| Subject | PCM | Medium | ENGLISH |
|---|---|---|---|
| Faculty | NV Sir,VKP Sir,SSI Sir,AS Sir | Status | AVAILABLE |
| Category | COMPLETE COURSE | Lecture | |
| Target | XI XII XIII | Books | QUESTION BANK ATTACHED |
| You May Pay in Installments through Credit Card | |||
| Product Type | Prices | Validity | |
|---|---|---|---|
| USB | 11000 10%OFF 9900 | 2 year |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Dalton atomic theory, isotope ,isobar, atomic mass, atomic mass unit amu, molecule, molecular mass | 41 Minutes |
| 02 | molar mass. Gram atomic mass, gram molecular mass, avogadro law | 48 Minutes |
| 03 | Relative atomic mass, relative density, vapour density, specific gravity, average atomic mass, average molar mass | 44 Minutes |
| 04 | Percentage composition, molecular formula, empirical formula, gay-lussac law | 30 Minutes |
| 05 |
Stoichiometry, mole-mole analysis, combustion of hydrocarbon |
34 Minutes |
| 06 |
limiting reagent, percentage yield , consecutive reaction |
39 Minutes |
| 07 | Principle of atomic conservation POAC | 37 Minutes |
| 08 | Percentage purity of sample, combustion of carbon, analysis of mixture | 29 Minutes |
| 09 | Numerical on analysis of mixture, law of mass conservation, law of definite proportions, law of multiple proportions, law of reciprocal proportions | 24 Minutes |
| 10 | Solution, solute , solvent, mole fraction, %w/w/, | 18 Minutes |
| 11 | %w/v, % v/v, strength of solution, molarity, molality, ppm | 35 Minutes |
| 12 | Interconversion of concentration terms | 46 Minutes |
| 13 | Molarity of pure water , volume strength of hydrogen peroxide solution, relation between volume strength and molarity | 35 Minutes |
| 14 | Silver salt method , Eudiometry | 38 Minutes |
| 15 | examples of eudiometry | 27 Minutes |
| 16 | Significant figure, rules for counting , rounding off, scientific notation, addition/subtraction, multiplication of significant figure | 42 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Oxidation number calculation, average O.N. individual O. N. | 44 Minutes |
| 02 | Oxidizing agent, reducing agent, disproportion reactions | 58 Minutes |
| 03 | Balancing of redox and disproportion reaction , balancing of molecular reaction | 46 Minutes |
| 04 | Equivalent concept. Law of chemical equivalence, relation between mole and equivalent, equivalent mass, valence factor calculation for acid & base | 45 Minutes |
| 05 | n- factor for salt, n - factor for disproportion reaction | 49 Minutes |
| 06 | Titration, acid base titration, permanganate titration, dichromate titration | 39 Minutes |
| 07 | Back titration , double titration | 34 Minutes |
| 08 | Numerical on double titration, iodometric titration, limitation of equivalent concept | 33 Minutes |
| 09 | Bleaching powder and calculation of available chlorine from bleaching powder sample | 31 Minutes |
| 10 | Hardne ss of water ( temporary & permanent hardness) strength of oleum | 35 Minutes |
| 11 | Volume strength of hydrogen peroxide solution | 20 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Reversible & irreversible reactions, physical and chemical eq, homogeneous and heterogeneous eq, properties of eq, Kp, Kc, Kx, relation between Kp & Kc, relation between Kp and Kx, degree of dissociation | 1 hr 13 Minutes |
| 02 | Effect of stoichiometry on kp & Kc, examples of homogeneous equilibrium | 38 Minutes |
| 03 | Numericals of homogeneous eq. | 29 Minutes |
| 04 | Heterogeneous eq., homogeneous liquid eq., significance of value of k, reaction quotient | 53 Minutes |
| 05 | Approximation during calculation, relation between vapour density and degree of dissociation | 53 Minutes |
| 06 | Thermodynamics for chemical eq, factor affecting composition of eq mixture , le-chatelier's principle, effect of concentration , effect of temperature | 38 Minutes |
| 07 | Effect of change in pressure and volume , effect of catalyst | 36 Minutes |
| 08 | Addition of inert gas at constant volume and constant pressure, le-chatelier's principle for physical eq, evaporation of water, boiling of water, melting of ice , melting of metal | 1 hr |
| 09 | Solubility of gas in liquid , allotropic change , simultaneous eq. | 42 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Strong electrolyte, weak electrolyte, strong acids, weak acids, strong base, weak base , acid base theory, arrhenius concept, bronsted lowry concept , amphiprotic species | 31 Minutes |
| 02 | Lewis concept , pH scale, properties of water, ionisation constant of water, ionic product of water | 45 Minutes |
| 03 | pH calculation for strong acid, strong base, mixture of strong acid , mixture of strong acid and base , common ion effect | 43 Minutes |
| 04 | pH for monobasic weak acid, weak base, ostwald dilution law, pH for very dilute strong acid | 41 Minutes |
| 05 | Very dilute weak base , mixture of weak acid and strong acid,polyprotic weak acid | 40 Minutes |
| 06 | Numerical on polyprotic weak acid, mixture of two weak acids | 33 Minutes |
| 07 | Hydrolysis of salt, salt of strong acid and strong base, salt of weak acid and strong base , salt of weak base and strong acid | 52 Minutes |
| 08 | Hydrolysis of salt of weak acid and weak base | 39 Minutes |
| 09 | pH for polyvalent anion, ph for amphiprotic anion , introduction of buffer solution | 37 Minutes |
| 10 | Acidic buffer and basic buffer | 43 Minutes |
| 11 | Buffer capacity, titration ( strong acid v/s strong base, strong acid v/s weak base , weak acid v/s strong base) | 53 Minutes |
| 12 | Titration of H3PO4 v/s NaOH | 35 Minutes |
| 13 | Indicator, phenolphthalein, methyl orange, pH range for a buffer ,double titration | 38 Minutes |
| 14 | Solubility of sparingly soluble salt, Ksp, effect of common ion on solubility, simultaneous solubility | 44 Minutes |
| 15 | Ionic product v/s solubility product,selective precipitation, | 41 Minutes |
| 16 | solubility of salt in buffer solution, complex formation by salt | 37 Minutes |
| 17 | Solubility of amphoteric insoluble hydroxide, solubility of salt if cation is hydrolyzed , solubility of salt if anion is hydrolyzed | 43 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | System ,surrounding,open system, closed system, isolated system, thermodynamic variable, process, open cycle ,closed cycle,intensive prop. Extensive prop., state function, path function, heat, work, heat capacity, molar heat capacity, specific heat capacity ,IUPAC , types of process, isothermal, isobaric, isochoric, adiabatic process,convention for heat and work | 41 Minutes |
| 02 | Reversible and irreversible process, reversible isothermal compression, single step isothermal compression, two stage isothermal compression | 56 Minutes |
| 03 | Reversible isothermal expansion, single stage isothermal expansion, two stage isothermal expansion, internal energy, degree of freedom, first law of thermodynamics | 50 Minutes |
| 04 | Enthalpy change , phase transformation | 46 Minutes |
| 05 | Free expansion, reversible adiabatic process, work calculation for reversible Adiabatic and irreversible Adiabatic processes | 43 Minutes |
| 06 | comparison between reversible adiabatic and irreversible adiabatic processes, comparison between reversible adiabatic and reversible isothermal processes | 42 Minutes |
| 07 | Spontaneous and nonspontaneous process, entropy, second law of thermodynamics , entropy change for system and surrounding | 55 Minutes |
| 08 | Numerical on entropy change , entropy change during free expansion | 40 Minutes |
| 09 | Gibbs energy change, heat pump, carnot cycle | 56 Minutes |
| 10 | Thermochemistry, enthalpy of formation, enthalpy of combustion | 48 Minutes |
| 11 | Enthalpy of fusion, vaporization,sublimation,bomb calorimeter, enthalpy of neutralisation, enthalpy of ionisation | 57 Minutes |
| 12 | Bond enthalpy, hess law, resonance energy. Lattice energy , hydration energy, enthalpy of formation of ion, kirchhoff equation, integral enthalpy of solution, calculation of lattice energy using born haber cycle | 1 hr 7 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | State of matter (solid, Liq, gas) ideal gas equation, Boyle’s law. | 32 Minutes |
| 02 | Barometer, faulty Barometer | 33 Minutes |
| 03 | Problems on barometer, Charles law | 40 Minutes |
| 04 | Gay-lussac’s law, Avogadro's law, ideal gas equation | 21 Minutes |
| 05 | Numerical | 45 Minutes |
| 06 | Graham’s law for diffusion. | 36 Minutes |
| 07 | Kinetic theory of gas, root mean square velocity | 40 Minutes |
| 08 | Compressibility factor (Z) pressure correction factor, volume correction factor, excluded volume, van der waal gas equation | 50 Minutes |
| 09 | Virial equation, liquification of gas, critical temperature (Tc) Critical pressure (Pc) Critical volume (Vc) Boyle’s temperature | 46 Minutes |
| 10 | Liquification of gas manometer (Open end, Closed end, reduced equation of state), Collision diameter, Collision frequency |
