Complete PCM For Class XI
Subject PCM Medium ENGLISH
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Category COMPLETE COURSE Lecture 578
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Syllabus

Mole concept

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

 

Equivalent concept

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

Chemical equilibrium

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

 

Ionic equilibrium

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

Thermodynamics & thermochemistry

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

Gaseous State

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

Atomic structure

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

 

Periodic table

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

Chemical bonding

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,𝞂 bond, Π bond, 𝛅 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 p𝚷 - d𝚷 bonding, p𝚷 - p𝚷 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

Boron & carbon Family group 13 & 14

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

S block

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  

STRUCTURAL ISOMERISM

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

 

STEREOISOMERISM

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

 

STRUCTURAL INDENTIFICATION & POC

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

GENERAL ORGANIC CHEMISTRY (GOC)

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

IUPAC NOMENCLATURE

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

 

MATHEMATICAL TOOLS

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

 

RECTILINEAR MOTION

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

PROJECTILE MOTION

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
  • Projectile from tower projected horizontally, , time of flight, net velocity, trajectory equation, horizontal range
  • Projectile from tower projected above horizontal, time of flight, net velocity, trajectory equation, maximum height.  horizontal range
  • Projectile from tower projected below horizontal. time of flight, net velocity, trajectory equation, horizontal range
40 Minutes
05 Problem on projectiles from tower 17 Minutes
06
  • Projectile from inclined plane, projected up the incline plane , time of flight, net velocity, trajectory equation, maximum height. range
  • Projectile from inclined plane, projected down the incline plane , time of flight, net velocity, trajectory equation, maximum height. Range
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

 

RELATIVE MOTION

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

 

Newton’s laws of motion (NLM)

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

FRICTION

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

WORK POWER AND ENERGY

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

 

CIRCULAR MOTION

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

 

CENTER OF MASS

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

 

SIMPLE HARMONIC MOTION (SHM)

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

KINETIC THEORY OF GASES & THERMODYNAMICS

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

FLUID MECHANICS

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

 

CALORIMETRY

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

 

THERMAL EXPANSION

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

 

SURFACE TENSION

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

 

WAVE ON STRING

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

 

SOUND WAVE

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

ELASTICITY AND VISCOSITY

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

 

UNIT & DIMENSION

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

 

GRAVITATION

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

ROTATIONAL MOTION

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

HEAT TRANSFER

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

 

Set Relation

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

Fundamentals of Mathematics

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.

 

Quadratic Equation

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)
(1) When a, b, c, ∈ R
(2) When a, b, c, ∈ Q
(3) When a = 1, b, c, ∈ I and D is Perfect square of integer
(4) when a, b, c ∉ R
(5) when D1 + D2 ≥ 0 (in a1x2 + b1x+ c1 = 0 and a2x2 + b2x+ c2 = 0 where

D1 = b12 –4a1c1 and D2 = b2 –4a2c2)
(6) Intermediate Mean Value Theorem (IMVT)
Questions based on nature of roots.

 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
y =L/Q , y

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

 

Sequence and Series

Lecture# Description Duration
01 Arithmetic progression (AP), Standard terms, General term or last term (tn or 𝓁) 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        n 
     Sn = 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
(1) First difference in AP. (2) Second difference in AP
(3) First difference in GP. (4) Second difference in GP;
Questions Based on method of differences.

 a-37 Min., b-35 Min.
08 Miscellaneous Series  1 Hrs
09 Miscellaneous Series  34 Minutes

 

Trigonometry

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,
Values of Trigonometry Ratios at θ = π÷8, θ = π÷24

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-
(1) Cosine product series,
(2) (A) Cosine summation series (B) Sine summation series
Questions, Trigonometric Equations,
General solutions on coordinate axes, General solution of sinθ = sin α, cosθ = cos α, tanθ = tan α.and

sin2 θ = sin2 α
cos2 θ = cos2 α
tan2 θ = tan2 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

 

Solutions of triangles

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.

 

Binomial theorem

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.

 

Straight lines

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.

Circle

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.

Conic sections

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) 𝓁 (LR) = 2 (HM of 𝓁1 & 𝓁2), where 𝓁1 = PS, 𝓁2 = 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 𝓁(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.

Permutations and combinations

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.

Complex number

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.

Basic Mathematics

Logarithem

Quadratic equation

Sequence & progression

Binomial Theorm

Permutations and Combinations

Trignometric Ratio and Identities

Trignometric Equation and Inequalities

SOT and POT Solution and Properties of Triangle

Straight Line circle

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