Complete PCM Class XII
Subject PCM Medium ENGLISH
Faculty NV Sir,VKP Sir,SSI Sir,AS Sir Status AVAILABLE
Category COMPLETE COURSE Lecture
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Solution & colligative properties

Lecture# Description Duration
01 Introduction
    Different concentration terms interconversion, colligative properties, van’t hoff factor calculation, osmotic pressure.
33 Minutes
02 Osmosis , Osmotic pressure (different cases) 47 Minutes
03 Numericals on osmotic pressure 46 Minutes
04 Vapour pressure, relative lowering of vapour pressure, 41 Minutes
05 Numericals on RLVP, Ostwald walker method 40 Minutes
06 Elevation in boiling point, calculation of Kb (molal elevation boiling point constant) . Depression in freezing point, Calculation of Kf, 54 Minutes
07 Numericals on elevation in boiling point and depression in freezing point 36 Minutes
08 Thermodynamic explanation of 𝝙Tb & 𝝙Tf 6 Minutes
09 Raoult’s law when two volatile liquids are mixed 49 Minutes
10 Ideal and nonideal solution 34 Minutes
11 Azeotropes, mixture of two immiscible liquids, solubility of gas in liquid, henry law 58 Minutes

Solid state

Lecture# Description Duration
01 Types of solid, Crystal, Amorphous, unit cell, 2D, 3D, space,lattice. 42 Minutes
02 Primitive, body centred, face centered contribution of atoms in cubic unit cell. Packing fraction of square packing and hexagonal packing 47 Minutes
03 Coordination Number, packing fraction, density of solid.,Simple cubic, BCC, FCC, CCP 44 Minutes
04 Closed packing in 3D HCP packing,
    Linear void, Triangular void, Tetrahedral void, octahedral void, Cubical void Types of void in FCC
57 Minutes
05 Voids in FCC,Different radius ratio for ionic compounds. 47 Minutes
06 Calculation of nearest, next nearest and next to next nearest atoms in SC, BCC, FCC. 29 Minutes
07 Structure of NaCl type, Zns type, CaF2 type, Na2O type, CSCl type, Diamond 50 Minutes
08 Spinal structure, perovskite corundum structure, packing fraction of NaCl, Defect In crystal, Schottky, Frenkel, Interstitial 39 Minutes
09 Non stoichiometric defect, cation excess defect cation deficiency defect, Paramagnetic, Diamagnetic Ferromagnetic, Ferrimagnetic, Antiferromagnetic compound 31 Minutes


Chemical kinetics

Lecture# Description Duration
01 Fast reaction , slow reaction, moderate reaction, average rate of reaction, instantaneous rate of reaction, relation of rate of reaction between various reagents , order 57 Minutes
02 Order law, zero order reaction 35 Minutes
03 First order reaction 28 Minutes
04 Half life period for first order reaction 27 Minutes
05 Average life period for first order, generation time , first order bacterial growth, second order reaction 24 Minutes
06 nth order reaction, pseudo first order reaction 35 Minutes
07 Rate of reaction of two or reactant are taken, calculation of order by half life method 32 Minutes
08 Initial rate method , integrated rate law, ostwald isolation method to determine order 40 Minutes
09 Monitoring of first order reaction using pressure measurement 30 Minutes
10 Monitoring of first order reaction using titration and optical rotation 42 Minutes
11 Arrhenius transition state theory 29 Minutes
12 Arrhenius equation 32 Minutes
13 Effect of catalyst on rate constant, temperature coefficient for reaction 39 Minutes
14 Simple and complex reaction, molecularity, rate determining step RDS 29 Minutes
15 Determination of rate if RDS is given , steady state approximation,complexity in first order reaction, parallel first order reactions 48 Minutes
16 Reversible first order reaction 29 Minutes
17 Consecutive first order reaction 19 Minutes


Lecture# Description Duration
01 Cause of radioactivity belt of stability , comparison between alpha particle, beta particle and gamma rays 15 Minutes
02 Group displacement law soddy fajan rule,, k– electron capture ,first order decay. 28 Minutes
03 Radioactive decay 28 Minutes
04 Carbon dating, Age of rock using U & Pb,Age of rock using U & He 53 Minutes
05 Mass defect ,Binding energy, Binding energy per nucleon. Nuclear fission and fusion. 51 Minutes


Surface chemistry

Lecture# Description Duration
01 Adsorption, Adsorbate, Adsorbent, Thermodynamics of Adsorption, Adsorption v/s Absorption, Physical Adsorption. 47 Minutes
02 Freundlich & Langmuir isotherm, catalytic action of Homogeneous catalyst & Heterogeneous catalyst, Positive & negative catalyst, Homogeneous catalyst, Promoters, Catalytic poison, zeolites, enzyme catalyst, Types of solution, Dispersed phase & Dispersion medium. 48 Minutes
03 Types of colloidal solution, Lyophobic, Lyophilic, macromolecular, micromolecular, Associated colloid/ micelle, cleansing action of soap, Bredig’s arc method,Peptization 43 Minutes
04 Chemical method to prepare colloidal solution, Tyndall effect, Brownian motion, Electrophoresis, coagulation, protection of colloid. 53 Minutes
05 Gold number, Helmholtz double layer theory ,emulsion. 22 Minutes



Lecture# Description Duration
01 Electrochemical cell, Oxidation half cell, Reduction half cell, Galvanic cell 1 hr 05 Minutes
02 Salt bridge, Daniel cell net cell reaction reaction Quotient cell representation relation between DG & E properties of DG & E,nernst equation 44 Minutes
03 Spontaneity of reaction in cell, nernst equation cell at equilibrium, concentration cell. Hydrogen electrode and standard hydrogen electrode 44 Minutes
045 Metal + insoluble salt + soluble anion type half cell
            Eg.   Ag + AgCl + Cl–
1 hr 15 Minutes
05 Calomel electrode, electrochemical series, thermodynamics for electrochemical cell, 𝝙G, 𝝙H, 𝝙S 59 Minutes
06 Electrolysis & electrolytic cell, electrolysis of nacl, nabr, H2SO4,H2O, first law of electrolysis Faraday law 1 hr 11 Minutes
07 Examples of first law of faraday, second law of faraday 51 Minutes
08 Primary cell ,leclanche cell, secondary cell, lead storage battery , Ni-Cd cell , H2-O2 fuel cell, electrolytic conduction 50 Minutes
09 Molar conductivity, equivalent conductivity , relation between molar cond. And equv. Cond., kohlrausch law, calculation of molar cond using wheatstone bridge , relation between molar cond. And concentration for weak electrolyte and strong electrolyte ,huckel onsager equation 54 Minutes
10 Ionic mobility, conductometric titration for strong acid V/s strong base , strong acid v/s weak base and other examples 51 Minutes



Lecture# Description Duration
01 Types of ore, Methods of metallurgy, crushing grinding, concentration, gravity separation, magnetic separation, froth floatation. 38 Minutes
02 Leaching, calcination, roasting, flux, slag, reduction with carbon, carbon monoxide, self reduction. Electrolytic reduction is fused / aqueous solution. 40 Minutes
03 Reduction with Al, Mg, H2, Thermal decomposition, metal displacement reduction, metallurgy of Aq & Au, Macarthur forrest cyanide method, copper extraction. 38 Minutes
04 Extraction of Pb, Zn, Hg, Sn, Fe, Al, bayer methode, Hall, serpeck, Hall-Heroult method. 42 Minutes
05 Extraction of Mg, Dow process, Extraction of sodium purification method Liquidation, Distillation Vapour phase refining, poling process, Mond process, Van Arkel method, Electrolytic refining. 46 Minutes

Parting with Cl2, concentrated H2So4, Parke process, Thermodynamic of metallurgy Ellingham diagram.


50 Minutes


Coordination compound

Lecture# Description Duration
01 Simple salt, mixed salt, double salt, coordination compound, central atom, ligand, coordination number, oxidation number :- 30 Minutes
02 Denticity, flexidentate, Ambidentate liquid 24 Minutes
03 Coordination polyhedron, Naming of central atom, cationic ligand, neutral ligand, anionic ligand 27 Minutes
04 Naming of anionic ligand , rules for naming of complex salt, formula of complex , naming of complex having bridging ligand 1 hr 02 Minutes
05 Name of complex containing bridging ligand, reaction with AgNO3, reaction with BaCl2 electrical conductivity 32 Minutes
06 Reaction with conc. H2SO4, Werner’s theory, Sidgwick EAN rule. 23 Minutes
07 Valence bond Theory (VBT) 40 Minutes
08 Crystal field theory for octahedral complex. 37 Minutes
09 Crystal field theory (octahedral complex Examples) 51 Minutes
10 Crystal field theory (octahedral complex Examples), CFT for square planar complex, CFT for tetrahedral complex, structural isomerism, ionisation, hydrate, ligand , linkage, coordination isomerism 1 hr 05 Minutes
11 Examples of tetrahedral complex, factors affecting crystal field splitting energy 54 Minutes
12 Stereoisomerism, geometrical & optical isomerism 57 Minutes
13 Optical isomerism in octahedral complex & factors affecting splitting 45 Minutes
14 Properties of coordination compound stability, magnetic nature, colour, d-d transition. 53 Minutes
15 Charge transfer in brown ring, sodium nitroprusside, back bonding in metal carbonyl, Delta bond, synergic bonding, bonded organometallic compound,ferrocene, zeise salt. 1 hr 01 Minute