52 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Cathode tube experiment anode rays, radioactive decay. | 33 Minutes |
| 02 | Thomson plum pudding model. Rutherford model, Nearest distance of approach. | 51 Minutes |
| 03 | Electromagnetic theory, Planck Quantum Theory, Blackbody radiation, electron volt. | 50 Minutes |
| 04 | Photoelectric effect, Work function, Threshold frequency stopping potential. | 41 Minutes |
| 05 | Photo current photo intensity, Bohr model, Bohr Radius | 34 Minutes |
| 06 | Velocity, Kinetic Energy, Total energy, Potential energy of electron in Bohr orbit | 29 Minutes |
| 07 | Time period, frequency, ionisation energy, ionisation potential, Excitation energy, excitation potential Binding energy. | 35 Minutes |
| 08 | Spectrum, emission, line spectrum, band spectrum , H-spectrum, lyman series. | 45 Minutes |
| 09 | Balmer series, Paschen, Brackett, Pfund, humphrey series, maximum number of spectral lines. | 50 Minutes |
| 10 | Limitations of bohr model, dual nature of particle, de broglie's equation | 41 Minutes |
| 11 | Heisenberg’s uncertainty principle Difference between orbit & orbital | 39 Minutes |
| 12 | Types of orbitals {s, p, d, f}, quantum numbers, (principal, azimuthal, magnetic, spin) | 37 Minutes |
| 13 | Electron filling rule, Aufbau principle, Hund’s rule, pauli’s exclusion principle, magnetic nature, magnetic moment | 47 Minutes |
| 14 | Wave quantum theory, schrodinger wave equation, radial node, angular node. | 42 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Dobereiner's triad, Newland’s octave law, lother meyer curve, Mendeleev's periodic table. Moseley's periodic table | 31 Minutes |
| 02 | Periodicity, blocks in periodic table, diagonal relationship, naming of element z > 100, Determination of period & block, Ionic radius | 37 Minutes |
| 03 | Covalent radius, vanderwaal radius, effective nuclear charge, shielding effect/screening effect, slater’s law | 34 Minutes |
| 04 | Factor affecting atomic radius. trend of atomic radius exception of atomic radius, lanthanide contraction. | 40 Minutes |
| 05 | Ionisation energy, Factors affective IE, Trend in I.E. | 27 Minutes |
| 06 | Exceptions in ionisation energy,Comparison of IE1 & IE2,Application of IE ionisation energy | 40 Minutes |
| 07 | Electron affinity, electron gain enthalpy, factor affecting electron affinity, | 41 Minutes |
| 08 | Second electron gain enthalpy,Electronegativity, Pauling scale, mulliken scale, Hanny smith of formula. | 44 Minutes |
| 09 | Nature of XOH Acidic, basic, neutral and amphoteric oxide, Nature of oxide, Hydroxide and oxyacids, Inert pair effect |
50 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Chemical bond, ionic bond, lattice energy, born haber cycle, Hess law | 46 Minutes |
| 02 | Properties of ionic compound, Hydration & Hydration energy. Solubility in water. | 39 Minutes |
| 03 | Factors affecting Hydration Energy, Solubility order, Covalent bond, Lewis concept. | 38 Minutes |
| 04 | Lewis structure, Exception of Lewis rule, Hypovalent, Hypervalent, odd electron species, coordinate bond formation, lewis acid & base. | 42 Minutes |
| 05 | Formal charge, Resonance | 46 Minutes |
| 06 | Valence bond theory (VBT) ,axial & Lateral overlapping,ðž‚ bond, Π bond, ð›… bond | 49 Minutes |
| 07 | Hybridisation-sp, sp2, sp3, sp3d, sp3d2, sp3d3 | 48 Minutes |
| 08 | Steric number rule for hybridisation, Valence shell electron pair repulsion theory VSEPR | 48 Minutes |
| 09 | Examples of sp & sp2 Hybridisation | 41 Minutes |
| 10 | Fullerenes, diamond, Compounds of phosphorus & sulphur. | 53 Minutes |
| 11 | Compounds of silicon, Silica, orthosilicate, pyrosilicate, chain silicate, cyclic silicate, double chain silicate |
50 Minutes |
| 12 | Silicons, equivalent and nonequivalent hybrid orbitals bent rule | 42 Minutes |
| 13 | Examples of sp3d, sp3d2 & sp3d3 Hybridisation, Drago’s rule. | 40 Minutes |
| 14 | Molecular orbital theory (MOT), linear combination of atomic orbital (LCAO) | 46 Minutes |
| 15 | MOT examples , s-p mixing ,O2, F2, H2, N2, Ne2 | 1 hrs |
| 16 | HOMO & LUMO,GERADE & UNGERADE,Dipole moment & ionic character in ionic compound | 37 Minutes |
| 17 | Application of dipole moment % ionic character by dipole moment fazan, rule, covalent character in ionic compound | 57 Minutes |
| 18 | Application of fajan's rule, Banana bonding in diborane. | 50 Minutes |
| 19 | Back bonding in BF3 examples of back bonding | 44 Minutes |
| 20 | Bond angle comparison bond length & bond strength comparison. | 37 Minutes |
| 21 | pðš· - dðš· bonding, pðš· - pðš· bonding Solubility due to hydrolysis of BF3, SiCl4, PCl3, compound, Interhalogen |
21 Minutes |
| 22 | Metallic bonding, H bonding, intermolecular H-bonding Intramolecular H bonding | 49 Minutes |
| 23 | Examples of h-bonding, van der waal forces( ion-dipole, dipole-dipole , ion-induced dipole, dipole-induced dipole, london dispersion forces) | 55 Minutes |
| 24 | Factors affecting van der waal forces , existence and nonexistence of molecules | 43 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Member of boron family. Physical properties (radius, oxidation state, ionisation energy, electronegativity, density) Chemical properties (reactivity with air) Anomalous behaviour of B Diagonal relationship between B & Si. |
28 Minutes |
| 02 | Formation of boron, compounds of boron, B3O3, boric acid, borax bead test. | 27 Minutes |
| 03 | Diborane, borazine, boron nitride, back bonding in BF3. | 49 Minutes |
| 04 | Aluminium, Compounds, Al2O3, Al(OH)3, AlCl3 ,Carbon family, Inert Pair effect, order of ionisation energy, electronegativity, Atomic radius, Anomalous behaviour of carbon. | 38 Minutes |
| 05 | Allotropes of carbon, diamond, graphite, fullerene, reactivity with O2., H2O & X2. | 34 Minutes |
| 06 | Compound of carbon,Carbon monoxide,Carbon dioxide,Carbonic acid,Compounds of silicon,Silica | 27 Minutes |
| 07 | Ortho silicate,Pyrosilicate ,Cyclic silicate,Chain silicate,Double chain silicate,Sheet silicate,3D silicate,Silicates,Compounds of tin & & Lead | 29 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Physical and chemical properties of alkali metal( ionisation energy, atomic radius , physical appearance, b.p. And m.p.) | 32 Minutes |
| 02 | Reaction of alkali metal with O2, h2O, halogen, carbon, reducing nature of alkali metal , solution in liquid ammonia, anomalous behaviour of lithium | 44 Minutes |
| 03 | Diagonal relationship between lithium and magnesium, compounds of sodium Na2O2, formation of NaOH | 29 Minutes |
| 04 | Properties of NaOH, , Na2CO3, sovay process , NaHCO3 | 22 Minutes |
| 05 | Microcosmic salt, compounds of potassium, solution in liq. Ammonia | 8 Minutes |
| 06 | Physical and chemical properties of alkaline earth metal( ionisation energy, atomic radius , physical appearance, b.p. And m.p.) | 38 Minutes |
| 07 | Hydride , hydroxide, oxide , nitride of alkaline earth metal | 20 Minutes |
| 08 | anomalous behaviour of berylium,Diagonal relationship between berylium and aluminium, compounds of Mg and Ca, gypsum and plaster of paris |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Definition of isomerism, Classification of isomerism, Chain isomerism, Positional isomerism | 45 Minutes |
| 02 | Functional isomerism, Ring-chain isomerism, Metamerism | 40 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Introduction, Classification of stereoisomerism, Geometrical Isomerism (G.I.) | 20 Minutes |
| 02 |
G.I. in C=C system , G.I. in Ring system , G.I. due to double bond inside the ring , Cummulenes |
55 Minutes |
| 03 | G.I. in C=N system, E/Z Nomenclature | 55 Minutes |
| 04 | Number of geometrical Isomers, Cummulenes, Spiranes, Cycloalkylidenes, Diphenyl system, Physical properties of geometrical isomers | 58 Minutes |
| 05 | Optical Isomerism , Plane polarised light , Chiral centre , Chirality ' Assymmetric molecules , Dissymmetric molecules , Plane of symmetry (POS), Centre of symmetry (COS) | 1 Hr 09 Minutes |
| 06 | POS, COS. Chirality, Optical activity | 55 Minutes |
| 07 | Wedge-Dash projection fromula , Fischer–Projection formula , Absolute configuration (R/S-configuration) , CIP-Rule | 52 Minutes |
| 08 | Enantiomers , Diastereomers , Axis of symmetry (AOS) | |
| 09 | Erythro enantiomers, Threo enatiomers, D/L- Configuration (Relative configuration) , Number of stereoisomers , Pseudo chiral carbon (PCC), Racemic mixture (or, R/S-mixture) , Polarimeter , Functioning of polarimeter , Percentage enantiomeric excess (%EE), Optical purity | 58 Minutes |
| 10 | Optical Resolution , Tertiary amine optical activity , Optical activity in absence of chiral centre , Cummulenes , Spiranes , Cycloalkylidene, Diphenyls , Alternating axis of symmetry (AAOS) , Conformational Isomerism | Minutes |
| 11 | Conformational isomers , Newmann projection formula , Dihedral angle (DHA) , Tortional strain (T.S.) , Vander waals strain (V.S.) , Angle strain (A.S.) , Definition of conformational isomers, Conformational analysis , Sawhorse projection formula | 57 Minutes |
