ProSyllabus Journal CBSE Class 12 Board Examination Complete Summary and Solutions for Supplementary Chemistry Material – NCERT Class XII Chemistry Part I Supplementary Resources – Additional Examples, Problems, and Explanations Detailed supplementary material for NCERT Class XII Chemistry Part I, providing additional solved examples, practice questions, explanations, and resources aligned with the main textbook chapters, designed to reinforce and enhance understanding of core chemistry concepts for class XII students.
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Chemistry Appendices - Ultimate Study Guide 2025
Elements, their Atomic Number and Molar Mass
Some Useful Conversion Factors
Standard potentials at 298 K in electrochemical order
Logarithms
Elements, their Atomic Number and Molar Mass
Overview & Key Concepts
Content : Alphabetical table of elements with symbols, atomic numbers, and molar masses (g/mol). Values in parentheses indicate the molar mass of the isotope with the longest known half-life for unstable elements.Importance : Essential for stoichiometry, calculating molecular weights, and understanding periodic trends. Use in mole calculations, empirical formulas, and reaction balancing.Applications : Lab weighing, formula mass determination. Real-world: Material science, pharmaceuticals. Debates: Periodic updates to atomic masses by IUPAC.
Detailed Table
Element Symbol Atomic Number Molar mass (g mol⁻¹)
Actinium Ac 89 227.03 Aluminium Al 13 26.98 Americium Am 95 (243) Antimony Sb 51 121.75 Argon Ar 18 39.95 Arsenic As 33 74.92 Astatine At 85 210 Barium Ba 56 137.34 Berkelium Bk 97 (247) Beryllium Be 4 9.01 Bismuth Bi 83 208.98 Bohrium Bh 107 (264) Boron B 5 10.81 Bromine Br 35 79.91 Cadmium Cd 48 112.40 Caesium Cs 55 132.91 Calcium Ca 20 40.08 Californium Cf 98 251.08 Carbon C 6 12.01 Cerium Ce 58 140.12 Chlorine Cl 17 35.45 Chromium Cr 24 52.00 Cobalt Co 27 58.93 Copper Cu 29 63.54 Curium Cm 96 247.07 Dubnium Db 105 (263) Dysprosium Dy 66 162.50 Einsteinium Es 99 (252) Erbium Er 68 167.26 Europium Eu 63 151.96 Fermium Fm 100 (257.10) Fluorine F 9 19.00 Francium Fr 87 (223) Gadolinium Gd 64 157.25 Gallium Ga 31 69.72 Germanium Ge 32 72.61 Gold Au 79 196.97 Hafnium Hf 72 178.49 Hassium Hs 108 (269) Helium He 2 4.00 Holmium Ho 67 164.93 Hydrogen H 1 1.0079 Indium In 49 114.82 Iodine I 53 126.90 Iridium Ir 77 192.2 Iron Fe 26 55.85 Krypton Kr 36 83.80 Lanthanum La 57 138.91 Lawrencium Lr 103 (262.1) Lead Pb 82 207.19 Lithium Li 3 6.94 Lutetium Lu 71 174.96 Magnesium Mg 12 24.31 Manganese Mn 25 54.94 Meitnerium Mt 109 (268) Mendelevium Md 101 258.10 Mercury Hg 80 200.59 Molybdenum Mo 42 95.94 Neodymium Nd 60 144.24 Neon Ne 10 20.18 Neptunium Np 93 (237.05) Nickel Ni 28 58.71 Niobium Nb 41 92.91 Nitrogen N 7 14.0067 Nobelium No 102 (259) Osmium Os 76 190.2 Oxygen O 8 16.00 Palladium Pd 46 106.4 Phosphorus P 15 30.97 Platinum Pt 78 195.09 Plutonium Pu 94 (244) Polonium Po 84 210 Potassium K 19 39.10 Praseodymium Pr 59 140.91 Promethium Pm 61 (145) Protactinium Pa 91 231.04 Radium Ra 88 (226) Radon Rn 86 (222) Rhenium Re 75 186.2 Rhodium Rh 45 102.91 Rubidium Rb 37 85.47 Ruthenium Ru 44 101.07 Rutherfordium Rf 104 (261) Samarium Sm 62 150.35 Scandium Sc 21 44.96 Seaborgium Sg 106 (266) Selenium Se 34 78.96 Silicon Si 14 28.08 Silver Ag 47 107.87 Sodium Na 11 22.99 Strontium Sr 38 87.62 Sulphur S 16 32.06 Tantalum Ta 73 180.95 Technetium Tc 43 (98.91) Tellurium Te 52 127.60 Terbium Tb 65 158.92 Thallium Tl 81 204.37 Thorium Th 90 232.04 Thulium Tm 69 168.93 Tin Sn 50 118.69 Titanium Ti 22 47.88 Tungsten W 74 183.85 Ununbium Uub 112 (277) Ununnilium Uun 110 (269) Unununium Uuu 111 (272) Uranium U 92 238.03 Vanadium V 23 50.94 Xenon Xe 54 131.30 Ytterbium Yb 70 173.04 Yttrium Y 39 88.91 Zinc Zn 30 65.37 Zirconium Zr 40 91.22
Conceptual Diagram: Alphabetical Element List
Not in periodic order; quick reference for atomic data. Use for calculations like moles = mass / molar mass.