Nitrogen family & Oxygen family group 15 & 16

Lecture# Description Duration
01 Physical properties of nitrogen family (atomic radius, Ionisation energy, Electronegativity, Oxidation state), Chemical properties (Hydride, Oxide, Halide) 46 Minutes
02 Compounds of Nitrogen,
    N2, NH3, N2O, NO
34 Minutes
03 Compounds of Nitrogen
    N2O3, N2O4, N2O5, HNO2, HNO3 allotropes of phosphorus (white, red, black)
31 Minutes
04 Compounds of phosphorus, PH3, P4O6, P4O10, PCl3, PCl5 30 Minutes
05 Physical properties of oxygen family (atomic radius, Ionisation energy, Electronegativity, Oxidation state), Chemical properties (Hydride, Oxide, Halide), dioxygen, types of oxide(acidic,basic,neutral,amphoteric,mixed oxide), ozone ,hydrogen peroxide 34 Minutes
06 Allotropes of sulphur, H2S, SO2, SO3, Hypo solution Na2S2O3 20 Minutes

Halogen family & noble gas family Group 17 & 18

Lecture# Description Duration
01 Properties of Halogen family members, Atomic radius,Ionisation,enthalpy,Electronegativity, Bond energy,Anomalous behaviour of fluorine 27 Minutes
02 Properties of F2, Cl2, Br2, I2 Haloger acid HCl, HBr, HI 28 Minutes
03 Properties of HF, CaOCl2, HOCl, HClO2, HClO3. Bleaching powder CaOCl2 32 Minutes
04 HClO4, Interhalogen Compounds & their Hydrolysis, Pseudo halide, Pseudo Halogen
Noble gas
22 Minutes
05 Properties (atomic radius, Mp, b.p. ionisation energy) of noble gas family
Reaction with xenon with F2 & H2, addition compound, Hydrolysis reaction
21 Minutes

d block Element

Lecture# Description Duration
01 Transition metal, general configuration atomic radius, ionization energy. 33 Minutes
02 Density, melting point, oxidation state, standard electrode potential, colour, magnetic properties, nature of oxide, interstitial compound, catalytic properties, alloy formation 33 Minutes
03 Potassium dichromate, Potassium permanganate ,AgBr photography. 39 Minutes


Qualitative analysis

Lecture# Description Duration
01 Preliminary test, Dry Heating test, Flame test, Borax bead test, Charcoal cavity test. Cobalt nitrate test. 35 Minutes
02 Group A anion, radial 25 Minutes
03 ,s2- 20 Minutes
04 starch / iodide test, Brown ring test, CH3 COO- 25 Minutes
05 ,Iodometry test 25 Minutes
06 Cl- , F- , Br- , I- 59 Minutes
07 Nitrate,oxalate, borate ion 36 Minutes
08 Group B anion Sulphate,phosphate,permanganate,chromate anion 26 Minutes
09 Cation (basic radical) Zero group- Ist group- Pb+2 15 Minutes
10 Ist group - Ag+ , Hg+2 29 Minutes
11 II A group - IIA & IIB IIA - Cu+2 , Bi+3 , Pb+2 , Cd+2 , Hg+2 40 Minutes
12 III group - Al+3 , Fe+3 , Cr+3 IV group - Mn+2 30 Minutes
13 V group - Ba+2 , Sr+2 , Ca+2 VI group - Mg+2 26 Minutes



Lecture# Description Duration
01 Carbocations C+, Hybridisation of carbocations , Stability of carbocations , Rearrangement of carbocations , Type of shifts , Migratory aptitude 36 Minutes
02 Migratory aptitude of aromatic group , Rearrangement in cyclic carbocations , Ring expansion (RE),  Ring contracting (RC) , Cyclopropyl methyl carbocations (CPM–C+), Stability order of carbocations , Some extra ordinary stable carbocations, CPM carbocation , Aromatic carbocations 42 Minutes
03 Rearrangement of carbocation,  Reaction mechanism , Solvents , Polar protic solvents (PPS),  Polar aprotic solvents (PAs) , Reagents , Nucleophiles, Nu,  Electrophilic E+ 35 Minutes
04 Electrophiles, E+,  Nucleophiles, Nu,  Nucleophilicity , Experimental order of Nu,  Strong Nu with weak basic character , Strong Nu with strong basic character,  Weak Nu with weak basic character , Solvation of Nu 47 Minutes
05 Leaving group (l.g.), Leaving group ability , Unimolecular nucleophilic substitution reaction of first order (for R–X) i.e SN1 of R–X , Kinetics of SN1, Stereo of SN1, PE- diagram of SN1, SN1 with rearrangement in C+, Rate of SN1 reaction 36 Minutes
06 SN1 or R–X,  Solvolysis reaction , Factors affecting the rate of SN1 reactions , SN1 of alcohol R–OH 50 Minutes
07 SN1 of R–OH, Lucas reaction , SN1 of ethers , Hydrolysis of ethers , SN2 reaction of (R–X), Kinetics of SN2 reaction , Stereochemistry of SN2 Rxn , PE-diagram of SN2 Rxn 43 Minutes
08 Walden's experiment , Walden Inversion , Factors affecting the rate of SN2 Rxn , Halogen exchange reaction , Finkelstien reaction , Swart's reaction , SN2 Rxn  of alcohol (R–OH), SNi reaction of alcohol with SOCl2 48 Minutes
09 SN2 of ether , Reaction of epoxides , Williamson's ether synthesis 29 Minutes
10 Intramolecular SN2 reactions , Neighbouring group participation (NGP) , Comparison between SN1 and SN2 , SN1 Vs SN2 41 Minutes
11 Elimination Reaction , E1 elimination (of R–X), Saytzeff's rule , Regioselectivity , E1 of Alcohols, Acid catalysed dehydroation of alcohol, Dienone- Phenol rearrangement ,  Pinacol - Pinacolone rearrangement , Semipinacol- Pinacolone rearrangement 51 Minutes
12 E2 Rxn of (R–X), Stereoselectivity and sterospecificity , Reagents of E–2 Reaction , Order of Rate of E–2, Major Hofmann Alkene 37 Minutes
13 Summary of SN1/ SN2/E1/E2, Stereo selectivity of E–2 reaction , E1CB reaction , Cases when Hofmann Alkene is the major product 40 Minutes
14 Tetraalkyl ammonium hydroxide , E–2 Rxn, Didehalogenation , Stereoselectivity , Isotope effect (KH/KD) 24 Minutes



Lecture# Description Duration
01 Organometallic compounds , Preparation of G.R.    12 Minutes
02 Preparation of GR, Solvents of GR, Reaction of GR, Acid-base reaction of GR, Zerewitinoff's active hydrogen determination 33 Minutes
03 Nucleophilic addition reaction of GR, SN2- Th reaction of GR 30 Minutes
04 Unstable GR, Mono GR is not possible with dihalide , Reaction of GR with CO2, Reaction of GR with O2, Reaction of GR with RCN, Digrignard reagent , Reactions of digrignard reagent 40 Minutes
05 Attack of GR on weak bond, 1,2-addtion & 1,4-additon , Reaction of GR with metal halides , REDUCTION , Definition of reduction , Table of reducing agents , Catalytic hydrogenation 42 Minutes
06 Catalylic hydrogenation , Stereoselectivity ,) Partial hydrogenation , Lindlar's catalyst , P-2 catalyst (Nickle Boride), Birch reduction 44 Minutes
07 Hydroboration Reduction (HBR), Transfer Hydrogenation, Clemmensen reduction , Wolf-Kishner reduction, Lithium aluminium hydride (LiAlH4) 54 Minutes
08 Sodiumboro hydride (NaBH4) (SBH), Triphenyltin hydride Ph3SnH (TPH), DiBAl-H- Diisobutyl Aluminium hydride , Red –P + HI, Mozingo reduction , MPV- reduction , Oppeneaus Oxidation  , Bauvealt-Blanc reduction , ALKANES, Free Radicals , Formation of free radicals , F.R. Catalyst/ Initiators / Promotors , F.R. Inhibitors/ Scavangers/Poisons , Stability of free radicals , Reactions of free radicals , Combination Reactions , Disproportionation reaction 53 Minutes
09 Reactions of Free radicals , Stability of free radicals , Preparation of Alkanes , Wurtz Reaction (WR), Wurtz-Fitting reaction , Fitting reaction , Frankland reaction , Kolbe's Electrolytic synthesis (KES), Corey-House Reaction 41 Minutes
10 Corey House reaction, Decarboxylation , Decarboxylation by soda lime , Decarboxylation by heating 40 Minutes
11 Properties of Alkanes , Chemical properties of Alkanes , Free Radical substitution reaction , PE-diagrams , Reactivity order , Conditions of halogenation 25 Minutes
12 reactivity and selectivity , Percentage yield , Quantum yield , Isomerisation reaction of alkanes , Aromatisation reaction of alkanes , Petroleum , Physical Properties of alkanes 39 Minutes