| 12 | Conversion of Fischer to Newmann, Conformational analysis of cyclohexane , Energy profile | 51 Minutes |
| 13 | Conformational analysis of dimethyl cyclohexane | 15 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Structural Identification, Degree of unsaturation (DU), Catalytic hydrogenation H2/cat, Monochlorination Cl2/hn | 29 Minutes |
| 02 | Structural Identification , Monochlorination Cl2/hv , Ozonolysis , Reductive ozonalysis , Oxidation ozonalysis , Practical organic chemistry (POC), POC-I , Lassaigne’s test, Elemental analysis | 54 Minutes |
| 03 | Elemental anlaysis , Test of unsaturation, Test of terminal alkyne , Test of alcohols , Test of carbonyl compounds , Tests of aldehydes | 35 Minutes |
| 04 | Iodoform Test, Sodium metal test | 19 Minutes |
| 05 | Sodiumbicarbonate test (NaHCO3), Test of phenols and enols , Test of nitro compounds , Test of amines , Hinseberg’s test , POC-II | 33 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Electornic effect , Inductive effect | 36 Minutes |
| 02 | Applications of I-Effect , Resonance , Conjugated system | 47 Minutes |
| 03 | When double bond is in conjugation with vacant -p , When double bond is in conjugation with fully filled -p | 28 Minutes |
| 04 | When double bond is in conjugation with fully filled -p, When double bond is in conjugation with half filled-p , When +ve charge and lone pair are adjacent , d-orbital resonance , Conditions of Resonance, Mesomeric effect (M) | 53 Minutes |
| 05 | Stability of resonating structures (R.S), Steric Inhibition of Resonance (SIR) , Equivalent R.S. | 35 Minutes |
| 06 | Equivalent R.S. , Hyperconjugation HC , Hyperconjugation in carbocations , Hyperconjugation in Alkenes , Heat of hydrogenation (HOH) | 54 Minutes |
| 07 | Hyperconjugation in Toluene, Hyperconjugation in Free Radicals, Electromeric effect (E), Applications of electronic effects , Dipole moment, Bond length , Aromaticity , Benzenoids and Non-benzenoids | 38 Minutes |
| 08 | Examples of aromatic compounds , Heterocyclic aromatic compounds | 27 Minutes |
| 09 | M.O. Diagram, Polycyclic aromatic compounds | 24 Minutes |
| 10 | Examples of aromatic systems, [n] Annulenes , NMR- definition of Aromaticity , Resonance energy (RE) | 37 Minutes |
| 11 | Acidic strength of acids , Acidic strength of dicarboxylic acids | 44 Minutes |
| 12 | Aromatic acids , Ortho effect, Acidic strength of phenols , Feasibility of reactions , Sodium bicarbonate test of acids | 52 Minutes |
| 13 | Basic strength , Organic Nitrogenous bases. | 12 Minutes |
| 14 | Basic strngth of Aliphatiec amines , Aromatic amines | 43 Minutes |
| 15 | Basic strength of Amidines , Basic strength of Guanidines, Proton sponges, Site of protonation , Feasibility of Reaction | 31 Minutes |
| 16 | Carbanions (C-), Reactions in which carbanions are formed , Organometallic compounds, Active methylene group., Tautomerism, Types of Tautomerism | 38 Minutes |
| 17 | Enolisable –H, Keto-enol Tautomerism, Mechanism of keto-enol Tautomerism | 23 Minutes |
| 18 | Stability of enol (Percentage enol-content), Racemisation due to enolisation | 43 Minutes |
| 19 | D-Excharge , Tautomerism in phenols , Ring-chain Tautomerism , Unsymmetrical alpha-hydroxy ketones | 37 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Basic organic chemistry, Definition of organic compound , Representation of organic compound , Hybridisation | 12 Minutes |
| 02 | Number of Sigma and PI bonds , Degree of carbon , Degree of hydrogen , Degree of Alkyl halides, Degree of Alcohols , Degree of Amines , Degree of unsaturation (DU) , Calculation of DU , Fundamental definition of DU, Homologous series (H.S.) | 46 Minutes |
| 03 | Classification of organic compound , Aromatic compounds , Homocyclic compounds , Heterocyclic compounds , IUPAC- Nomenclature , Scheme of IUPAC, Naming of Alkanes | 38 Minutes |
| 04 | Scheme of IUPAC, Naming of alkanes , Retained Names , Naming of alkenes | 59 Minutes |
| 05 | Naming of Alkene, Naming of Alkynes , Naming of cycloalkanes | 33 Minutes |
| 06 | Naming of cycloalkenes , Alkylidenes , Naming of cycloalkynes , Naming of Bicyclo compounds | 42 Minutes |
| 07 | Functional Groups (F.G.), Naming of carboxylic acids, Special Name of carboxylic acids , Naming of dicarboxylic acids | 33 Minutes |
| 08 | Naming of sulphonic acid , Naming of Alcohols , Naming of Amines , Naming of thioalcohols, Naming of Aldehydes , Special name of Aldehydes | 49 Minutes |
| 09 | Naming of Ketones , Naming of cyanides , Special name of cyanides , Naming of isocyanides , Naming of Amides , Special name of amides , Naming of acid halides | 46 Minutes |
| 10 | naming of acid halide, naming of acid anhydride, naming of esters, special name of ester | 41 Minutes |
| 11 | Naming of haloalkanes , Naming of Nitro compounds , Naming of Nitroso compounds , Naming of Aromatic compound , Benzene , Other aromatic compound | 38 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Variables, functions, angles, units of angles (Degree & radion) , conversion of units, Trigonometric ratios/ functions, values of trigonometric ratios, values of trigonometric ratios for angles grater than 90°, | 36 Minutes |
| 02 | unit circle method, CAST rule. Trigonometric formula, sine rule & cosine rule , Logrithem , exponential and inverse functions. | 1 Hr 03 Minutes |
| 03 | oordinate geometry , slope of a line , equation of straight line, parabola , ellipse, circle and rtectangular hyperbola. | 30 Minutes |
| 04 | Differentiation, geometrical meaning of differentiation, slope of a line, formulae for differentiation, rules of differentiation- addition/subtraction rule, product rule, quotient rule, constant multiple rule, chain rule. | 43 Minutes |
| 05 | Higher order Differentiation , implicit functions , important problems . | 25 Minutes |
| 06 | Differentiation as rate measurement, maxima & minima. | 50 Minutes |
| 07 | Integration, geometrical meaning of integration, formulae of integration, | 16 Minutes |
| 08 | Definite integration, rules of integration, addition/ subtraction rule, method of substitution. Integration by parts, Integration as area under curve, indefinite integration , area under curve. | 48 Minutes |
| 09 | ntroduction to vectors, null vector, unit vector, negative of a vector, graphical representation and mathematical representation of a vector, angle b/w two given vectors, | 36 Minutes |
| 10 | Resolution of vector.Addition of vectors, triangle method and parallelogram method, substraction of vectors. | 26 Minutes |
| 11 | Dot product and its uses. | 27 Minutes |
| 12 | Cross product and its uses , right hand screw rule | 48 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Rest & motion, distance & displacement, speed, average speed , time average and space average, instantaneous speed, Uniform speed and non uniform speed, | 49 Minutes |
| 02 | velocity, average and instantaneous velocity, acceleration, average and instantaneous acceleration. | 41 Minutes |
| 03 | Equations of kinematics with constant acceleration, steps used to solve the problems based on equation of kinematics, motion under gravity. | 41 Minutes |
| 04 | graphical analysis, some important graphs, conversion of graphs, information collected from graphs. | 16 Minutes |
| 05 | Variable acceleration, steps used to solve the problems based on variable acceleration, when acceleration is dependent on time, distance and velocity. | 21 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Ground to ground projectile, time of flight, net velocity, trajectory equation, maximum height, | 40 Minutes |
| 02 | horizontal range.Projection at complementary angles from ground, some important relations and problems. | 22 Minutes |
| 03 | Problems based on ground to ground projectile. | 20 Minutes |
| 04 |
|
40 Minutes |
| 05 | Problem on projectiles from tower | 17 Minutes |
| 06 |
|
41 Minutes |
| 07 | Problems based on projectile on incline plane. | 19 Minutes |
| 08 |
Projectiles from moving platform, Collision of a projectile with vertical wall, some miscellaneous examples. |
41 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Introduction to relative motion, one dimensional relative motion and two dimensional relative motion . Uses of equations of kinematics in 1D relative motion. | 48 Minutes |
| 02 | uses of equations of kinematics in 2D relative motion , Velocity of approach and velocity of separation in 1D, Velocity of approach and velocity of separation in 2D, condition for two particles to collide, minimum separation b/w two moving particle, time taken to come at minimum separation miscellaneous problems . | 45 Minutes |
| 03 | miscellaneous problems | 32 Minutes |
| 04 | River boat problem in one dimension. | 18 Minutes |
