenes.
  • 10. Nature of C–X Bond in Haloarenes.
  • 11. Substitution Reactions of Haloarenes.
  • 12. Directive Influence of Halogens in Monosubstituted Compounds.
  • 13. Dichloromethane (CH₂Cl₂).
  • 14. Uses of Dichloromethane.
  • 15. Environmental Effects of Dichloromethane.
  • 16. Trichloromethane (Chloroform, CHCl₃).
  • 17. Uses of Trichloromethane.
  • 18. Environmental Effects of Trichloromethane.
  • 19. Tetrachloromethane (Carbon Tetrachloride, CCl₄).
  • 20. Uses of Tetrachloromethane.
  • 21. Environmental Effects of Tetrachloromethane.
  • 22. Iodoform (CHI₃).
  • 23. Uses of Iodoform.
  • 24. Environmental Effects of Iodoform.
  • 25. Freons.
  • 26. Uses of Freons.
  • 27. Environmental Effects of Freons.
  • 28. DDT.
  • 29. Uses of DDT.
  • 30. Environmental Effects of DDT.
8. Alcohols, Phenols and Ethers
  • 1. Alcohols.
  • 2. Nomenclature of Alcohols.
  • 3. Methods of Preparation of Alcohols.
  • 4. Physical Properties of Alcohols.
  • 5. Chemical Properties of Primary Alcohols.
  • 6. Primary Alcohols.
  • 7. Secondary Alcohols.
  • 8. Tertiary Alcohols.
  • 9. Identification of Primary Alcohols.
  • 10. Identification of Secondary Alcohols.
  • 11. Identification of Tertiary Alcohols.
  • 12. Dehydration of Alcohols.
  • 13. Mechanism of Dehydration of Alcohols.
  • 14. Methanol.
  • 15. Uses of Methanol.
  • 16. Ethanol.
  • 17. Uses of Ethanol.
  • 18. Phenols.
  • 19. Nomenclature of Phenols.
  • 20. Methods of Preparation of Phenols.
  • 21. Physical Properties of Phenols.
  • 22. Chemical Properties of Phenols.
  • 23. Acidic Nature of Phenol.
  • 24. Electrophilic Substitution Reactions of Phenols.
  • 25. Uses of Phenols.
  • 26. Ethers.
  • 27. Nomenclature of Ethers.
  • 28. Methods of Preparation of Ethers.
  • 29. Physical Properties of Ethers.
  • 30. Chemical Properties of Ethers.
  • 31. Uses of Ethers.
9. Aldehydes, Ketones and Carboxylic Acids
  • 1. Aldehydes.
  • 2. Ketones.
  • 3. Nomenclature of Aldehydes.
  • 4. Nomenclature of Ketones.
  • 5. Carbonyl Group.
  • 6. Nature of Carbonyl Group.
  • 7. Methods of Preparation of Aldehydes.
  • 8. Methods of Preparation of Ketones.
  • 9. Physical Properties of Aldehydes.
  • 10. Physical Properties of Ketones.
  • 11. Chemical Properties of Aldehydes.
  • 12. Chemical Properties of Ketones.
  • 13. Nucleophilic Addition Reactions.
  • 14. Mechanism of Nucleophilic Addition.
  • 15. Alpha Hydrogen in Aldehydes.
  • 16. Reactivity of Alpha Hydrogen in Aldehydes.
  • 17. Uses of Aldehydes.
  • 18. Uses of Ketones.
  • 19. Carboxylic Acids.
  • 20. Nomenclature of Carboxylic Acids.
  • 21. Acidic Nature of Carboxylic Acids.
  • 22. Methods of Preparation of Carboxylic Acids.
  • 23. Physical Properties of Carboxylic Acids.
  • 24. Chemical Properties of Carboxylic Acids.
  • 25. Uses of Carboxylic Acids.
10. Organic Compounds Containing Nitrogen
  • 1. Amines.
  • 2. Nomenclature of Amines.
  • 3. Classification of Amines.
  • 4. Structure of Amines.
  • 5. Methods of Preparation of Amines.
  • 6. Physical Properties of Amines.