Lecture# Description Duration
01 Alkenes , Preparation of Alkene , Pyrolysis of ester , Pyrolysis of xanthates (Chaugave reaction ) , Cope reaction , Didehalogenations 37 Minutes
02 Chemical reactions of Alkenes , Electrophilic addition reaction (AE Rxn), Classical carbocation mechanism , Non-Classical carbocation mechanism , Markowni Koff's rule , Addition of H–X, Antimarkowni Koff's rule 52 Minutes
03 Addition of H2O on Alkenes , Acid-catalysed hydration of Alkenes , Oxymercuration- Demercuration reaction  (OM/DM), Hydroboration -oxidation (HBO), Alkoxymercuration Demercuration , Addition of X2 on Alkenes 47 Minutes
04 Addition of HOX on alkenes , Stereoselectivity , Order of rate of addition of X2 on alkene , Chemical reaction of Alkynes , Addition of H-X on alkynes , Addition of H2O on alkynes , Hydration of alkyne with dil H2SO4 and HgSO4, Hydroboration – Oxidation 48 Minutes
05 Addition of HOX on alkynes , Preparation of alkynes , Isomerisation  24 Minutes
06 Isomerisation mechanism , Reaction of terminal alkynes , Dienes , Conjugated diene , Addition NOCl on alkene , Allylic substitution , NBS- N-bromosuccinimide 35 Minutes
07 Reaction of NBS, MnO2- Oxidising agent , Carbenes , Sources of carbenes  , Types of carbenes 21 Minutes
08 Reaction of carbene , Reimmer-Tiemann reaction , Carbyl amine reaction , OXIDATION , definition of oxidation  , Oxidation of alkenes and alkynes , Ozonolysis of Alkenes and alkynes , Oxidation of Ketone , Perhydroxylation of Alkenes (Formation of diols), Baiyer reaction – Baeyer's reagent , Osmium tetraoxide (OsO4), Epoxidation by per acid 49 Minutes
09 Oxidation-strong oxidising agent , Potassium dichromate K2Cr2O7/H2SO4, Alkaline KMnO4/ OH-, H2CrO4 or CrO3 + H2O, Table of oxidising agents , Oxidation of alcohols , Mild oxidising agents , Oxidation of periodic acid HIO4, Oxidation of aldehydes , Oxidation with NBS, Tollen's reagent , Fehling's Reagent , Benedict's solution , Schiff's reagent 38 Minutes
10 Oxidation of seleniumdioxide SeO2, Side-Chain oxidation 13 Minutes



Lecture# Description Duration
01 Aromaticity , Benzenoids and Non-Benzenoids , NMR-definition of Aromaticity  , Anti Aromaticity , Polycyclic aromatic compound , Azulenes , Reaction of AgNO3 and Na-metal , (n)-Annulenes , Peripheral aromaticity 44 Minutes
02 Electrophilic aromatic substitution reaction , Halogenation of Benzene , Baltz-Schiemann reaction , Nitration of benzene , Kinetic Isotope effect , Sulphonation of benzene , Friedel-Craft reaction (F.C. Rxn), F.C. Alkylation 49 Minutes
03 Ring-Closure at C-1 and C–2, Dehydrogenation , Limitations of F.C. reaction , Friedel Craft Acylation , Ring closure , Directive influence or Directive effect , Table of activating and deactivating groups 44 Minutes
04 Ortho-para ratio , Direction effect on disubstituted benzene , Directive influence in monosubstituted benzene , Directive influence in naphthalene , Directive influence in diphenyl , Directive influence in Anthracene and phenanthrene, Directive influence in pyridine & pyrrole , SN2 Ar reaction , PHENOL, Preparation of phenol 37 Minutes
05 Preparation of phenol from acid hydrolysis of cumene , Chemical reaction of phenol , Halogenation of phenol , Protection of –OH group, Nitration of Phenol , Sulphonation of Phenol, Reimer-Tiemann Reaction , Reimer-Tiemann formylation , Reimer-Tiemann carboxylation , Comparison of Reimer-Tiemann and carbyl amine reactions , Kolbe-Schmidt reaction , Some medicinally important compounds , Aspirine, Salol, Oil of winter green  39 Minutes
06 Nitrosation of phenol , Use of phenol as nucleophile, ANILINE, Preparation of aniline from reduction of nitrobenzene , Selective reduction , Chemical reactions of aniline , Halogenation of Aniline , Nitration of Aniline, Sulphonation of Aniline 26 Minutes
07 Fries rearrangment reaction in Phenol , Claisen rearrangement , Diazotisation of Aniline , Reaction of Benzene diazonium chloride (BDC) , Sandmeyer reaction , Baltz-scheimann reaction , Experimental evidence of formation of phenyl cation , Amination – Deamination 43 Minutes
08 AMINES, Preparation of Amines , Hofmann Bromamide reaction , Hofmann methylation , Gabriel phthalimide reaction , Coupling reaction of BDC 32 Minutes
09 Test of Amines ,Isocyanide Test of 1º Amine , Test with nitrous acid HNO2, CYANIDES and ISOCYANIDES , Preparation of cyanides and isocyamide , Hydrolysis of cyanides and isocyanides , IPSO-Substitution 23 Minutes
10 Basic Strength, Definition of bases  , Scales of basic strength , Organic Nitrogenous bases 12 Minutes
11 Basic strength of Aliphatic amines , Basic strength of Aromatic amines , SH of H2O, SIR effect on Aromatic amines , Basic strength of pyridine and pyarole 43 Minutes
12 Amidine-basic strength , Guanidine- basic strength , Kb order , Proton sponges , Site of protonation , Feasibility of reaction 31 Minutes



Lecture# Description Duration
01 Preparation of aldehydes & Ketones , Dehydrogenation , Hydrolysis of gem. dihalide , From dry distillation of Col. salt of fatty acid , From acid chloride (Rossenmund's) , Formylation of benzene (Gattermann Koch Ald. Synthesis) , Chemical reaction of carbonyl compound , Nucleophilic addition reaction , Addition of H2O (Formation of hydrates) 41 Minutes
02 Addition of R–OH (Formation acetal/Ketal), Addition of G.R., Addition of HCN (Formation of cyanohydrin), Addition of NH3, Addition of Ammonia derivative 35 Minutes
03 Addition of NaHSO3 (Sodium bisulphite) , Backmann rearrrangment , Cyclic Ketone 29 Minutes
04 Condensation reaction , Aldol condensation reaction , Cross Aldol , Intramolecular Aldol reaction 40 Minutes
05 Perkin condensation reaction , Classen Ester condenstion , Cross-Claisen , Intramolecular claisen (Dieckmann's reaction ) , knoevenagel reaction 22 Minutes
06 Reformatsky reaction , Favorskii reaction , Cannizaro reaction 23 Minutes
07 Cross Aldol , Cross Cannizaro , Intramolecular cannizaro , Tischenko reaction , Alpha-Halogenation , Haloform reaction , Iodoform test 44 Minutes
08 Baeyer - Villiger Oxidation , Benzil - Benzilic acid Rearrangement , D-exchange reaction , Witting reaction , Benzoin condensation  33 Minutes



Lecture# Description Duration
01 Carboxylic acid preparation , Arndt-Eistert reaction (Homologation of acid), Chemical reactions of carboxylic acids , Hunsdiecker reaction 18 Minutes
02 Decarboxylication reaction , Decarboxylation of acids by soda lime (SL), Decarboxylation by heating , Hell-Volhard-Zelinsky (HVZ) reaction , Acid derivatives , Preparation of acid derivatives , SN2 Th reaction , Esters- preparation , Type-I mechanism of esterification, Type-II mechanism of esterification 44 Minutes
03 Examples of esterification, Hydrolysis of ester , Acid hydrolysis of ester and saponification , Acid amide , Hofmann Bromamide reaction , Curtius reaction , Schmidt reaction , Lossen reaction 28 Minutes



Lecture# Description Duration
01 Carbohydrates , definition , Classification of carbohydrates , Based on number of units , Based on water solubility , Based on reducing properties 18 Minutes
02 Monosaccharides - Aldoses and Ketoses, D/L-configuration (Relative configuration) , Glucose , Cyclic hemiacetal structure of glucose , ANOMERS , EPIMERS , Haworth structure of glucose- glucopyranose structure, Formation of methyl-O-glucoside , Mutarotation, FRUTOSE , cyclic hemiacetal structure of fructose , Haworth structure of fructose- Fructofuranose structure   47 Minutes
03 SUCROSE, Inversion of sugar , Glycosidic linkage , Maltose ,Lactose , Starch , Amylose and amylopectin , Cellulose , Reaction of carbohydrates , Osazone formation of glucose and fructose 45 Minutes
04 Amino acids , Types of Alpha-Amino acids (AA), Neutral Alpha-AA, Acidic Alpha-AA, Basic Alpha-AA, Zwitter ion , Iso-electric point (pI), Calculation of pI value 21 Minutes
05 Peptides , Dipeptides , Peptide link, Polypeptides , Protein , Examples of Amino acids 18 Minutes
06 Polymerisation , Classification of polymer , Based on source , Base on Intermolecular force of attraction , Elastromers , Fibres , Thermoplastics, Thermosettings , Polyethylene , Nylon-6, Nylon-6,6, Natural Rubber , Synthetic Rubber- Neoprene , Buna-S, Buna-N , Dacron , Low density polyethylene (LDPE) 33 Minutes
07 High density polyethylene (HDPE) , Polypropylene , Poly isobutylene , Poly vinyl chloride (PVC), Poly tetrafluoro ethylene (PTFEW Tefflon) , Poly acrylonitrile (PAN or orlon), Poly styrene , Poly methyl methanacrylate (PMMA or Lucite)  or (Plexiglas or prespex), Natural Rubber- Polyisoprene , Gutta-percha, Vinylidene chloride- Vinyl chloride polymer , Lexan-Poly carbonate , Glyptal , Bakelite (or phenol- formaldehyde Resin), Melamine- formaldehyde (Melmac) , Polyurethane 33 Minutes