| 05 | River boat problem in two dimensions, direct crossing, minimum time taken to cross the river, minimum drift , minimum velocity | 45 Minutes |
| 06 | Wind-aeroplane problem. Rain man problem, some illustrations. | 48 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Force, fundamental forces, normal force, tension force, Newton’s lst law, 2nd law , and 3rd law, equation of motion, Inertia. | 50 Minutes |
| 02 | free body diagram ,Equilibrium, types of equilibrium, steps to solve the problems based on equilibrium, problems | 48 Minutes |
| 03 | steps used to solve the problems of accelerated motion, problems , atwood machine | 32 Minutes |
| 04 | Constrained motion, string constraint, displacement method, tension method, differentiation method, two block one pulley system, | 36 Minutes |
| 05 | constrained motion when string is inclined, wedge constraint. | 32 Minutes |
| 06 | Weighing machine, motion inside lift, apparent weight, weightlessness, spring balance , spring and spring force. | 42 Minutes |
| 07 | Reference frame, inertial frame and non-inertial frame, pseudo force, illustrations | 31 Minutes |
| 08 | Newton’s laws for system , problems | 25 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Introduction to friction, properties of friction. Kinetic friction,coefficient of kinetic friction. | 45 Minutes |
| 02 | Static friction, coefficient of static friction, self adjustable nature of static friction, driving force, graph relating friction with driving force. | 46 Minutes |
| 03 | Contact force, angle of friction, minimum force required to slide a block , why pulling is easier than pushing? | 31 Minutes |
| 04 | Angle of repose, minimum and maximum force on the inclined plane so that block does not move , graph | 27 Minutes |
| 05 | System of two blocks, steps used to check the slipping b/w two blocks, problems | 39 Minutes |
| 06 | System of three blocks and miscellaneous examples. | 29 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Introduction to work, definition of work, point of application of force. Calculation of work done when force is constant | 35 Minutes |
| 02 | Sign of work done . work done by variable force, | 28 Minutes |
| 03 | work done from force-displacement graph, work done by friction, normal and gravity | 24 Minutes |
| 04 | work done by spring force.Work done by variable force along given path, conservative and non-conservative forces | 28 Minutes |
| 05 | methods to identify conservative forces , Del-operator, curl, Potential energy, its definition, external agent, | 42 Minutes |
| 06 | relation b/w conservative force and potential energy, how to find P.E. if conservative force is given and vise-versa. Refrence line , gravitational Potential energy and spring potential energy | 41 Minutes |
| 07 | Equilibrium, types of equilibrium, stable, unstable and neutral equilibrium. | 26 Minutes |
| 08 | Kinetic energy , Work energy theorem, some examples. | 17 Minutes |
| 09 | Problems based on work energy theorem | 26 Minutes |
| 10 | Energy conservation, some examples, power, instantaneous power and average power. | 26 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Similarities b/w translational and rotational motion, angular displacement and its direction . | 34 Minutes |
| 02 | angular velocity and angular acceleration, equations of circular kinematics. | 37 Minutes |
| 03 | Relation b/w linear and rotational quantities, tangential acceleration centripetal/redial/normal acceleration. Total acceleration. | 33 Minutes |
| 04 | Time period , frequency , angular frequency , Problems | 23 Minutes |
| 05 | Radius of curvature of path, radius of curvature in projectile motion. | 32 Minutes |
| 06 | Types of circular motion, horizontal circular motion. Some important examples. Steps used to solve the problems based on circular dynamics. Vertical circular motion, some important examples. | 50 Minutes |
| 07 | Vertical circular motion of a ball attached with string , vertical circular motion of a ball attached with light rod. | 35 Minutes |
| 08 | Problems , Banking of roads with and without friction. | 26 Minutes |
| 09 | Centrifugal force, its direction and magnitude. Some examples. | 33 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Center of Mas, definitions, Type of mass distribution, discrete and continuous mass distribution, linear mass density, surface mass density, volume mass density. Calculation of com for system of particles. Com of system of two particles. | 42 Minutes |
| 02 | Calculation of com for continuous mass distribution, com of rod, semi-circular ring, semi-circular disc, solid hemi-sphere, hollow hemi-sphere, solid cone. | 51 Minutes |
| 03 | Com of a body with hole, problems | 25 Minutes |
| 04 | Motion of com, velocity of com, acceleration of com, impulsive force, impulse, impulse-momentum equation, important examples.Conservation of momentum, some important conclusions and examples. | 48 Minutes |
| 05 | Miscellaneous problems | 19 Minutes |
| 06 | Some important points related to center of mass and miscellaneous problems. | 40 Minutes |
| 07 | Spring mass system, steps to solve the problems based on spring-mass-system. Problems , Collision, line of impact, coefficient of restitution, | 39 Minutes |
| 08 | classification of collision, head-on-inelastic collision, head on elastic collision, head on-perfectly in elastic collision. Problems on collision. | 39 Minutes |
| 09 | collision with heavy mass. Oblique collision, problems | 30 Minutes |
| 10 | oblique collision with wall , problems | 27 Minutes |
| 11 | Variable mass, thrust force, rocket propulsion. | 28 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Definitions of periodic motion, oscillatory motion, and SHM, frequency, time period, amplitude, angular frequency.Differential equation of SHM, equation of SHM, | 32 Minutes |
| 02 | SHM as projection of uniform circular motion, phase, | 30 Minutes |
| 03 | Problems on phase , equation of SHM when mean position is not at origin. | 30 Minutes |
| 04 | Velocity, acceleration and displacement of particle in terms of time (t) and displacement (x). Graphs, potential, kinetic and total energy in terms of time (t) and displacement (x), important graphs. | 54 Minutes |
| 05 | Force method to find the time period, spring mass system , | 47 Minutes |
| 06 | problems on force method, combinations of springs , springs in series , springs in parallel, | 17 Minutes |
| 07 | energy methods to find the time period and Problems on spring mass system | 46 Minutes |
| 08 | Angular SHM ,Differential equation of angular SHM, equation of angular SHM, method to find the time period in angular SHM | 30 Minutes |
| 09 | Time period of simple pendulum, time period of simple pendulum when forces other than gravity and tension are also present, effective g. Fractional and percentage error , error in measurement of g, time period of simple pendulum when length of wire is comparable to radius of earth, Compound pendulum, its time period, minimum time period, | 52 Minutes |
| 10 | Problems on compound pendulum , Torsional pendulum. | 22 Minutes |
| 11 | Superposition of two parallel SHMs and perpendicular SHMs. | 40 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Assumptions for Ideal gas, Average velocity, Average speed, RMS speed, Most Probable speed, Maxwell’s velocity distribution graph. | 31 Minutes |
| 02 | Miscellaneous problems related to calculation of RMS speed , average speed , most probable speed. | 20 Minutes |
| 03 | Derivation of Ideal gas equation, calculation of kinetic energy of molecules | 23 Minutes |
| 04 | Degree of Freedom, Maxwell’s law of Equipartition of energy and Internal energy. | 17 Minutes |
| 05 | Mean Free Path, Some miscellaneous problems. | 33 Minutes |
| 06 | Specific Heat Capacity, Adiabatic Exponent and gaseous mixture , molecular weight , Cp , Cv and γ of gaseous mixture. | 33 Minutes |
| 07 | Work done by gas when pressure is constant and when pressure is variable, indirect method of calculation of work done by gas, work done from PV diagram. | 26 Minutes |
| 08 | Problems based on calculation of work done by gas. | 35 Minutes |
| 09 | Zeroth law of Thermodynamics, first law of Thermodynamics, Sign convention for Heat supplied, work done by gas and change in Interval energy .problems based on 1st law of thermodynamics. | 39 Minutes |
| 10 | Thermodynamics processes ,Isochoric process, Isobaric process, Isothermal process, , calculation of heat supplied & Specific Heat Capacity of all the processes. | 25 Minutes |
| 11 | Adiabatic process , Polytropic process, calculation of heat supplied & Specific Heat Capacity of these processes. | 31 Minutes |
| 12 | Cyclic process, Heat Engine and its Efficiency, carnot cycle | 27 Minutes |
| 13 | Refrigerator and its Coefficient of Performance, | 20 Minutes |
| 14 | Miscellaneous problems and Free Expansion. | 31 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Variation in pressure inside liquid with height, problems | 32 Minutes |