  • 7. Chemical Properties of Amines.
  • 8. Uses of Amines.
  • 9. Primary Amines.
  • 10. Secondary Amines.
  • 11. Tertiary Amines.
  • 12. Identification of Primary Amines.
  • 13. Identification of Secondary Amines.
  • 14. Identification of Tertiary Amines.
  • 15. Diazonium Salts.
  • 16. Preparation of Diazonium Salts.
  • 17. Chemical Reactions of Diazonium Salts.
  • 18. Sandmeyer Reaction.
  • 19. Gattermann Reaction.
  • 20. Coupling Reactions of Diazonium Salts.
  • 21. Importance of Diazonium Salts in Synthetic Organic Chemistry.
11. Biomolecules
  • 1. Carbohydrates.
  • 2. Classification of Carbohydrates.
  • 3. Aldoses.
  • 4. Ketoses.
  • 5. Monosaccharides.
  • 6. Glucose.
  • 7. Fructose.
  • 8. D-L Configuration.
  • 9. Oligosaccharides.
  • 10. Sucrose.
  • 11. Lactose.
  • 12. Maltose.
  • 13. Polysaccharides.
  • 14. Starch.
  • 15. Cellulose.
  • 16. Glycogen.
  • 17. Importance of Carbohydrates.
  • 18. Proteins.
  • 19. Amino Acids.
  • 20. Peptide Bond.
  • 21. Polypeptides.
  • 22. Structure of Proteins.
  • 23. Primary Structure of Proteins.
  • 24. Secondary Structure of Proteins.
  • 25. Tertiary Structure of Proteins.
  • 26. Quaternary Structure of Proteins.
  • 27. Denaturation of Proteins.
  • 28. Enzymes.
  • 29. Hormones.
  • 30. Elementary Concept of Hormones.
  • 31. Vitamins.
  • 32. Classification of Vitamins.
  • 33. Functions of Vitamins.
  • 34. Nucleic Acids.
  • 35. DNA (Deoxyribonucleic Acid).
  • 36. RNA (Ribonucleic Acid).



Mathematics

Class XI :



1. Sets
  • 1. Definition of Sets.
  • 2. Representation of Sets in Set Theory.
  • 3. Roster Form.
  • 4. Set-Builder Form.
  • 5. Interval Notation.
  • 6. Special Sets.
  • 7. Elements of a Set.
  • 8. Types of Sets.
  • 9. Null Set.
  • 10. Empty Set.
  • 11. Void Set.
  • 12. Singleton Set.
  • 13. Finite Set.
  • 14. Infinite Set.
  • 15. Subset.
  • 16. Proper Subset.
  • 17. Universal Set.
  • 18. Power Set.
  • 19. Equivalent Set.
  • 20. Equal Set.
  • 21. Disjoint Sets.
  • 22. Operations on Sets.
  • 23. Cardinality of a Set.
  • 24. Union of Sets.
  • 25. Intersection of Sets.
  • 26. Complement of Sets.
  • 27. Difference of Sets.
  • 28. Cartesian Product of Sets.
  • 29. Set Formulas.
  • 30. Venn Diagrams.
  • 31. Properties of Sets.
  • 32. Associative Property.
  • 33. Distributive Property.
  • 34. De Morgan's Law.
  • 35. Complement Law.
  • 36. Idempotent Law.
  • 37. Law of Null Set.
  • 38. Law of Universal Set.
  • 39. Solved Examples.
2. Relations and Functions
  • 1. Definition of Relation.
  • 2. Domain and Range of a Relation.
  • 3. Types of Relations.
  • 4. Universal Relations.
  • 5. Void Relations.
  • 6. Identity Relations.
  • 7. Reflexive Relations.
  • 8. Symmetric Relations.
  • 9. Transitive Relations.
  • 10. Equivalence Relations.
  • 11. Function.
  • 12. Types of Function.
  • 13. Identity Function.
  • 14. Constant Function.
  • 15. Polynomial Function.
  • 16. Modulus Function.
  • 17. Signum Function.
  • 18. Greatest Integer Function.
  • 19. Difference Between Relation and Function.