Geometrical optics

Lecture# Description Duration
01 law of rectilinear propagation of light, Law of independence of light rays, Law of reversibility, Laws of reflections, types of reflection, regular  and  diffused reflection, Plane  mirror, definition of Object and Image, virtual and real Object/Image. Image formation by plane mirror, Important points about Image formation by plane mirror, motion of object and its Image 52 Minutes
02 Problems on motion of object and image in 3D, Rotation of Mirror and Incident ray  46 Minutes
03 Problems , Images formed by two mutually inclined mirrors, field of view-  50 Minutes
04 Problems, Angle of deviation due to reflection  16 Minutes
05 Curved mirrors, some definitions (terms) related with curved mirrors. Paraxial rays, focal plane.  42 Minutes
06 sign conventions,  Mirror formula, magnifications 28  Minutes
07 ray diagram  28 Minutes
08 problems, some examples, multiple reflections  34 Minutes
09 motion of object and image, lateral magnifications  46 Minutes
10 1/v versus 1/u graphs, U-V graphs, Newton’s mirror formula  59 Minutes
11 Refraction, Refractive index, Snell’s laws, some important points to remember, refraction through plane surface and parallel slabs.  46 Minutes
12 Image formation due to refraction through plane surface, actual depth and apparent depth, problems 41  Minutes
13 Lateral shift, Normal shift, combination of mirror and slabs 42  Minutes
14 critical angle, total internal reflection, circle of illuminance, deviation due to refraction through plane surface  40 Minutes
15 Prsim, Prism angle, angle of emergence, deviation by prism, condition for no emergence, angle of  deviation by prism in terms of angle of incidence and angle of emergence. Condition for minimum deviation, minimum deviation  41 Minutes
16 maximum deviation,thin prisms,  deviation by thin prism 23  Minutes
17 Cauchy’s equation, dispersion, mean deviation, angular dispersion, Dispersive power of Prism, combination of Prisms, Achromatic combination ,combination for direct vision  54 Minutes
18 Refraction through curved surface, formula relating “v” and “u”,  27 Minutes
19 Problems lateral and longitudinal magnification, motion of object and image.  27 Minutes
20 Thin lenses, classification of thin lenses, Lens maker’s formula and Lens formula-  35 Minutes
21 lateral and longitudinal magnification, Ray diagrams,  28 Minutes
22 sign convention, Image formation, Problems,  45 Minutes
23 problems , some important points to remember  28 Minutes
24 motion of Object and  image, , 1/v versus 1/u graphs, U-V graphs-  39 Minutes
25 power of lens, combination of lenses in contact. Combination of two lenses separated by distance “d”, combination of lenses and mirror in contact, focal  length when one face of a thin lens is silvered  56 Minutes
26 Displacement method to find the focal length of a lens,  15 Minutes



Lecture# Description Duration
01 Introduction to charge, properties of charge 43  Minutes
02 Coulombs law, permittivity, relative permittivity, principal of superposition 52 Minutes
03 Electric field and its strength due to a point charge , due to circular arc , due to circular ring 35 Minutes
04 Electric field due to circular disc, infinite layer of charge , due to large conducting and non conducting sheets 43 Minutes
05 Electric field due to straight conductor and related problems 40 Minutes
06 Electric field due to non conducting solid sphere , hollow sphere and related problems 43 Minutes
07 Electric field inside cavity and electrostatic pressure. 25 Minutes
08 Electric potential, Electric potential due to a point charge , due to circular arc , due to circular ring , due to circular disc 31 Minutes
09 Relation between electric field and electric potentials , Electric field due to Non conducting solid sphere and hollow sphere 48 Minutes
10 potential difference due to infinite layer of charge and infinitely long line charge, Equipotential surface 34 Minutes
11 Electric potential energy, potential energy of two point charge system , potential energy of point charge system, methods to find the potential energy of point charge system 42 Minutes
12 self energy of hollow sphere, self energy of solid sphere, energy density , Potential energy of interaction 41 Minutes
13 Problems on self energy and interaction energy ,  Electric line of forces (ELOF), properties of  ELOF 17 Minutes
14 Electric flux, solid angle and use of solid angle to find the electric flux 58 Minutes
15 Gauss theorem, uses of Gauss theorem to find electric field due to hollow sphere 28 Minutes
16 Electric field due to solid sphere/long line charge/solid cylindrical charged body/hollow cylindrical charged body by using gauss theorem 31 Minutes
17 Electric dipole, Electric dipole moment, Electric field due to dipole on axial point/equatorial line/at general point 32 Minutes
18 Electric potential due to dipole on axial point/equatorial line/at general point, Force and Torque experienced by a dipole in external uniform electric field, potential energy of dipole in external uniform electric field, force on dipole in non uniform electric field, force between two dipoles 52 Minutes
19 Conductor, Earthing of  a conductor , electrostatic shielding 28 Minutes
20 charge distribution on inner and outer surface of concentric conducting spheres, , when two charged conductors are connected by a conducting wire 39 Minutes
21 charge distribution on a conductor surfaces in the presence of external electric field 52 Minutes

Current Electricitty

Lecture# Description Duration
01 Current definition, Instantaneous current, Average current, current due to Circular and Translational motion of charge, Current through a conductor, Current density 33 Minutes
02 mechanism of current flow. Relaxation time. Mean Free Path, Drift velocity, Resistance, Resistivity, Conductivity, Ohm’s law, Relation b/w current density & Electric field 29 Minutes
03 Calculation of Resistance in different cases, , dependence of resistance on length & cross sectional area when wire is stretched, Effect of temperature on Resistance, Resistance in 2 D & 3 D current flow. 31 Minutes
04 Battery, EMF, some important points about electrical circuits, Potential difference across battery, short circuit, and maximum power dissipated by a battery 1 Hrs 04 Minutes
05 Kirchhoff’s junction law and voltage/loop law. Point potential method to solve the circuits. 37 Minutes
06 combination of resistances, series and parallel combinations, Wheat stone bridge, 39 Minutes
07 Method of symmetry, Infinite series of Resistances 38 Minutes
08 combination of batteries .series and parallel combination of batteries,mixed combinations, combination of ideal batteries. 40 Minutes
09 Electrical instruments, Galvanometer, sensitivity of Galvanometer, conversion of Galvanometer into Ammeter and Voltmeter. 45 Minutes
10 Problems on galvanometer, ammeter and voltmeter 28 Minutes
11 Potentiometer, Uses of Potentiometer to compare the EMF's of two batteries, to find the internal resistance and EMF of a battery, Meter bridge, zero error 51 Minutes
12 Post-office box, rating of electrical instruments like bulb and heater 45 Minutes


Lecture# Description Duration
01 Introduction to capacitor, types of capacitor, parallel plate capacitor, spherical capacitor, cylindrical capacitor 43 Minutes
02 energy stored in a capacitor, work done by battery, heat loss, energy density,some problems.a conductor as a capacitor  41 Minutes
03 Combination of capacitors, series & parallel combination. wheat stone bridge 36 Minutes
04 Method of symmetry, Infinite series, point potential method, important problems Combination of two charged capacitors, some important problems 49 Minutes
05 Problems on combinations of charged capacitors, combinations of conductors- 42 Minutes
06 Charging of capacitor, variation of charge , voltage and current with time ,steady state, graphs 34 Minutes
07 Discharging of capacitor, time constant, variation in charge, voltage, current with time. Method to find the time constant of a circuit 39 Minutes
08 Circuits with capacitors and resistors, problems 31 Minutes
09 Dielectrics b/w plates of capacitor change in capacitance, charge and energy with dielectric. 29 Minutes
10 Some important problems related to dielectric 29 Minutes
11 Force on dielectric when battery remains connected, motion of dielectric. Force on dielectric when battery is removed, leakage current, dielectric strength 36 Minutes

Magnetic field

Lecture# Description Duration
01 Natural magnet ,pole strength , magnetic dipole moment 20 Minutes
02 magnetic field produced by Natural magnet at axial point , at Equatorial point and at general point, natural magnet in external magnetic field, Force ,Torque and potential energy of a magnet in external magnetic field. Force between two magnets- 37 Minutes
03 magnetic effect of  charge and current, some important points , Right hand screw rule 28 Minutes
04 Biot savort’s law , Right hand palm rule. Magnetic field produced by straight conductor 30 Minutes
05 Shape of magnetic lines of forces around a conductor, some important problems 43 Minutes
06 Circular arc and circular loop, solenoid and troid, magnetic field produced by solenoid and toroid 53 Minutes
07 Magnetic field produced by moving charge, Biot savort’s law for moving charge. Magnetic field due to circular motion of charge 26 Minutes
08 closed loop as a magnet . . magnetic dipole moment of closed loop, magnetic dipole moment of rotating charged bodies 26 Minutes
09 ampere’s law , application of ampere’s law to find the magnetic field due to straight long conductor and long cylindrical conductor 29 Minutes
10 problems on  magnetic field due to cylindrical cavity inside a cylindrical conductor 25 Minutes
11 Lorentz’s force, magnetic force on moving charge, motion of charge in external magnetic field , motion on circular path, important problems 47 Minutes
12 motion of charge  on helical path with constant pitch, motion on helical path with increasing pitch, 34 Minutes
13 Motion of charge  on cycloid path 27 Minutes
14 magnetic force on a current carrying conductor, magnetic force between two straight current carrying conductors 27 Minutes
15 Important problems ,magnetic force and torque on closed loop in external magnetic field 28 Minutes
16 Earth as a magnet, magnetic and geographical axis, magnetic and geographical meridian, angle of declination, angle of dip, horizontal & vertical component of earth’s magnetic field 29 Minutes

Electromagnetic induction (EMI)

Lecture# Description Duration
01 Magnetic flux, Faraday’s law, EMF induced, EMF induced due to change in area of loop, due to change in magnetic field ,due to rotation of loop, Lenz’s rule, examples 35 Minutes
02 Important Examples on Lenz’s rule 23 Minutes
03 Motional EMF, calculation of motional EMF, use of Motional EMF in circuit as battery, 32 Minutes
04 Important problems on motional EMF 38 Minutes
05 motional EMF due to rotation of conductor in external magnetic field. 24 Minutes
06 Induced electric field due to varying magnetic field, Calculation of Induced electric field in varying magnetic field in cylindrical region 36 Minutes
07 Self inductance, Inductor, potential difference across an inductor, Energy stored in an inductor, Inductor in a circuit 27 Minutes
08 Current Growth in an inductor, Time constant, current decay in an inductor 37 Minutes
09 Mutual induction, Mutual Inductance ,combination of inductors, series and parallel combination, 35 Minutes
10 LC oscillator and problems 28 Minutes