| 02 | Problems , Inclination of liquid surface in static condition, rotation of container filled with liquid. | 44 Minutes |
| 03 | Archimedes principle and force of buoyancy , Pascal’s law, | 41 Minutes |
| 04 | atmospheric pressure, Gauge pressure, Absolute pressure, Barometer, and Manometer. | 20 Minutes |
| 05 | Force applied by liquid on base of container and wall of container.Center of gravity, Center of Buoyancy, Meta-center, stability of completely submerged body and partially submerged body , metacentre. | 56 Minutes |
| 06 | Types of flow, Uniform and Non-Uniform flow, Laminar and Turbulent flow, Reynolds number, Equation of continuity, Volume flow rate and Mass flow rate, Bernoulli theorem. | 42 Minutes |
| 07 | Applications of Bernoulli theorem, | 21 Minutes |
| 08 | Venturimeter, velocity of Efflux, Syphon action. | 29 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Specific Heat Capacity, Heat Capacity, Specific Heat Capacity of water, | 20 Minutes |
| 02 | definition of unit of Calorie, Latent heat, Latent Heat of Fusion, Latent Heat of Vaporization. | 20 Minutes |
| 03 | change of State (Phase) of water with Temperature, illustrations. | 18 Minutes |
| 04 | Problems , temperature scale.. | 44 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Linear expansion, Coefficient of Linear expansion, Differential expansion | 18 Minutes |
| 02 | effect of Temperature on pendulum clock, error in measurement by metallic scale, | 25 Minutes |
| 03 | Bimetallic strip, thermal stress | 22 Minutes |
| 04 | Areal expansion, Coefficient of Areal expansion, relation between α and β, expansion of holes inside metallic plate. Coefficient of Volume expansion, relation between α and γ, | 28 Minutes |
| 05 | Effect of Temperature on Density, Real and Apparent expansion of liquids. | 37 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Surface Tension ,wetted perimeter | 31 Minutes |
| 02 | Surface Energy, cause of Surface Tension.Excess Pressure inside liquid drop, Excess pressure inside Soap bubble. Radius of curvature of common surface of double bubble. | 49 Minutes |
| 03 | Cohesive force and Adhesive force, shape of liquid surface, Angle of contact.Capillary rise and illustrations. | 33 Minutes |
| 04 | Capillary action with mercury , radius of lower meniscus | 28 Minutes |
| 05 | Some miscellaneous problems | 18 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Definition and classification of wave, Mechanical & Non mechanical waves, Transverse & Longitudinal waves, Progressive and Stationary waves | 29 Minutes |
| 02 | Differential form of wave equation, General form of equation of Progressive wave, information that can be collected from general form of wave equation | 26 Minutes |
| 03 | How to find wave equation in terms of x and t when equation is given in terms of either x or t. wave on string introduction,Wavelength,Time period ,Frequency, Angular frequency, Wave number, Wave speed and velocity of particle, acceleration of particle, slope of string, direction of velocity of particle, | 51 Minutes |
| 04 | Expanded form of standard equation of wave . relation b/w Phase difference and Path difference, relation b/w Phase difference and Time difference | 34 Minutes |
| 05 | Derivation of speed of wave on string, examples | 25 Minutes |
| 06 | Instantaneous and Average power transmitted by wave, Instantaneous and average intensity of a wave on string | 33 Minutes |
| 07 | Superposition of waves,Interference,Resultant intensity, Constructive and Destructive Interference , miscellaneous problems. | 1 Hr 02 Minutes |
| 08 | Reflection and Transmission of wave from one to other medium, effect of Reflection and Transmission on frequency, speed, Wavelength and Phase. equation of reflected and transmitted waves. Amplitudes of reflected and transmitted wave |
32 Minutes |
| 09 | Stationary waves, Nodes and Anti-nodes, Phase difference, properties of stationary waves. | 59 Minutes |
| 10 | Equation of stationary waves , vibration of string fixed at both ends, vibration of string fixed at one end.Resonance, Sonometer, Melde's experiment | 39 Minutes |
| 11 | kinetic energy and potential energy of small element of string. | 30 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Introduction to Sound wave, variation of pressure with time and distance, variation in density and position with time. | 24 Minutes |
| 02 | Equation of sound wave, relation b/w pressure Amplitude and Displacement Amplitude. Phase difference b/w Pressure wave and Displacement wave. Speed of Sound wave, Newton’s formula and La-place corrections. | 32 Minutes |
| 03 | Dependence of speed of sound on Temperature, Pressure and relative Humidity. Intensity of sound wave, Wave front, Shape of wave-front for point source, Line source and Plane source. Variation of Intensity with distance from source. | 44 Minutes |
| 04 | Comparison of two sound waves. Sound level, relative Sound Level, Pitch , waveform and quality of sound. Superposition of two sound waves, interference constructive and destructive interference, Reflection of Sound, Echo. | 44 Minutes |
| 05 | Stationary wave in sound, vibrations of Air column in Organ pipes, Open Organ Pipe and Closed Organ Pipe | 36 Minutes |
| 06 | Resonance Tube method to find the speed of sound, Beats. | 30 Minutes |
| 07 | Doppler’s effect, when observer is moving and source is stationery, when source is moving and observer is stationary, when both source and observer are moving. | 40 Minutes |
| 08 | Doppler’s effect When medium is also moving.miscelleneous problems. | 44 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Elasticity, Plasticity, Deforming force, The reason behind Elastic and Plastic behaviour, Restoring force, Stress, Longitudinal Stress, Shear Stress and Bulk Stress, Strain, Longitudinal Strain, Shear Strain, Bulk Strain. Hook’s law, Modulus of Elasticity, Young’s Modulus, Modulus of Rigidity, Bulk Modulus, Compressibility, | 41 Minutes |
| 02 | Variation of Strain with Deforming force, Elastic Limit, Yield point, Fracture point, elongation in wire due to self weight. Analogy with spring, Spring constant of a wire Elastic Potential energy stored in the deformed wire. | 25 Minutes |
| 03 | Viscosity, Velocity Gradient, Viscous Force, Stoke’s forces Terminal Velocity. | 28 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Fundamental Quantities, Derived Quantities and Supplementary Quantities, Dimensions, Dimensional formula, some important concept (points) about dimensions, | 27 Minutes |
| 02 | Problems on dimensions, Dimensional Analysis. Units, System of Units and conversion of Units. | 26 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Newton’s law of gravitation, gravitational field due to point mass, circular arc, circular ring, circular disc, long rod, infinite plate, hollow sphere and solid sphere | 43 Minutes |
| 02 | variation in acceleration due to gravity with height and depth, effect of rotation of earth, effect of shape of earth. | 27 Minutes |
| 03 | Gravitational potential, gravitational potential due to point mass, circular arc, circular ring, circular disc, hollow sphere, solid sphere, relation b/w gravitational field and gravitational potential . | 31 Minutes |
| 04 | Gravitational potential energy, P.E. of two point mass system, self energy of hollow sphere and solid sphere, miscellaneous examples. | 30 Minutes |
| 05 | Motion of satellite, orbital velocity, time period, energy of satellite, binding energy, escape velocity, geostationary satellite. | 26 Minutes |
| 06 | Kepler's laws, path of a satellite according to its projection velocity. Miscellaneous examples. | 47 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Introduction, similarities b/w rotational and translational motion. Rigid body, types of motion of rigid body. | 32 Minutes |
| 02 | Moment of inertia definitions, calculation of MOI of a point mass, MOI of system of particles, MOI of a rod, | 33 Minutes |
| 03 | MOI of ring, MOI of disc, MOI of solid sphere, MOI of hollow sphere, MOI of cone, MOI of solid cylinder, MOI of hollow cylinder | 1 Hr |
| 04 | Perpendicular axes theorem, parallel axes theorem. MOI of a body with hole | 1 Hr 08 Minutes |
| 05 | Radius of Gyration. Torque, Calculation of torque, | 55 Minutes |
| 06 | Force couple, point of application. | 20 Minutes |
| 07 | Rotational and translational equilibrium. | 33 Minutes |
| 08 | Rotational equation of motion accelerated rotational motion. Some important examples. | 54 Minutes |
| 09 | Combined motion, rolling motion, slipping, skidding, perfect rolling, | 1 Hr 01 Minutes |
| 10 | Some important problems, trajectory of a point on wheel performing perfect rolling and radius of curvature of trajectory. | 31 Minutes |
| 11 | instantaneous axis of rotation, rotational K.E. , conversion of imperfect rolling to perfect rolling | 1 Hr 14 Minutes |