Key Definitions & Terms
Atomic Number
Number of protons; defines element. Ex: C 6. Relevance: Element identity. Detailed: Defines position in periodic table.
Molar Mass
Mass 1 mol (g/mol). Ex: C 12.01. Relevance: Stoichiometry. Detailed: Average isotopes, parentheses longest half-life.
Half-Life
Time half decay. Ex: (243) Am. Relevance: Unstable isotopes. Detailed: Molar mass given for longest.
Atomic Mass Unit
1.6606×10^-24 g. Relevance: Atoms. Detailed: 1/12 C-12.
Tip: Group by appendix; examples for recall. Depth: Debates (e.g., cal vs J). Errors: Confuse characteristic sign. Interlinks: To main chapters (e.g., potentials to electrochem). Advanced: Log uses in pH. Real-Life: Conversions in cooking. Graphs: None major. Coherent: Evidence → Interpretation. For easy learning: Flashcard per term with value.
60+ Questions & Answers - Based on Appendix I
10 1 mark, 10 4 marks, 10 6 marks. Answers point-wise in black text.
Part A: 1 Mark Questions (10 Qs - Short)
1. Atomic number of Carbon?
6. What does (243) mean for Americium?
10. Atomic number Helium?
Part B: 4 Marks Questions (10 Qs - Medium, Exactly 5 Lines Each)
1. Explain parentheses in molar mass.
2. How to calculate molecular mass using table.
Part C: 6 Marks Questions (10 Qs - Long, Exactly 8 Lines Each)
1. Discuss importance of molar mass in Chemistry.
6 Marks Answer:
Molar mass is mass of 1 mol substance in g/mol.
Used to convert mass to moles.
Essential for stoichiometry ratios.
Ex: In reactions, balance using moles.
Average of isotopes for stable.
Parentheses for unstable isotopes.
Links to Avogadro number.
Applications in lab, industry.
Key Formulas & Tables
Key Formula: Moles = mass / molar mass
Element Symbol Atomic Number Molar mass (g mol⁻¹)
Derivations & Calculations
Molar Mass of Compound
Step 1: Identify formula.
Step 2: Lookup atomic masses.
Step 3: Multiply by coefficients.
Step 4: Sum.
Ex: NaCl = 22.99 + 35.45 = 58.44 g/mol.
Solved Examples & Problems
Example: Molar mass of CO2
12.01 + 2*16.00 = 44.01 g/mol.
Problem: Moles in 88 g CO2
88 / 44.01 ≈ 2 moles.
Activities & Applications
Activity: Calculate Molar Mass
Step 1: Choose compound.
Step 2: Use table.
Step 3: Sum.
Observation: Accurate for calculations.
Precaution: Use correct values.
Key Concepts
Atomic Number
Steps: Defines element. Ex: Trends. Pitfall: Confuse with mass number. Interlink: Periodic table.
Molar Mass
Steps: Average or isotope. Ex: Calculations. Pitfall: Forget parentheses. Interlink: Stoich.
Interactive Quiz (10 Q)
Interactive Quiz - Elements
10 MCQs; test your knowledge.
Start Quiz
Quick Revision Notes & Mnemonics
Alphabetical list.