Alternating current (AC)

Lecture# Description Duration
01 AC/DC introduction, RMS and Average value of Alternating EMF and current, 35 Minutes
02 Important problems , AC circuits, circuit containing Resistor only, circuit containing capacitor  only, circuit containing Inductor  only 36 Minutes
03 Steps to find instantaneous current in AC circuit, reactance, Impendence,  phasor diagram, LCR series circuit, Quality factor 38 Minutes
04 LC circuit, RC circuit, LR circuit. Examples on AC series circuits 32 Minutes
05 Average  and instantaneous power , Apparent  power , power factor, wattles current Parallel AC circuits 52 Minutes
06 Problems on parallel circuits , Choke coil and Transformer 50 Minutes


Modern Physics

Lecture# Description Duration
01 Dual nature of Light, matter-waves, Debroglie’s formula for wavelength of  matter-waves. Graphes relating different parameters of Photon and matter waves, example 41 Minutes
02 Photometry, Energy of Photon, power incident and Intensity of light assuming particle nature of light, Impulse , Force & Pressure exerted by incident Photons 56 Minutes
03 Problems on photometry, motion of Photon under gravity 24 Minutes
04 Photo electric Effect, Work function of a metal, Threshold Energy/Threshold frequency/Threshold wavelength of an incident photon, Maximum kinetic energy of photo-electron, Graphs 37 Minutes
05 Photo-current, Saturation current, stopping potential, problems 50 Minutes
06 graphs plotted by Einstein and conclusions from those graphs, Failure of classical wave theory and  explanations given by quantum theory 23 Minutes
07 Atomic structure, Dalton’s law, Thomson’s Plums pudding theory, Rutherford’s Atomic model, Bohr’s  Atomic model and his 4 postulates 24 Minutes
08 Bohr model and  Derivations for Radius of orbit, Energy of Orbit, velocity of electron in an orbit, frequency of electron 31 Minutes
09 q/m ratio in an orbit,Ground and Excited states, Ionisation Energy and ionisation  potential, Excitation Energy and Excitation potential, Binding energy of electrons 28 Minutes
10 Hydrogen emission spectrum, Lymen series, Balmer series, Paschen series, Pfund series, series limits 38 Minutes
11 Recoil speed of atoms , problems on atomic structure ,Hydrogen absorption spectrum 28 Minutes
12 Atomic collisions, problems on atomic collisions 27 Minutes
13 Energy and radius of orbit when nucleus in motion.X-ray introduction, Production of X-ray, Types of  X-rays, continuous X rays. accelerating voltage 41 Minutes
14 Characteristics X-rays, cut-off wavelength, ,K-alpha/K-beta/L-alpha/L-beta characteristics X-rays and their wavelength/ frequency, Mosley’s law ,Graphs and problems on X-rays 35 Minutes

Nuclear Physics

Lecture# Description Duration
01 introduction to nucleus , Atomic number, mass number, Isotopes, Isobars, Isotones,   Radius of nucleus, density of nucleus, forces inside nucleus, strong nuclear force, stability   of nucleus & N/Z ratio. 27 Minutes
02 Mass defect, Binding Energy, calculation of Binding energy, examples, alpha-particles, Beta particles, positron, neutrino, anti-neutrino 34 Minutes

Alpha particle emission, kinetic energy of alpha- particle and Gama-particle, Beta

         particle Emission, positron emission, K-capture
35 Minutes
04 Radioactivity, Law of disintegration, statistical law , decay constant, Activity of a sample ,Half life of a sample, Average life of a sample, Carbon Dating 37 Minutes
05 disintegration with production, successive Disintegration, simultaneous disintegration 27 Minutes
06 Binding energy per nucleon, stability of a nucleus depending on B/A, fission reaction, Fusion reaction, 24 Minutes
07 Nuclear reactor, types of reactors, Moderator, coolant, control rods,   Critical mass 25 Minutes


Wave Optics

Lecture# Description Duration
01 Wave nature of light, Wave front, wave fronts for point source/line source/plane source. Hygiene’s principle for wave nature of light, Maxwell’s electromagnetic wave theory of light, 34 Minutes
02  Interference of light waves, constructive and destructive interference of light, sustainable interference 31 Minutes
03 Young’s double slit experiment (YDSE), path difference, positions of bright and dark fringes, Fringe width, Total no. of maximas and minimas formed on screen, 26 Minutes
04 Problems on YDSE , YDSE with white light 23 Minutes
05 optical path difference, shift in fringe pattern when slabs are placed in front of slits , YDSE with oblique incidence 31 Minutes
06 YDSE with slabs and oblique incidence ,YDSE when apparatus Immersed inside liquid and slabs are also placed in front of slits, when slits are placed horizontally instead of vertical.Interference through thin films, Lloyd’s mirror, Fresnel’s Biprism 39 Minutes


Error & Measurement

Lecture# Description Duration
01 significant figures ,Least count , maximum uncertainity , rules to find significant figures  

Significant figures in arithmetic operations like addition/substraction/multiplication/division , rules of rounding , Least count , maximum permissible error, problems

03 Maximum permissible error in a dependent quantity. Fractional error, percentage error , other types of errors like errors due to external causes , instrumental errors , personal error/ chance errors. Errors in averaging in experiment, absolute errors. Example.  

measurement by screw gauge , its Least count , measurement by vernier callipers , its Least count  , zero error , examples.




Lecture# Description Duration
01 Energy band , valence band , conduction band , P type semi conductor and N type semi conductor , Holes , Doping 31 Minutes
02 Motion of Holes , current in semiconductor , conductivity of semiconductor , mobility of holes and electrons 21 Minutes
03 PN junction, biasing of PN junction, forward biased PN junction and Reversed biased PN junction, diffusion current and drift current, break down of PN junction diode, Zener and avalanche breakdown. 35 Minutes
04 Uses of PN junction as Rectifier , half wave rectifier , full wave rectifier, transistor , PNP transistor and NPN transistor 36 Minutes
05 Biasing of a transistor , basic transistor circuits , how transistor works? Uses of transistor as amplifier 37 Minutes
06 Uses of transistor as switch and in LC oscillation circuit , digital electronics, number systems ,decimal and binary number system 37 Minutes
07 Logic gates, Boolean expressions , OR gate ,  AND gate , NOT gate and truth table. 28 Minutes
08 NOR gate , NAND gate and XOR gate 23 Minutes

Electromagnetic waves

Lecture# Description Duration
01 Ampere Maxwell law, displacement current, electromagnetic wave, its properties and equation of electromagnetic waves. Intensity of Electromagnetic waves. Different types of Electromagnetic waves , their wavelength , their production and Detection 27 Minutes
02 some important problems on Displacement current and Electromagnetic waves 20 Minutes



Lecture# Description Duration
01 communication system  , modes of communications ,Transducer and Transmitter , signal , Noise , Receiver , Attenuation , Amplification , Range , Band width , Modulation , Demodulation 27 Minutes
02 Band widths of signal , analog signal and digital signal , Band widths of transmission medium , Line communication , Radio communication , Optical communication , Types of wave propagation , Ground wave propagation , sky wave propagation , space wave propagation. Height of Tower and maximum distance covered by transmission 39 Minutes
03 modulation and its necessity ,minimum length of antenna , types of modulation.Amplitude modulation ,side band frequencies , modulation index , disadvantages of amplitude modulation 26 Minutes
04 Frequency modulation ,frequency deviation , carrier swing , modulation index , frequency spectrum , deviation ratio.percent modulation,  Pulse modulation ,pulse amplitude modulation (PAM) , pulse width modulation (PWM) , pulse position modulation (PPM),Demodulation , important problems 31 Minutes


Optical Instruments

Lecture# Description Duration
01 Human eye, near point, far point, least distance of distinct vision, Eye defects, Near sightedness (myopia) and its remedy, far sightedness (Hypermetropia) and its remedy. Problems 36 Minutes
02 Magnifying power of optical instruments, simple microscope (magnifying glass), Magnification when image is formed at Least distance of distinct vision and magnification when image is formed at infinity. Compound microscope (magnifying glass) ,magnification when image is formed at Least distance of distinct vision and magnification when image is formed at infinity. 42 Minutes

Telescope, astronomical telescope , its magnification when image is formed at Least distance of distinct vision and magnification when image is formed at infinity. -

Terrestrial telescope , magnification when image is formed at Least distance of distinct vision and magnification when image is formed at infinity.