| 12 | Direction of friction in perfect rolling , Angular momentum, calculation of angular momentum, | 36 Minutes |
| 13 | calculation of angular momentum, | 30 Minutes |
| 14 | conservation of angular momentum in pure rotational motion , in pure translational motion and in combined motion , angular impulse momentum equation. | 39 Minutes |
| 15 | Collision of a particle with rigid body | 23 Minutes |
| 16 | Toppling and sliding. | 34 Minutes |
| Lecture# | Description | Duration |
|---|---|---|
| 01 | Methods of heat transfer, conduction, convection and radiation. steady state, temperature gradient. Laws of conduction. Analogy with electric current | 31 Minutes |
| 02 | Problems on conduction, 1D heat transfer, 2D heat transfer, 3D heat transfer. Formation of ice layer on lake water surface. | 36 Minutes |
| 03 | Convection, Radiation, Reflection power, Absorption power, Transmittance power, Black body. Ferry’s block body. Emissive power of a body, Spectral emissive power, absorptive power, spectral absorptive power. Emissivity of a body, Prevost's heat exchange theory | 34 Minutes |
| 04 | Kirchhoff’s law of radiation, Stefan’s law of heat radiation, rate of cooling Newton’s law of cooling |
24 Minutes |
| 05 | Average temperature method, integration method. Black body radiation, Wien's displacement law, solar constant | 27 Minutes |
| Lecture# | Description | Duration |
| 1 | Definition of set, Methods to represent sets : (1) Roster form or tabular method (2) Set builder (Property method), Inter-conversion of Roster form into set builder form or vice-versa; Types of sets: (1) Null Set (2) Singleton set (3) Finite set & Cardinal number of set (4) Equivalent sets. (5) Equal sets |
34 Minutes |
| 02 | Subsets, Proper subset, Total number of subsets, Idea of intervals: (1) Close interval (2) Open-interval (3) Discrete interval or curly bracket, Operation on sets (By venn-diagram) (1) Union of 2 sets (2) Intersection of 2 sets (3) Set A and its complement |
43 Minutes |
| 03 | (4) Set A but not B (5) Set B but not A (6) Neither A nor B #Demorgan’s Law (7) Atleast one set out of three sets A, B, C (8) Atleast 2 sets out of 3 sets (9) Exact 2 sets out of 3 sets (10) Exact 1 set out of 3 sets (11) Neither A, B nor C. Laws of Algebra of sets |
44 Minutes |
| 04 | Cartesian Product ordered pair, ordered triplets, Cartesian Product of 2 sets or 3 sets, Introduction of Relations |
52 Minutes |
| 05 | Relations, Total number of relations, types of relations: (1) Void relation (2) Universal Relation (3) Identity Relation (4) Reflexive Relation (5) Symmetric Relation (6) Transitive Relation (7) Equivalence Relation |
1 Hrs 02 Minutes |
| 06 | Definition of function, Its domain and co-domain and range. | 43 Minutes |
| Lecture# | Description | Duration |
| 01 | Number systems: (1) Natural numbers (2) Whole numbers (W) (3) Integers (I or Z) (4) Prime Numbers (5) Composite numbers (6) Co-prime numbers (Relatively prime numbers) (7) Twin-prime numbers (8) Rational numbers : (a) Terminating rational numbers (b) Repeating rational numbers (9) Irrational numbers (Q’ or Qc) (10) Real numbers (R) (11) Complex numbers (C or Z) Algebra of complex numbers, converting into a + ib (i = √-1) form, square root of a complex number. |
1 Hrs 24 Minutes |
| 02 | Basics of Mathematics - About the concept helpful to solve inequalities, Domain of a function, About the functions - (1) Rational functions (2) Irrational functions (3) Polynomial functions |
58 Minutes |
| 03 | Some important identities, Factor or remainder theorems, Cramer’s method to solve linear equations in two variables, Ratios and Proportion, Squaring in case of inequalities. |
53 Minutes |
| 04 | When we cross multiply the denominator incase of inequalities? Rational (Polynomial) Inequalities - Steps to solving inequalities (For Non-repeated and repeated linear factors), Questions |
54 Minutes |
| 05 | Questions of Rational inequalities containing repeated linear factors, Modulus functions (Absolute - Value functions) , Domain, Range and Graphs of basic modulus functions, Removal of modulus functions, Properties of Modulus functions, Equations based on |x| = a (a≥0) |
55 Minutes |
| 06 | Defining modulus functions, Removal of modulus, Basic Graphs and Graphs of combination of Modulus functions, Modulus equations. |
a-14 Min., b-51 Min. |
| 07 | Modulus inequalities. | 1 Hrs |
| 08 | Questions of Modulus - inequalities. | 56 Minutes |
| 09 | (a) Irrational function - domain, Range and Graph of y = √x , Irrational equations. (b) Irrational Inequalities. |
1 Hrs 02 Minutes |
| 10 | Exponential and Logarithmic functions, domain-range and graph of basic exponential & log functions, Properties formulae, Simplification of log functions. |
53 Minutes |
| 11 | Basic questions to simplify the Log functions, Log-equations. | a-35 Min., b-19 Min. |
| 12 | Logarithmic and Exponential equations. | 46 Minutes |
| 13 | Exponential and Log inequalities. | 41 Minutes |
| 14 | Log-inequalities when base is variable, Domain of functions including irrational or log functions. | a-33 Min., b-48 Min. |
| 15 | Greatest integer function (GIF), Domain-Range and basic graph of GIF, Properties, Fractional-part function (FPF), Domain-Range and Basic Graph, Properties, Signum function, Domain-Range and Graph. |
1 Hrs 01 Minutes |
| 16 | Questions based on GIF, FPF and Signum function. | a-39 Min., b-32 Min. |
| Lecture# | Description | Duration |
| 01 | Polynomial functions, Roots (zeros), Solutions, Equation vs Identity, Questions, Methods of finding roots (i) Factorisation |
1 hrs 08 Minutes |
| 02 | Methods of finding roots- (ii) Transformation method. (iii) Dharacharya Method (Perfect square), Questions. |
1 hrs 07 Minutes |
| 03 | Questions based on finding roots. | 1 Hrs 02 Minutes |
| 04 |
Nature of roots : in ax2 + bx + c = 0 (a≠0) D1 = b12 –4a1c1 and D2 = b2 –4a2c2) |
1 Hrs 03 Minutes |
| 05 | Plotting of quadratic expression (Graph) when a > 0 or a < 0 in y = ax2 + bx + c (a≠0), Range of y = ax2 + bx + c when x ∈ R Sign of a, b, c, D, Range in an interval x ∈[x1, x2], Questions. |
1 Hrs 11 Minutes |
| 06 |
Sign of quadratic expression, Range of Q/ Q |
1 hrs 10 Minutes |
| 07 | Range by substitution, condition of common roots- (1) when 1 root common (2) when both the roots are common Location of roots- (1) When both the roots are greater than k (k∈R) (2) When both the roots are less than k (3) When 1 root < k and other root > k (4) When both the roots lies in interval (k1, k2) (5) When only 1 root lies in (k1, k2) |
1 Hrs 27 Minutes |
| 08 | Questions based on location of Roots, Pseudo-Quadratic equation, Questions based on it. |
1 Hrs 26 Minutes |
| Lecture# | Description | Duration |
| 01 | Arithmetic progression (AP), Standard terms, General term or last term (tn or ð“) of AP, Condition for 3 terms in AP, Arithmetic mean (AM) of n numbers, Middle terms, Sum of First n terms (sn) of AP, Properties of AP, n Arithmetic means inserted between 2 numbers, sum of n Arithmetic mean inserted between two numbers, Properties of AP. |
45 Minutes |
| 02 | Questions based on Arithmetic progression and their properties. | 1 Hrs 07 Minutes |
| 03 | Summation series based on AP, Geometric progression (GP), Standard terms, General term of GP, Sum of first n terms of GP, Sum of ∞ terms of GP, supposition of terms in GP, n Geometric means between 2 positive numbers, Properties of GP. |
1 Hrs 09 Minutes |
| 04 | Questions based on GP and their properties. | 41 Minutes |
| 05 | Summation Series based on G.P., Harmonic Progression (HP), General term of Harmonic Progression, Harmonic Means of n numbers, Questions based on Harmonic Progression. |
59 Minutes |
| 06 | Relation between AM, GM, HM, Solving inequalities based on AM ≥ GM ≥ HM. Arithmetic Geometric Progression (AGP), General Term, Sum of first n terms of AGP, Sum of ∞ numbers of terms in AGP, Summation series of AGP. |
a- 43 Min., b-42 Min. |
| 07 |
(a) Summation of series based on product of terms in GP but with non-AP; Summation of series, i.e. n n n n nSn = ∑tr, (Vn - Vn-1 )method, Evaluating the value of ∑1, ∑r, ∑r2, ∑r3, r=1 r=1 r=1 r=1 r=1 (b) Method of differences |
a-37 Min., b-35 Min. |
| 08 | Miscellaneous Series | 1 Hrs |
| 09 | Miscellaneous Series | 34 Minutes |
| Lecture# | Description | Duration |
| 01 | Basic Trigonometric Ratios (T-Ratios), and Identities, Questions based on Basic Trigonometry identities, elimination of angle θ. |
57 Minutes |
| 02 | Trigonometry Ratios of allied angles, General solutions on coordinate axes, values of Trigonometry Ratios in [0, 90°],Questions based on allied angles, Graph of Trigonometry ratios, their domain-range and fundamental period. |
1 Hrs 17 Minutes |
| 03 | Compound angles of trigonometry ratios, transformation formulae, values of trigonometry ratios at 15°(π÷12),75°(5π÷12), Questions | a-35 Min., b-42 Min. |