Mnemonic: For common elements - He Li Be B C N O F Ne (Helicopters Lift Beautiful Balloons Carrying New Oxygen For New Explorers).
Key Terms & Formulas
Term Description Example Usage
Atomic Number Protons C 6 Identity Molar Mass g/mol C 12.01 Moles
Key Processes & Tables
Process: Finding Element Data
Step 1: Search name alphabetically.
Step 2: Read symbol, atomic no, molar mass.
Step 3: Note if parentheses for isotope.
Some Useful Conversion Factors
Overview & Key Concepts
Content : Common units for mass, weight, volume, energy, length, force, pressure, temperature. Notes on force, calorie, electron volt.Importance : Standardize measurements; SI vs common. Essential for lab, calculations.Applications : Unit conversion in problems. Real-world: Science, engineering.
Detailed List
Category Conversion
Mass and Weight 1 pound = 453.59 grams Mass and Weight 1 pound = 0.45359 kilogram Mass and Weight 1 kilogram = 1000 grams = 2.205 pounds Mass and Weight 1 gram = 10 decigrams = 100 centigrams = 1000 milligrams Mass and Weight 1 gram = 6.022 × 10^23 atomic mass units or u Mass and Weight 1 atomic mass unit = 1.6606 × 10–24 gram Mass and Weight 1 metric tonne = 1000 kilograms = 2205 pounds Volume 1 quart = 0.9463 litre Volume 1 litre = 1.056 quarts Volume 1 litre = 1 cubic decimetre = 1000 cubic centimetres = 0.001 cubic metre Volume 1 millilitre = 1 cubic centimetre = 0.001 litre = 1.056 × 10-3 quart Volume 1 cubic foot = 28.316 litres = 29.902 quarts = 7.475 gallons Energy 1 joule = 1 × 10^7 ergs Energy 1 thermochemical calorie = 4.184 joules = 4.184 × 10^7 ergs = 4.129 × 10–2 litre-atmospheres = 2.612 × 10^19 electron volts Energy 1 ergs = 1 × 10–7 joule = 2.3901 × 10–8 calorie Energy 1 electron volt = 1.6022 × 10–19 joule = 1.6022 × 10–12 erg = 96.487 kJ/mol Energy 1 litre-atmosphere = 24.217 calories = 101.32 joules = 1.0132 ×10^9 ergs Energy 1 British thermal unit = 1055.06 joules = 1.05506 ×10^10 ergs = 252.2 calories Length 1 inch = 2.54 centimetres (exactly) Length 1 mile = 5280 feet = 1.609 kilometres Length 1 yard = 36 inches = 0.9144 metre Length 1 metre = 100 centimetres = 39.37 inches = 3.281 feet = 1.094 yards Length 1 kilometre = 1000 metres = 1094 yards = 0.6215 mile Length 1 Angstrom = 1.0 × 10–8 centimetre = 0.10 nanometre = 1.0 × 10–10 metre = 3.937 × 10–9 inch Force and Pressure 1 atmosphere = 760 millimetres of mercury = 1.013 × 10^5 pascals = 14.70 pounds per square inch Force and Pressure 1 bar = 10^5 pascals Force and Pressure 1 torr = 1 millimetre of mercury Force and Pressure 1 pascal = 1 kg/ms^2 = 1 N/m^2 Temperature SI Base Unit: Kelvin (K) Temperature K = -273.15°C Temperature K = °C + 273.15 Temperature °F = 1.8(°C) + 32 Temperature °C = (°F - 32)/1.8
Conceptual Diagram: Unit Conversion Chain
From imperial to metric; use factors for accuracy.
Key Definitions & Terms
SI Unit
Standard international. Ex: kg mass. Relevance: Consistency. Detailed: Kelvin temp, Pascal pressure.
Conversion Factor
Ratio units. Ex: 1 inch=2.54 cm. Relevance: Change systems. Detailed: Mass, volume, energy, etc.
Thermochemical Calorie
Heat 1g water 14.5-15.5°C. Ex: 4.184 J. Relevance: Energy. Detailed: Note per particle units.
Pascal
Pressure unit. Ex: 1 Pa=1 N/m². Relevance: Force/area. Detailed: 1 atm=1.013×10^5 Pa.
Kelvin
Absolute temp. Ex: 0 K=-273.15°C. Relevance: Thermo. Detailed: Conversion formulas.