 Galilean Telescope , magnification when image is formed at Least distance of distinct vision and magnification when image is formed at infinity
37 Minutes


Diffraction,Resolution & Polarization

Lecture# Description Duration
01 Diffraction ,single slit Diffraction, some important points about diffraction, difference between Interference and diffraction 51 Minutes
02 Resolution , Rayleigh criteria for resolution , Resolution by simple microscope , resolution by telescope 33 Minutes
03 Polarization , polarizer , analyzer , plane of polarization , polarization by reflection , angle of polarization ,Brewster’s law 25 Minutes


Magnetic materials

Lecture# Description Duration
01 magnetic materials , paramagnetic ,ferromagnetic , Domain  and Diamagnetic materials,intensity of magnetisation 27 Minutes
02 magnetic intensity , magnetic susceptibility , curies law , permeability of medium , hysteresis loop , retentivity ,coercive force ,hysteresis loop of iron and steel 37 Minutes


Sets and Relation

Lecture# Description Duration
01 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


Function and Inverse Trigonometric functions

Lecture# Description Duration
01 Definition of Function, Domain, Co-domain, Range, Mapping diagram, Graphical definition of function,
Rational (or Polynomial) Functions, Basic concepts, Rational inequalities, Steps to solve Rational-Inequalities.
 1 Hrs 14 Minutes
02 Solving Rational-inequalities (Non-repeated and repeated linear factors), How to take square and reciprocal
in case of inequalities.
 1 Hrs 04 Minutes
03 Modulus or Absolute value functions, Formulae of modulus-functions, Removal of Modulus-Functions, Graphs
of Modulus-Function, Modulus - Inequalities.
 1 Hrs 05 Minutes
04 Modulus-Equations and Inequalities.  55 Minutes
05 Irrational-functions, their domain and Range, Irrational Equations and inequalities, Determining domain of
irrational functions.
 1 hrs 03 Minutes
06 Irrational-Inequalities, Exponential & Logarithmic functions, their basic graphs, formulae.  1 hrs 05 Minutes
07 Formulae of Log functions, Log and exponential equations.  50 Minutes
08 Exponential and Log-inequalities when base is positive fractional or greater than one. 41 Minutes
09 (a) Log-inequalities when base is variable
(b) Log-inequalities when base is variable. Determining domain of Log-functions.

(a) 33 Minutes

(b) 48 Minutes

10 Greatest integer function (GIF), Basic graph, Formulae, Fractional Part function (FPF), Basic Graph, Formulae,
Signum-function, Basic graph. Questions.
 1 Hrs
11 (a,b) Questions on GIF, FPF and Signum functions.

(a) 39 Minutes

(b) 32 Minutes

12 (a) Trigonometric equations, General Solutions, Fundamental and General period of Basic T-Ratios,
(b) Questions the determining General and Particular solutions of T-Equations.

 (a) 1 Hr. 04 Minutes

(b) 32 Minutes.

13 (a) Questions, T-inequalities
(b) T-inequalities, Domain of T-Functions.

(a) 42 Minutes

(b) 35 Minutes

14 Inverse -trigonometric functions, condition for defining inverse of a function, classification of functions.
One-One (Injective) or many one functions, onto (Surjective) or into functions, bijective functions, Basic
Graphs of 6 inverse trigonometric - functions. Properties of ITF, Defining T (T–1(x)) or T–1 (T(x))
 1 Hrs 15 Minutes
15 Finding basic values of ITF, Domain of all types of functions.  1 hrs 06 Minutes
16 Domain of functions, Range of Functions
Method of determining Range of functions
M-1 Represent x or function of x in terms of y
M-2 Range by Using Monotonocity
 1 hrs 12 Minutes
17 M-3 Range of L / L, Q / L, L / Q,  Q / Q
M-4 Range of composite functions
 1Hrs 15 Minutes
18 Domain and Range of composite functions by defining them in one-interval or in different-different intervals.
(Using graphical method)
 1 Hrs 10 Minutes
19 Composite functions in different intervals.
Types of functions: (1) one-one (injective function)
Condition of injectivity by differentiation
(2) Onto (surjective) functions.
(3) Bijective functions. Inverse of a function
1 Hrs 17  Minutes
20 Number of 1-1 mappings, number of surjective (onto) mapping, questions on classification of functions.  1 hrs 04 Minutes
21 Questions on classification of functions and determining inverse of a function.  58 Minutes
22 Inequalities of Inverse trigonometric functions, graphs of y = T (T–1 (x)) = x (Non-Periodic Functions)
Graphs of y = T–1 (T(x)) (Periodic Functions)
 1 Hrs
23 Graphs of y = T–1 (T(x)), Questions,
Inter-conversion between various ITF’s.
 1 hrs 06 Minutes
24 Equal or Identical functions; Simplification of Miscellaneous ITF’s, Graphs.  1 hrs 11 Minutes
25 (a) Simplification of Miscellaneous ITF’s, Inverse-trigonometric functions of tan–1x ± tan–1y,
sin–1x ± sin–1y or cos–1x ± cos–1y, Questions
(b) Solving Inverse trigonometric equations.

(a) 51 Minutes

(b) 40 Minutes

26 Summation series of inverse-trigonometric functions, even or odd functions. 1 hrs 01  Minutes
27 Even or odd functions, periodic functions, fundamental or general periods of basic functions, properties
related to periodicity of functions.
1 Hrs 05 Minutes
28 Determining the fundamental period of functions, Range by period of function, functional equations to
determining period.
1 hrs 02  Minutes

(a) Functional-Equations.
(b) Questions on functional equations,

Symmetry of graphs.
Transformation of curves
(G1) Graph of y = f(x) + a
(G2) Graph of y = a f (x)
(G3) Graph of y = f (x + a)
(G4) Graph of y = f (ax)
(G5) Graph of y = –f(x)
(G6) Graph of y = f (–x)
(G7) Graph of y = | f(x)|
(G8) Graph of y = f(|x|)
(G9) Graph of y = f (–|x|)
(G10) Graph of |y| = f (x)

(a) 47 Minutes

(b) 54 Minutes 

30 Curve tracing using differential calculus.
Graph of maximum/minimum of functions between two or more than 2 functions.
1 Hrs 12 Minutes
31 Maximum-Minimum of a Curve, Miscellaneous graphs 54 Minutes

Limit, Continuity and Differentiability

Lecture# Description Duration
01 (a) Concept of Limit, Left Hand Side Limit (LHL) and Right Hand Side Limit (RHL) , Algebra on limits
(b) 7 Indeterminant forms, Steps to determining limit of a function when x→a, where to evaluate LHL & RHL separately (Doubtful points)

(a) 52 Minutes

(b) 36 Minutes

02 (a) Identify type of indeterminant forms, Method of solving Limits
(i) Factorisation (ii) Rationalization
(b) Questions on factorisation and Rationalisation
 (a-50 Min., b-25 Min.)
03 (a) M-3- Evaluate of limit when x →∞ or x→ –∞
(b) Questions based on method no.3
 (a-34 Min., b-33 Min.)
04 (a) M-4- Series expansion by Maclaurin’s Series, Series Expansion of Basic functions,
(b) Determining unknown parameters by series expansion.
M-5- Standard - Limits
(a-37 Min., b-27 Min.)
05 (a) Formulae of standard-limits, Questions based on standard limits.
(b) Standard limits using substitution method.
M-6- Limit in form of 1
 (a-47 Min., b-28 Min.)
06 (a) Questions on 1 form. L’Hospital’s rule (LH-Rule).
(b) Questions based on LH-Rule
 (a-36 Min., b-22 Min.)
07 (a) 0° or ∞° forms.
(b) Miscellaneous questions of limit
(a-41 Min., b-36 Min.)
08 Sandwitch Theorem ( or Squeeze - Play Theorem)
Continuity of a function y = f(x) at point x = a
Types of discontinuity:
(1) First kind of discontinuity (removable discontinuity) (In this case limit exist)
(A) Missing point discontinuity.
(B) Isolated point discontinuity.
(2) Non-Removable Discontinuity (Limit does not exist)
(A) Finite Non-removable discontinuity, Jump of discontinuity = | RHL – LHL |
(B) Infinite Non-removable discontinuity.
(C) Oscillating discontinuity.
Jump of discontinuity = | RHL – LHL |
 55 Minutes
09 (a, b) Continuity at a point,
Continuity in an interval, determining unknown parameters using concept of continuity at a point.
 (a-32 Min., b-18 Min.)
10 (a, b) Differentiability of a function at a point, Equation of tangent at a point,
Questions to check continuity and differentiability at a point
 (a-45 Min., b-20 Min.)
11 (a) Determining unknown parameters using concepts of continuity and differentiability at a point.
Continuity and differentiability of higher order derivatives.
(b) Questions based on LH rule and differentiation.
 (a-38 Min., b-30 Min.)
12 (a, b) Differentiability in an interval, questions based to check continuity and differentiability in an interval.  (a-29 Min., b-27 Min.)
13 (a) Graphical method to check differentiability,
Differentiability of maximum-minimum of two or more than 2 functions.
(b) Graphical method to check differentiability
 (a-32 Min., b-30 Min.)
14 (a) Determination of a function using differentiation
(b) Miscellaneous questions based on LCD.
(a-25 Min., b-24 Min.)
15 (a, b) Miscellaneous questions based on LCD.  (a-33 Min., b-34 Min.)



Lecture# Description Duration
01 (a) Some basic differentiation by using first principle (AB-Initio method), Rules of differentiation
(b) Formulae of differentiation, Properties of differentiation , Differentiation of Product of two functions,
Chain Rule, Differentiation of
u/v, Differentiation of composite functions,
Differentiation of Parametric functions, Differentiation of one function w.r.t. other functions.
 (a-30 Min., b-41.22 Min.)
02 Questions of Differentiation of functions.  55 Minutes
03 (a, b) Differentiation of Log-functions.  (a-29 Min., b-23 Min.)
04 (a) Derivative of inverse - functions.
(b) Derivative of inverse - functions by substitution method.
(a-16 Min., b-38 Min.)
05 (a) Derivative of Inverse - Functions by substitution method
(b) Derivative of Inverse - Functions and derivative of higher order Inverse functions.
(c) Questions based on differentiation of ITFs, Parametric differentiation
(a-25 Min., b-33 Min., c-25 Min.)
06 (a,b) Parametric Differentiation, Differentiation of Implicit functions.  (a-37 Min., b-21 Min.)
07 (a) Derivative of functions represented by infinite series, Differentiation of determinants.
(b) Higher order derivatives.
 (a-28 Min., b-25 Min.)
08 (a,b) Higher order derivatives.  (a-24 Min., b-25 Min.)