| 04 |
Multiple and sub-multiple angles, θ = 52*10÷2, θ = 142*10÷2, value of sin 180 (180 = π÷10), cos360(360 = π÷5), Questions. |
a-53 Min., b-38 Min. |
| 05 | Questions based on multiple and sub-multiple angles. | 60 Minutes |
| 06 | Questions. Conversion of sin5A in terms of sinA and Conversion of cos5A in terms of cosA. |
a-32 Min., b-32 Min. |
| 07 | Conditional identities and Range of Trigonometric functions. | a-25 Min., b-34 Min. |
| 08 | Range by using concept of differentiation . | a-40 Min., b-19 Min. |
| 09 |
Trigonometric series- sin2 θ = sin2 α |
a-29 Min., b-38 Min. |
| 10 | Basic Trigonometric equations directly formula based. | a-24 Min., b-27 Min. |
| 11 | Trigonometric equations based on trigonometric identities, Questions based on Boundary values, solving simultaneous trigonometric equations. |
a-33 Min., b-25 Min. |
| 12 | Advanced Level Trigonometric equations. | a-34 Min., b-38 Min. |
| 13 | Advanced Level Trigonometric equations, Trigonometric-Inequalities. | a-25 Min., b-41 Min. |
| 14 | Domain of trigonometric functions. | 40 Minutes |
| Lecture# | Description | Duration |
| 01 | About the triangle, (1) Sine rule (2) Area of ΔABC. (3) Napier’s analogy (Law’s of tangent) (4) Cosine-formula (5) Projection formula (6) T-Ratios of half- angles, Questions |
43 Minutes |
| 02 | Questions | a-53 Min. |
| 03 | Questions, m-n rule, circles connected to a triangle- (1) Circumcircle (2) Incircle (3) Ex-circles (4) Centroid (5) orthocentre (6) Circum-centre. |
a-31 Min., b-40 Min., c-34 Min. |
| 04 | (1) Length of angle Bisectors. (2) Length of Medians. (3) Length of altitudes, Distances of special points from vertices (A, B, C) and sides (AB, AC, BC) (1) Circumcentre (O), (2) Incentre (I) (3) Centroid (G) (4) Excentres (I1, I2, I3) Questions. |
49 Minutes |
| 05 | Questions | a-32 Min., b-22 Min. |
| 06 | Questions, Pedal-triangle (ΔLMN), its all parameters. | a-44 Min., b-34 Min. |
| 07 | Ex-central-triangle (ΔI1 I2 I3), its all parameters, Distance between two special points- (1) Distance between circumcentre (o) & orthocentre (H), (2) Distance between circumcentre (0) and Incentre (I) (3) Distance between circumcentre and excentres (I1, I2, I3) (4) Distance between orthocentre (H) and Incentre (I) (5) Distance between centroid (G) and circumcentre (o) |
a-35 Min., b- Min. |
| Lecture# | Description | Duration |
| 01 | About factorial n (n!,⌊n ), Domain-Range and Properties of factorial n. About nCr, nPr, formulae based on n! , nCr and nPr, Binomial expansion (for n ∈ N), Pascal-Triangle, General term, mth term from ending, middle term (for n odd, n even), Questions based on Binomial expansion and determining terms in Binomial expansion. |
a-50 Min., b-20 Min. |
| 02 | Questions based to determine middle term in Binomial expansion, Questions based to determine coefficient of xr in Binomial expansion, Questions based to determine the term independent of x. |
a-36 Min., b-31 Min. |
| 03 | Questions based on determining coefficient in product of 2 Binomial expansions, Multinomial theorem. | a-25 Min., b-39 Min. |
| 04 | Coefficient determining by concept of permutation and combination and by using multinomial theorem; total number of terms in multinomial expansion; Number of terms free from fractional or irrational powers in Binomial expansion. |
a-34 Min., b-28 Min. |
| 05 | Numerically-Greatest term in the expansion of (x + a)n (n ∈ N), Algebraically - Greatest and least term in the expansion of (x + a)n (n ∈ N); Questions based on Ι + ƒ . |
a-31 Min., b-35 Min. |
| 06 | Questions based on Ι + ƒ , exponent of prime number (p) in ⌊n ; Questions based on divisibility and remainder, Last digit by cyclicity, Last digit, Last two digits, Last 3 digits in a number. |
a-29 Min., b-43 Min. |
| 07 | Summation of series. | a-42 Min., b-33 Min. |
| 08 | Questions based on Sigma, Summation of Binomial Coefficients taken two at a time, Summation when upper index is variable. |
a-47 Min., b-35 Min. |
| 09 | Questions based on summation of Binomial coefficients taken two at a time when upper index is variable. | 32 Minutes |
| 10 | Double-Sigma, Binomial expansion for negative or fractional power, Some-important expansions, Questions based on determining Coefficient in negative or fractional power in Binomial expansion. |
a-43 Min., b-34 Min. |
| Lecture# | Description | Duration |
| 01 | Point, Rectangular - Cartesian Coordinate system, Parametric and Polar Coordinates of a point, distance between 2 points, section formula, Harmonic conjugate, Questions, About the Quadrilateral, Area of triangle, Condition of collinearity of three points, Concurrent lines, condition of concurrency of three lines. |
a-44 Min., b-38 Min. |
| 02 | Area of quadrilateral, Area of n sided polygon. | 29 Minutes |
| 03 | Special points of triangle : (1) Centroid (G) (2) Incentre (I) (3) Excentres (I1, I2, I3) (4) Orthocentre (H) (5) Circum-centre(o) Types of straight lines- (1) General equation (2) Slope - intercept form (3) (a) Equation of a line parallel to x-axis. (b) Equation of line perpendicular to x-axis. (c) Equation of line coincident to x-axis. (d) Equation of line coincident to y-axis. (e) Equation of coordinates axes. (4) Slope point form (5) Two points form (6) Determinant form (7) Intercept form (8) Normal or Perpendicular form. Angle between two lines, condition of two lines to be parallel or perpendicular. |
a-43 Min., b-46 Min. |
| 04 | Condition of lines to be intersecting, Parallel, Coincident, Measurement of interior angle of Δ, Questions based on point, special points and types of lines. |
a-41 Min., b-49 Min. |
| 05 | Questions based on special points and types of lines. | a-45 Min., b-37 Min. |
| 06 | Equations of lines passing through P(x1, y1) and making an angle α with the line y = mx + C, slope of a line equally inclined to the two given lines, Questions. Parametric or distance form of a line. |
a-35 Min., b-49 Min. |
| 07 | Perpendicular distance, foot of perpendicular, foot of perpendicular, image of a point (x1, y1) w.r.t. line ax + by + c = 0, distance between two parallel lines, Area of parallelogram, About the parallelogram, positions of two points w.r.t. line/plotting of linear-inequations, condition that a point lies inside of a triangle. |
a-48 Min., b-37 Min. |
| 08 | Questions based on perpendicular distance, foot of perpendicular and image. | a-45 Min., b-34 Min. |
| 09 | Locus, Steps how to evaluate locus of a point, questions, angle bisectors, types of angles bisectors, how to identify type of angle bisector, angle bisectors containing a point P(x1, y1). |
a-43 Min., b-51 Min. |
| 10 | Questions based on angle-bisectors, family of lines (concurrent lines), Questions based on family of lines. | a-47 Min., b-24 Min. |
| 11 | Pair of lines (combined or joint equations), Non-homogenous equation of second degree, homogeneous equation of second degree, angle between pair of lines, separate equations from second degree, condition that second degree non-homogenous equations represents pair of lines, point of intersection of pair of lines, combined equations of angles bisectors of pair of lines. |
a-39 Min., b-34 Min. |
| 12 | Questions, distance between two parallel pairs of lines, Homogenisation. | a-39 Min., b-20 Min. |
| Lecture# | Description | Duration |
| 01 | Definition of Circle, Types of Circles- (1) Centre - Radius form (2) General equation : Equation of Circle passing through 3 non-collinear points. |
39 Minutes |
| 02 | Basic questions on circle, types of circles : (3) Diameter form (4) Standard equation of circle (5) Parametric Form (6) Point - Circle, Intercepts formed by circle on coordinate axes, position of points w.r.t. circle, Some Important notes related to Circle, Different-2 positions of circles, Questions. |
a- 60 Min., b- 25 Min. |
| 03 | Questions | a-40 Min., b-25 Min. |
| 04 | Position of Line w.r.t. Circle, Length of chord Intercepted by the circle on, Tangent, Types of tangent- (1) Slope - Form, (2) Point - Form, Normal of Circle (3) Parametric - Form (4) Equation of tangent to the curve at (0, 0), number of tangents to the circle, Questions, Application of tangents - (1) Length of tangents (2) Power of points P(x1, y1) w.r.t. circle (3) Area of quadrilateral PACB (4) Angle between two tangents (5) Chord of contact (6) Equation of chord whose mid point is given (7) Director circle (8) Separate equations of tangents (9) Combined equations or pair of tangents (10) Equation of circle circumscribing the ΔPAB (11) PA.PB = PC. PD = PT2 (12) OA.OB = OC.OD (13) Area of triangle formed by pair of tangents with their chord of contact, Questions |
a-45 Min., b-45 Min., c-37 Min |
| 05 | Questions | a-38 Min., b-32 Min. |