  • 20. Relation and Function Formulas (R: A, Relations and Functions Exam.
3. Complex Numbers
  • 1. What is a Complex Number.
  • 2. Conjugate of a Complex Number.
  • 3. Modulus of a Complex Number.
  • 4. Polar Form of a Complex Number.
  • 5. Argument of a Complex Number.
  • 6. Complex Number Formula.
  • 7. Multiplicative Inverse of a Complex Number.
  • 8. Euler's Formula.
  • 9. Solved Example of a Complex Number.
  • 10. Sample Questions for Complex Numbers.
4. Quadratic Equations
  • 1. Quadratic Equation Definition.
  • 2. Standard Form of Quadratic Equations.
  • 3. Quadratic Equation Formula.
  • 4. Quadratic Equation Examples.
  • 5. How To Solve Quadratic Equations.
  • 6. Relation Between Roots and Coefficient.
  • 7. Quadratic Equation JEE Questions.
  • 8. Solved Questions for Quadratic Equation.
5. Matrices and Determinants
  • 1. What Are Matrices and Determinants?
  • 2. Difference Between Matrices and Determinants.
  • 3. Properties of Matrices and Determinants.
  • 4. Matrices and Determinants Solved Examples.
  • 5. Matrices and Determinants Practice problems.
  • 6. Sample Questions on Determinants and Matrices.
6. Permutations and Combinations
  • 1. What are Permutations and Combinations.
  • 2. Definition of Permutation.
  • 3. Definition of Combination.
  • 4. Permutations and Combinations Formulas.
  • 5. Permutation Formula.
  • 6. Combination Formula.
  • 7. Difference Between Permutations and Combinations.
7. Binomial Theorem and Applications
  • 1. What Is the Binomial Theorem.
  • 2. Example: Expanding.
  • 3. Why Is the Binomial Theorem Useful.
  • 4. Quick Expansions Without Multiplying.
  • 5. Finding Specific Terms in an Expansion.
  • 6. Applications in Probability.
  • 7. Pascal’s Triangle.
  • 8. Practical Applications of the Binomial Theorem.
8. Sequence and Series
  • 1. Sequence and Series Definition.
  • 2. Types of Sequence and Series.
  • 3. Difference between Sequence and Series.
  • 4. Sequence.
  • 5. Series.
  • 6. Sequence and Series Formula.
  • 7. Sequence and Series Jee Mains Question.
  • 8. Sequence and Series Jee Advanced Question.
  • 9. Sequence and Series Solved Problem.
  • 10. Sample Question on Sequence and Series.
9. Limit and Continuity
  • 1. What Are Limits and Continuity.
  • 2. Definition of Limits and Continuity.
  • 3. The Difference Between Limits and Continuity.
  • 4. Types of Discontinuity.
  • 5. Solved Examples of Limits and Continuity.
  • 6. Practice Questions on Limits and Continuity.
  • 7. Sample Questions on Limits and Continuity.
10. Differentiability
  • 1. Differentiability Definition.
  • 2. Existence of Derivative at x = a for the function f(x).
  • 3. Right Hand Derivative.
  • 4. Left Hand Derivative.
  • 5. Derivability over an Interval.
  • 6. Differentiability and Continuity.
  • 7. Differentiability Formulas.
  • 8. Differentiability Properties of Functions.
  • 9. Geometrical interpretation of differentiability.
  • 10. How To Determine Differentiability.
  • 11. Differentiability Solved Examples.
  • 12. Differentiability Practice Problems.
11. Integral Calculus
  • 1. Integration Definition.
  • 2. Indefinite Integral.
  • 3. Definite Integral.
  • 4. Integration Formulas.
  • 5. Some definite Formulas are.
  • 6. Double and Triple Integrals.
  • 7. Double Integrals.
  • 8. Triple Integrals.
  • 9. Integral of Inverse Trigonometric Functions .
  • 10. Solved Examples on Integrals.
  • 11. Practice Problems on Integrals.
  • 12. Sample Questions on Integrals.
12. Differential Equations
  • 1. Order Of Differential Equations.
  • 2. Degree of Differential Equations.