Application of Derivatives

Lecture# Description Duration
01 (a) Brief Revision of Straight Line and Tangent-Normal:
Equation of tangent and Normal to the curve y = f (x) at a point, Length of tangent,
Length of subtangent, Length of normal, Length of subnormal, Tangent to the curve at (0, 0)
(b) Questions based on concept of tangent and normal when point lies on the curve.
(a-27 Min., b-42 Min.)
02 (a) Questions based on tangent and normal when curve given in parametric form.
(b) Tangent and normal from an external point.
(a-26 Min., b-34 Min.)
03 (a) Questions based on tangents and normals from an external point.
(b) Tangent on the curve - intersecting the curve again.
(a-35 Min., b-23 Min.)
04 (a) Common-tangents.
(b) Angle of intersection of two curves; shortest -distance between 2 non-intersecting curves.
(a-36 Min., b-39 Min.)
05 (a) Rate of change
(b) Approximate value of a number, Monotonocity of a function, strictly increasing (SI),
Strictly decreasing (SD), Monotonically increasing (MI), Monotonically decreasing (MD) functions,
Monotonocity at a point and in an interval, Condition for monotonocity for differentiable functions,
Monotonocity of discontinuous functions.
(a-26 Min., b-46 Min.)
06 (a, b) Questions on monotonicity of function at a point or in an interval. (a-35 Min., b-39 Min.)
07 (a) Questions of Monotonocity.
(b) Proving inequalities by using monotonocity.
(a-35 Min., b-32 Min.)
08 (a) Concavity, Convexity and point of inflexion (POI) of curve.
(b) Curve tracing by using concept of differential calculus.
(a-30 Min., b-29 Min.)
09 (a, b) Rolle’s theorem, Langrange’s Mean Value theorem (LMVT) (a-30 Min., b-35 Min.)
10 (a, b, c) Maxima and minima at a point, local maxima and local minima and absolute maxima and absolute
minima. Range of a function in an interval. Using concept of maxima and minima.
(a-28 Min., b-20 Min., c-29 Min.)
11 (a, b) Questions. (a-28 Min., b-28 Min.)
12 (a) Questions of Maxima and Minima based on location of roots.
Theory of equations using maxima and minima.
(b) Questions.
(c) Optimization of Geometrical problems by maxima and minima.
(a-33 Min., b-40 Min., c-55 Min.)
13 (a, b) Geometry Problems. (a-43 Min., b-41 Min.)
14 Geometry Problems.  33 Minutes

Indefinite Integration

Lecture# Description Duration
01 (a) Concept of integration, Standard formulae
(b) Defining all standard formulae.
(a-34 Min., b-23 Min.)
02 (a, b) Basic integration directly formulae based. (a-39 Min., b-39 Min.)
03 (a) Substitution method; Formulae of some standard substitution.
(b) Questions based on substitution method.
(a-27 Min., b-33 Min.)
04 (a) Integral in the form of : ∫sinm x cosn x dx ; ∫ tanm x secn x dx
(b) Integral in the form of : ∫ xm(a + bxn )dx , Questions on substitution method.
(a-40 Min., b-31 Min.)
05 (a) Questions on substitution method in irrational functions.
(b) Questions on substitution method.
(a-34 Min., b-38 Min.)
06 (a) Integration by parts.
(b) Integration by parts, Using
(A) ∫ex (f(x) + f '(x))dx = f(x)ex + C   OR   (B) ∫(f(x) + xf '(x))dx = xf(x) + C
(a-35 Min., b-36 Min.)
07 (a) Questions based on integration by parts.
(b) Questions based on integration by parts, Integration of Rational function - by partial fraction method-
(i) When non-repeated linear factors in denominator
(ii) Repeated linear factors in denominator
(iii) Quadratic factors in denominator (D<0)
(a-29 Min., b-38 Min.)

(a) Questions on partial fraction method
Integration in the form of : ∫ dx ÷ ax2 + bx + c

Integration in the form of : ∫ (px+q)dx ÷ ax2+bx+c

(b) Integration in the form of : ∫ (x2 ± a2)dx ÷ x4+kx2+a4 or ∫ dx ÷ x4+kx2+a4

Integration in the form of : (a) ∫ dx ÷ x(xn + 1) (b) ∫ dx ÷ xn (1+xn)1/n (c) ∫ dx ÷ x2(xn+1)n-1/n

(a-44 Min., b-32 Min.)

(a) Integration of Irrational Functions
Integration in the form of : ∫ dx ÷ √ax2+bx+c OR ∫ √ax2+bx+c dx

Integration in the form of : ∫ (px+q)dx ÷ √ax2+bx+c OR ∫(px+q) √ax2+bx+c dx

(b) Integration in the form of :

(A) ∫ dx ÷ (px+q)√ax+b       (B)  ∫ dx ÷ (px2+qx+r)√ax+b

(C) ∫ dx ÷ (px+q)√ax2+bx+c (D)  ∫ dx ÷ (px2+qx+r)√ax2+bx+c

(c) Questions based on Integration of Irrational functions.
Integration in the form of : ∫ dx ÷ a + b sin2 x OR ∫ dx ÷ a + b cos2 x OR ∫ dx ÷ a cos2 x + b sin2 x OR ∫ dx ÷ a + b cos2 x + c sin2 x OR ∫ dx ÷ (a sin x + b cos x)2 OR ∫ f(tan x)dx ÷ a sin x + b sin x cos x + c cos2 x

(a-35 Min., b-25 Min.)

(a) Integration in the form of : ∫ dx ÷ a + bsin x OR ∫ dx ÷ a + bcos x

∫ dx ÷ asinx ± bcos x OR ∫ dx ÷ a sinx ± b cos x + c OR ∫ (p sin x + qcos x + r) ÷ (a cos x + b sin x + c) * dx

Integration in the form of :

∫ (a sin x + b) dx ÷ (a+b sin x)2 OR ∫ (a cos x+b) dx ÷ (a+b cos x)2

Integration in the form of ∫(sinx + cos x)f(sin2x)dx

(b) Integration in the form of :

∫ f(eax )dx OR ∫ (aex + be-x ) ÷ (pex + qe-x )*dx , Reduction Formulae.

(a-42 Min., b-38 Min.)
11 (a, b) Miscellaneous Questions (a-25 Min., b-38 Min.)
12 (a, b) Miscellaneous Questions (a-33 Min., b-29 Min.)


Definite Integration

Lecture# Description Duration

(a, b) Introduction of definite integral (DI), Geometrical interpretation of definite integral,
                         b              a
Property No. 1:  ∫ f(x)dx =- ∫ f(x)dx
                         a              b


                         b             b
Property No. 2:  ∫ f(x)dx = ∫ f(t)dt , Questions.
                         a             a

(a-49 Min., b-35 Min.)

(a, b) Questions based on P1, P2 and Concepts of indefinite integration.

(a-38 Min., b-33 Min.)

                                                    b             c          b
(a, b) Questions, property no. 3:  ∫ f(x)dx =  ∫ f(x)dx+∫ f(x)dx where a < c < b
                                                    a             b          c

(a-33 Min., b-38 Min.)

                                                                                           b             b
  Questions based on P-3, Property no. 4(King-Property): ∫ f(x)dx =  ∫ f(a+b-x)dx,
                                                                                           a             a

                                       a             a
Modified property no. 4 : ∫ f(x)dx =  ∫ f(a-x)dx
                                       0             0

Questions based on P4.

(a-44 Min., b-40 Min.)

(a, b) Questions based on P4,

Questions based on P5, P6.

(a-41 Min., b-33 Min.)

(a, b) Property No. 7 (Based on periodicity of function) :


 nT            T
 ∫ f(x)dx = n ∫ f(x)dx (where T = Period of function y = f(x))
 0              0

Walle’s formulae, Leibnitz theorem, Modified Leibnitz theorem.

(a-37 Min., b-52 Min.)
07 (a) Questions based on Leibnitz theorem.
(b) Definite Integrals as the limit of a sum (AB-initio method).
(a-27 Min., b-47 Min.)
08 Questions based on integral as Limit of a sum. (a-35 Min.)

Area Under the Curve

Lecture# Description Duration
01 (a,b) Quadrature, How to evaluate area under the curve with x-axis or with y-axis, area bounded by the
two intersecting curves, area bounded by the curves in different-2 conditions.
(a-37 Min., b-17 Min.)
02 (a, b, c) Questions based on area under the curves. (a-28 Min., b-24 Min., c-29 Min.)
03 (a, b) Questions, Questions based on determining parameters. (a-36 Min., b-29 Min.)
04 (a, b) Questions based on determining the parameters, area under the curves using inequalities. (a-36 Min., b-39 Min.)
05 (a, b) Area under the curves using functional inequalities, area bounded with f(x) and its inverse f–1 (x).
Miscellaneous Questions.
(a-30 Min., b-30 Min.)