| 06 | Questions, Position of 2 circles and their common tangents- (1) When 2 circles are separated of each other, length of external and internal common tangent (2) When two circles touches externally (3) When two circles intersect at two real and distinct points, common chord of two circles, equation of common chord and its length, maximum length of common chord, angle of intersection of 2 circles, orthogonal circles and condition of orthogonality, (4) When two circles touches internally (5) When one circle lies completely inside of other, Questions. |
a-58 Min., b-38 Min. |
| 07 | Questions, Family of Circles- (1) Equations of family of circles passing through the point of intersection of circles, s = 0 and line L = 0 (2) Equation of family of circles passes through 2 points A & B. (3) Equation of family of circles passes through point of intersection of 2 circles. (4) Equation of family of circles touching a curve at a point, Questions |
a-44 Min., b-30 Min. |
| 08 | Questions, Radical axis/Radical centre, Equation of circle cuts three given circles orthogonally, pole and polar. |
a-30 Min., b-32 Min. |
| Lecture# | Description | Duration |
| 01 | Introduction of Conic Section, Definition of Conic-Section, General equation of conic section, Locus of a moving point P will be conic when focus(s) lies on directrix and does not lies on directrix, Questions, some definitions related to conic -section (1) Focus (2) Directrix (3) Axis (4) Vertex (5) Centre (6) Focal- chord (7) Double- ordinate (8) Latus-Rectum (LR) Standard parabola - Its all parameters, two questions. |
a-36 Min., b-32 Min., c-25 Min. |
| 02 | Questions based on parameters of parabola, position of point w.r.t. parabola, Questions. | a-25 Min., b-27 Min., c-25 Min. |
| 03 | (1) Parametric equation of a chord (2) Length of parametric chord (3) Focal chord (4) Minimum length of focal chord (5) Focal distance (6) ð“ (LR) = 2 (HM of ð“1 & ð“2), where ð“1 = PS, ð“2 = QS and P & Q are 2 moving points on parabola, S = focus, (7) (a) If focal chord of parabola makes ∠angle with its axis then ð“(LR) = 4a cosec2 α. (b) Length of focal chord at a distance p from vertex is 4a3÷p2 (8) If P1Q1 and P2Q2 are two focal chords of parabola y2 = 4ax then chords P1P2 & Q1Q2 intersect on its directrix. (9) If P1P2 and Q1Q2 are two focal chord of parabola are at right angle then area of quadrilateral P1Q1 and P2Q2 is minimum when chords are inclined at an angle π/4 to the axis and its minimum area is 32a2. (10) The circle described on any focal chord of parabola as diameter touches its directrix. (11) A line having slope (m) passes through focus(s) cuts the parabola at two real & distinct points if m ∈ R-{0}, Questions |
a-27 Min., b-33 Min. |
| 04 | Questions, Position of line w.r.t. Parabola, Condition of tangency Types of tangent - (1) Point form (2) Parametric form Questions based on tangents. |
a-31 Min., b-40 Min., c-23 Min. |
| 05 | Questions based on tangents, common tangents of two curves, Properties of tangents : P1, P2, P3, P4 |
a-40 Min., b-40 Min. |
| 06 | Properties of tangents: P5, P6, P7, P8 Questions based on Properties of tangents, Normal, Types- (1) Point form (2) Parametric form (3) Slope- form, condition of normality, Questions based on normals, properties of normal, P1, P2, P3 (a, b, c, d), P4, P5 . |
a-32 Min., b-29 Min., c-28 Min. |
| 07 | Properties of Normal- P6 , P7 (a, b), P8, P9- Reflection property, P10, P11 (a, b, c) P-11- Condition of three real & distinct normal to parabola, Questions based on normal and its properties, (1) Number of tangents to a parabola, (2) Pair of tangents (3) Director - Circle (4) Chord of contact (5) Chord whose mid point is given, Questions |
a-38 Min., b-20 Min., c-42 Min., d-34 Min. |
| 08 | Introduction of ellipse and hyperbola, standard ellipse (when a > b and a < b) and standard hyperbola and conjugate hyperbola, its basic parameters, auxiliary - Circle/Parametric coordinates of ellipse and hyperbola, Alternate definition of ellipse and hyperbola, Some important notes, Questions determining the basic parameters of ellipse and hyperbola. |
a-38 Min., b-31 Min., c-30 Min., d-25 Min. |
| 09 | Basic questions on ellipse and hyperbola, Questions based on Locus, Questions based on Parametric coordinates. |
a-36 Min., b-34 Min., c-32 Min., d-18 Min. |
| 10 | Parametric equation of chord of ellipse and hyperbola, questions on parametric chord, position of line w.r.t. ellipse Hyperbola, Condition of tangency, types of tangent- (1) Slope form (2) Point form (3) Parametric Form, Properties of tangents, Questions based on tangents. |
a- 38 Min., b-47 Min. |
| 11 | Questions based on tangents and its properties, Pair of tangents, Equation of chord of contact, Equation of chord whose mid point is given #Director Circle, Questions, Normal of ellipse and Hyperbola, Types- (1) Point Form (2) Parametric Form (3) Slope Form. |
a-43 Min., b-39 Min., c-14 Min. |
| 12 | Questions based on normal of ellipse Hyperbola, Reflection Property of ellipse - Hyperbola, Asymptotes of Hyperbola and conjugate Hyperbola, Properties of Asymptotes, Questions. |
a-26 Min., b-44 Min., c-34 Min. |
| 13 | Rectangular (Equilateral) Hyperbola, Rectangular Hyperbola considered coordinate axes as its asymptotes, its all parameters, tangents and normals, Questions. |
a-32 Min., b-31 Min. |
| Lecture# | Description | Duration |
| 01 | Introduction of factorial n ( ⌊n or n!) , nCr, nPr, Physical interpretation of n!, nCr, nPr. | 19 Minutes |
| 02 | Fundamental - Principles of counting (i) Multiplication - Rule (ii) Addition- Rule Basic Questions based on multiplication and addition-Rule; Sample-space. |
a-51 Min., b-49 Min. |
| 03 | Questions, Number Problems. | a-40 Min., b-35 Min. |
| 04 | Number problems based on divisible by 3, 4, 5, 25, Theorem-1: Selection and Permutation of r things out of n. Theorem-2 : Permutation of n things in which some things are of same kind. |
a-46 Min., b-28 Min. |
| 05 | Questions considering the word “RAKESH MODI” Questions, problem of forming words of 7 letters taking 3 vowels and 4 consonants using letters of word : “DIFFERENTIATION”. Problem of forming the words each consisting 3 consonants and 3 vowels by using letters of words “CIRCUMFERENCE”. |
a-42 Min., b-25 Min., c-35 Min. |
| 06 | Rank (Position) of a word or numbers, sum of the numbers formed (No repetition or when repetition allowed), Circular Permutation. |
a-35 Min., b-33 Min., C-35 Min. |
| 07 | Number of selection of r consecutive things out of n distinct things, Geometrical Problems Number of total lines, number of diagonals, number of triangles (a) One side common with given polygon (b) Two sides common with given polygon (c) Three sides common with given polygon. (d) None of the side common with given polygon. Chess board problems - Number of total rectangles, Number of total squares. Problem based on moving from left bottom corner to the right top corner in a chess board. |
a-48 Min., b-57 Min. |
| 08 | Groupings & distribution of n differents things into groups or bundles. | a-30 Min., b-29 Min., c-27 Min. |
| 09 | Selection of none, one or more things when given things are different or identical, Total number of divisors, Total number of proper divisors, Sum of total divisors, Number of ways in which a number (N) can be resolved as a product of two factors which are relatively prime or co-prime. |
a-48 Min., b-45 Min., c-14 Min. |
| 10 | Multinomial theorem of permutation and combination, Beggar’s Method | a-45 Min., b-43 Min. |
| 11 | Questions based on multinomial theorem, Dearrangement of n different things. | a-31 Min., b-23 Min. |
| 12 | Miscellaneous questions | a-33 Min., b-34 Min. |
| 13 | Miscellaneous questions | a-30 Min., b-17 Min. |
| Lecture# | Description | Duration |
| 01 | Introduction of complex number, about iota (i), Algebra of complex numbers- (1) Addition/subtraction (2) Multiplication (3) Conjugate of a complex number (4) Division (5) Equality of two complex numbers (6) Square root of a complex numbers, Questions to solving complex equations. |
a-43 Min., b-28 Min., c-23 Min. |
| 02 | Questions, Representation of Complex number (Geometrical interpretation of Complex number) (1) Cartesian form (2) Polar or parametric form (3) Euler’s form # Demoiver’s theorem, Questions. |
a-48 Min., b-38 Min. |
| 03 | Properties of modulus/conjugate, Modulus - Inequalities (Triangular Inequalities), Properties of argument of complex number, Interconversion of complex number (z) into Cartesian form (x, y) or vice-versa. |
a-41 Min., b-29 Min. |
| 04 | Questions based on Properties of Modulus, conjugate, argument of complex number and modulus inequalities | a-46 Min., b-47 Min. |
| 05 | Geometrical meaning of arg(z) = θ. Solving questions graphical, cube-roots of unity, cube-roots of –1, Properties, Questions based on cube roots of 1 and cube roots of –1. |
a-46 Min., b-39 Min., c-29 Min. |
| 06 | nth roots of unity, Properties, Questions based on nth roots of unity, rotation theorem (Geometrical interpretation of ei θ). Questions based on Rotation theorem. |
a-41 Min., b-21 Min., c-44 Min. |