  • 3. Solution Of Differential Equations.
  • 4. Elementary Types of First Order and First-Degree Differential Equations.
  • 5. Separation of Variables.
  • 6. Homogeneous Differential Equations.
  • 7. Linear Differential Equations.
  • 8. Solved Examples of Differential Equations.
  • 9. Practice Question on Differential Equations.
13. Coordinate Geometry
  • 1. About Coordinate Geometry.
  • 2. Basic Coordinate Geometry Concepts.
  • 3. Exploring 3D Coordinate Geometry .
  • 4. Applications of Coordinate Geometry.
  • 5. Solved Examples on Coordinate Geometry .
  • 6. Practice Questions on Coordinate Geometry.
  • 7. Sample Questions on Coordinate Geometry.
14. Three Dimensional Geometry
  • 1. Introduction to Three Dimensional Geometry.
  • 2. Section Formula in 3D.
  • 3. Direction Cosines and Direction Ratios of a Line.
  • 4. Direction Cosines.
  • 5. Direction cosines of a line.
  • 6. Direction cosines of axes.
  • 7. Direction Ratios.
  • 8. Relation Between Direction Cosines and Direction Ratios.
  • 9. Direction Ratios and Direction Cosines of the Line Joining Two Points.
  • 10. Projection Of Line Segment Joining Two Points On Another Line.
  • 11. Angle Between Two Lines in 3 Dimensional Space.
  • 12. Equation Of A Line In Space.
  • 13. Equation of a line passing through a given point and parallel to.
  • 14. Angle between Two Lines.
  • 15. Angle Between a Line and a Plane.
  • 16. Shortest Distance Between Two Lines.
  • 17. Distance Between Two Skew Lines.
  • 18. Three Dimensional Geometry Solved Examples.
15. Vector Algebra
  • 1. What is Vector Algebra.
  • 2. Types of Vectors in Vector Algebra.
  • 3. Zero Vector (Null Vector).
  • 4. Unit Vector.
  • 5. Position Vector.
  • 6. Co-initial Vectors.
  • 7. Collinear Vectors.
  • 8. Equal Vectors.
  • 9. Negative of a Vector.
  • 10. Parallel Vectors.
  • 11. Orthogonal (Perpendicular) Vectors.
  • 12. Coplanar Vectors.
  • 13. Vector Algebra Operations.
  • 14. Vector Addition.
  • 15. Triangle Law of Addition of Vectors.
  • 16. Parallelogram Law of Addition of Vectors.
  • 17. Vector Subtraction.
  • 18. Scalar Multiplication or Scalar Product.
  • 19. Linear Combination.
  • 20. Dot Product.
  • 21. Cross Product.
  • 22. Vector Algebra Formulas.
  • 23. Vector Addition.
  • 24. Vector Subtraction.
  • 25. Scalar Multiplication.
  • 26. Dot Product.
  • 27. Cross Product.
  • 28. Vector Magnitude.
  • 29. Unit Vector.
  • 30. Projection of A onto B.
  • 31. Angle Between Two Vectors.
  • 32. Vector Algebra Examples.
  • 33. Solved Questions on Vector Algebra.
16. Statistics and Probability
  • 1. What is Probability.
  • 2. Basic Concepts of Probability.
  • 3. Probability Formula.
  • 4. What is Statistics.
  • 5. Measure of Central Tendency.
  • 6. Applications of Probability and Statistics.
  • 7. Solved Examples on Probability and Statistics.
  • 8. Practice Questions on Probability and Statistics.
  • 9. Sample Questions on Probability and Statistics.
17. Trigonometry
  • 1. Key Concepts of Trigonometry .
  • 2. Trigonometric Ratios and identities .
  • 3. Trigonometric Identities.
  • 4. Pythagorean Identity.
  • 5. Reciprocal Identities.
  • 6. Sum and Difference Identities.
  • 7. Transformation Formula.
  • 8. Multiple Angle Ratios.
  • 9. Trigonometric Functions of Angles.
  • 10. Trigonometric Equations.
  • 11. Graphs of Trigonometric Functions.
  • 12. Solved Problems .


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