Differential equation

Lecture# Description Duration
01 (a, b, c) Introduction of DE, Ordinary Differential Equation (ODE) and Partial Differential Equations (PDE),
Order and degree of DE, about constants, arbitrary constants and essential arbitrary constants,
Formation of differential equations, Methods of solving differential equations.
General solutions and particular solutions of differential equations.
Method no.1 : Variable separable form, in the form of dy÷dx= f(x).g(y).
(a-47 Min., b-18 Min., c-22 Min.)
02 (a, b) Method no. 2: (a) Reduces to variable separable form, i.e. in the form of dy÷dx = f(ax+by+c).
(b) Substitution method: in x2 + y2 = r2 , put x = r cos θ, y = r sin θ,
and in x2 – y2 = r2 , put x = r sec θ, y = r tan θ,
Method no. 3: Solution of Homogeneous differential equations, in the form of dy÷dx = f(y÷x) or dx÷dy=f(x÷y), Questions
(a-27 Min., b-34 Min.)
03 (a, b, c) Questions on method no. 3,
Method No. 4 :
Reduces to Homogeneous Differential equation, i.e. in the form of dy÷dx=ax+by+c÷Ax+By+k , Questions
Method no. 5 : Exact (direct) differential equations. Questions based on method no. 5.
(a-25 Min., b-34 Min., c-23 Min.)
04 (a, b) Method no. 6 : Linear differential equation, i.e. in the form of dy÷dx+Py=Q OR dx÷dy+Px=Q Method No.7 : Reduces to linear differential equations (Bernoulli’s equations) (a-40 Min., b-33 Min.)
05 (a, b, c) Geometrical applications of differential equations,
Tangent and normal to the curve y = f(x) at point (x, y), length of tangent,
Length of subtangent, Length of Normal, Length of subnormal, Radius-vector,
Higher Degree & order of differential equations, orthogonal trajectory (OT) of curves,
Clairaut’s differential equations.
(a-29 Min., b-35 Min., c-32 Min.)


Matrices and Determinants

Lecture# Description Duration

Definition of Matrix A = [ai j ]m x n
Its order, basic questions of formation of a matrix and based on its order.
Types of Matrices:
1. Row Matrix
2. Column Matrix
3. Null Matrix
4. Square Matrix : (a) Diagonal elements (b) Trace of square matrix and its properties
5. Diagonal Matrix: (a) Scalar Matrix (b) Identity or unit matrix and its properties.
6. Upper triangular matrix
7. Lower triangular matrix

# Algebra of matrices
(1) Comparable matrices
(2) Equal matrices
(3) Multiplication of scalar to a Matrix
(4) Addition and subtraction of matrices
(5) Multiplication of 2 matrices and properties of matrix multiplication

1:19 Hrs.
02 Questions based on types of matrices and Algebra of Matrices.
Questions based on Matrix - multiplication, transpose of matrix, properties of transpose.
(a-32 Min., b-42 Min.)

Questions based on Transpose and multiplication, some special types of square matrices :
(1) Symmetric matrix
(2) Skew - symmetric matrix
Properties of symmetric and skew symmetric matrices.
(3) Orthogonal matrix
(4) Nilpotent matrix
(5) Idempotent matrix
(6) Involutary matrix


1 Hr. 15 Min.
04 Questions (1), (2) and (3)
Solutions of questions No. (1), (2) and (3)
Question based on square matrices.
 54 Min.
05 Introduction of determinants,
Expansion of 2x2 and 3x3 order determinants,
Properties of determinants.
1 Hr. 35 Min.
06 (a) Questions on determinants
(b) Questions on determinants, product of 2 determinants, questions based on product of determinants.
(a-58 Min., b-45 Min.)
07 Questions on product of 2 determinants,
Differentiation and integration of determinants,
Summation of determinants,
System of Non-Homogenous Linear equations in 3 variables,
Cramer’s rule.
1 Hr. 2 Min.
08 System of linear equations in 2-variables,
Consistency and Inconsistency of linear equations,
Homogenous system of linear equations,
Trivial and Non-trivial solutions of Homogenous linear equations,
1 Hr. 1 Min.
09 (a) Adjoint of square matrix, inverse of a square matrix,
Properties of adjoint and Inverse of matrix,
Cancellation Law.
System of Linear equations by matrix method, questions.
(b) Questions, Elementary transformations along row (column),
Introduction of Rank of a matrix.
(c) Determination of Rank of a matrix.
(a-55 Min., b-39 Min., c-20 Min.)
10 (a) Consistency and Non-consistency of system of Linear equations by Rank method,
Solution of 3 equations in two variables.
(b) Matrices polynomial, characteristic matrix,
Caley-Hamilton theorem.
Inverse of a non-singular matrix by elementary transformation (along Row / Column) (Board Topic)
(a-52 Min., b-37 Min.)

Vectors - 3D

Lecture# Description Duration
01 Introduction of vector, types of vectors:
(1) Null vectors
(2) Unit Vector
Law’s of addition/subtraction in a parallelogram.
(3) Position vector (PV)
(4) Equal vectors
(5) Parallel or collinear vectors
1 Hr. 13 Min.
02 (a) (6) Coplanar vectors
(7) Reciprocal vectors
Geometry on vectors
(1) Distance formula
(2) Section formula (Internal section division and External section Division)
(3) Centroid
(4) Incentre.
Dot product (scalar-product) of two vectors.
Geometrical interpretation, projection of vector.
Component of vector.
(b) Projection and component of vector along and perpendicular to other vector,
Properties of dot product,
(a-55 Min., b-39 Min.)
03 Cross product (Vector - product) of two vectors,
Geometrical - interpretation, properties of cross-product,
 (1 Hr. 2 Min.)
04 Direction cosines (DC’s) and direction -Ratios (DR’s) of a line segment, questions.  (1 Hr. 20 Min.)
05 Vector equation of a line (parametric & non parametric form), Symmetrical form of a line (3-D Form)
Point of intersection of 2 lines,
50 Minutes
06 Questions based on line.  38 Minutes
07 Questions, Plane, Vector equation of a plane passing through a point and whose direction alongn n ,
General equation of plane, equation of a plane passing through 3 points,
Intercept form of plane, Condition of coplanarity of 4 points, angle between 2 planes,
Equation of plane parallel to given plane, Distance between two parallel planes, Perpendicular distance, Foot
of perpendicular, Image of a point w.r.t. plane. Angle bisectors of two planes.
 57 Minutes
08 Condition of acute or obtuse angle bisectors, position of points w.r.t. plane or angle bisector containing a
points; Angle between two planes, condition of line perpendicular to plane and condition of a line parallel to
Questions based on line and plane.
(1 Hr. 3 Min.)
09 Questions based on line & plane.  57 Minutes
10 Family of planes passing through line of intersection of 2 planes, symmetrical form of line, unsymmetrical
form of line, reduction of unsymmetrical form of line into symmetrical form.
Questions, Condition of co-planarity of two lines.
Equation of plane containing 2 lines. Questions
 56 Minutes
11 Questions, skew-lines, shortest distance (SD) between 2 skew-lines, condition for lines to be intersecting,
distance between two parallel lines.
 49 Minutes
12 Angle bisectors of two lines, Acute or obtuse angle bisectors. Questions  46 Minutes
13 Scalar triple product (STP) of 3 vectors. Geometrical interpretation. Volume of parallelopiped. Properties of
STP. Vector-triple product of three vectors (VTP). Geometrical - Interpretation.
(1 Hr. 11 Min.)
14 Questions on STP and VTP, Tetrahedron, its centroid, volume of tetrahedron, angle between any 2 faces of
regular tetrahedron.
(1 Hr. 5 Min.)
15 (a,b) Circum-radius and inradius of regular tetrahedron. Questions, Reciprocal-system of vectors,
Linearly Independent and Linearly dependent vectors (LILD), Sphere, Types of sphere,
Section of Sphere intersected by a plane, Questions of sphere.
(a-47 Min., b-60 Min.)



Lecture# Description Duration
01 Some definitions : (1) Experiment (2) Sample - space (3) Event (E)
Types of Events:
(a) Happening or occurance of an event
(b) Compliment (Non-occurance) of event,
Definition of Probability : p(A) =
Favourable elements of event A / Total elements
(c) Simple events
(d) Compound or mixed events
(e) Exclusive: Events
(f) Exhaustive events
(g) Equally likely events
(h) Independent events or dependent events
Questions based on permutation and combination.
(a- 47 Min., b-28 Min., c-26 Min., d-41 Min.)
02 Algebra of events:
(1) Event A
(2) Complement of event A
(3) Events A & B both
(4) Atleast event A or B
(5) Event A but not event B
(6) Event B but not event A
(7) Exactly one event out of 2 events
(8) None of events A or B
(9) Event A or B but not both
(10) Atleast one of the events A, B, C
(11) Exactly one event out of 3 events
(12) Exactly 2 events out of 3 events
(13) None of events out of 3 events.
(14) Occurance of events A & B but not C.
Questions based on Algebra of events,
Conditional probability, Multiplication theorems for dependent or Independent events, Complement Law,
Questions on Conditional Probability.
(a-34 Min., b-35 Min., c-25 Min., d-24 Min.)
03 Questions based on Conditional probability,
Questions based on dependent or independent events,
Law’s of total probability.
(a-26 Min., b-29 Min., c-31 Min., d-39 Min.)
04 Baye’s theorem (Reverse theorem). (a-27 Min., b-40 Min., c-24 Min., d-4 Min.)
05 Discrete - Random variable,
Probability - Distribution, Mean & Variance of discrete - random variable X,
Variance, Standard derivation,
#Binomial - Distribution, Mean and Variance of Binomial Distribution,
Questions based on them.
(a-35 Min., b- 32 Min., c-26 Min.)



Inverse Trignometric Function




Method of Differentiation

Tangent & Normal


Maxima & Minima

Indefinite Integration

Definite Integration

Area Under The curve




Complex Number

Matrix & Determinants




differential Equation


Inverse Trigonometric functions




Method of Differentiation

Tangent and Normal


Maxima and Minima

Indefinite Integration

Definite Integration

Area under the Curve

Differential equations

Matrices and Determinants


3D Geometry

Complex Number




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