Electron Volt
Energy 1.602×10^-19 J. Relevance: Atomic. Detailed: 96.487 kJ/mol.
British Thermal Unit
1055.06 J. Relevance: Heat. Detailed: 252.2 cal.
Torr
1 mmHg. Relevance: Pressure. Detailed: Vacuum.
Bar
10^5 Pa. Relevance: Atmos. Detailed: Approx 1 atm.
Metric Tonne
1000 kg. Relevance: Large mass. Detailed: 2205 lb.
Atomic Mass Unit
1.6606×10^-24 g. Relevance: Atoms. Detailed: 1/12 C-12.
Litre-Atmosphere
101.32 J. Relevance: Gas work. Detailed: 24.217 cal.
Erg
Energy unit. Ex: 10^-7 J. Relevance: Small scale. Detailed: In conversions.
Angstrom
Length 10^-10 m. Ex: Atomic sizes. Relevance: Micro. Detailed: 0.1 nm.
Newton
Force kg m/s². Ex: Pressure def. Relevance: Mechanics. Detailed: 1 N=1 kg m/s².
60+ Questions & Answers - Based on Appendix II
10 1 mark, 10 4 marks, 10 6 marks. Answers point-wise in black text.
Part A: 1 Mark Questions (10 Qs - Short)
Part B: 4 Marks Questions (10 Qs - Medium, Exactly 5 Lines Each)
1. Explain temperature conversions.
2. What is thermochemical calorie?
Part C: 6 Marks Questions (10 Qs - Long, Exactly 8 Lines Each)
1. Discuss energy conversions.
Key Formulas & Tables
Key Formula: Use factors for conversion, e.g., mass_new = mass_old * factor.
Derivations & Calculations
Convert 1 lb to kg
Step 1: Factor 0.45359 kg/lb.
Step 2: 1 * 0.45359 = 0.45359 kg.
Solved Examples & Problems
Example: Convert 32°F to °C
(32 - 32)/1.8 = 0 °C.
Activities & Applications
Activity: Unit Conversion Practice
Step 1: Choose unit.
Step 2: Apply factor.
Step 3: Calculate.
Observation: Consistent.
Precaution: Correct direction.
Key Concepts
SI Units
Steps: Preferred. Ex: Kelvin. Pitfall: Mix units. Interlink: Lab.
Interactive Quiz (10 Q)
Interactive Quiz - Conversions
10 MCQs; test your knowledge.
Start Quiz
Quick Revision Notes & Mnemonics
SI units preferred.
Mnemonic: King Henry Died By Drinking Chocolate Milk (kilo, hecto, deca, base, deci, centi, milli).
Key Terms & Formulas
Term Description Example Usage
Calorie Heat unit 4.184 J Energy
Key Processes & Tables
Process: Temperature Conversion
Step 1: Choose formula.
Step 2: Plug values.
Step 3: Calculate.
Standard potentials at 298 K in electrochemical order
Overview & Key Concepts
Content : Reduction half-reactions with E°/V in decreasing order from +3.0 to -3.05.Importance : Determine spontaneity of reactions, cell potentials.Applications : Galvanic cells, electrolysis. Real-world: Batteries, corrosion.
Detailed Table
Reduction half-reaction E°/V
H4XeO6 + 2H+ + 2e– → XeO3 + 3H2O +3.0 F2 + 2e– → 2F– +2.87 O3 + 2H+ + 2e– → O2 + H2O +2.07 S2O8^2– + 2e– → 2SO4^2– +2.05 Ag2+ + e– → Ag+ +1.98 Co3+ + e– → Co2+ +1.81 H2O2 + 2H+ + 2e– → 2H2O +1.78 Au+ + e– → Au +1.69 Pb4+ + 2e– → Pb2+ +1.67 2HClO + 2H+ + 2e– → Cl2 + 2H2O +1.63 Ce4+ + e– → Ce3+ +1.61 2HBrO + 2H+ + 2e– → Br2 + 2H2O +1.60 MnO4– + 8H+ + 5e– → Mn2+ + 4H2O +1.51 Mn3+ + e– → Mn2+ +1.51 Au3+ + 3e– → Au +1.40 Cl2 + 2e– → 2Cl– +1.36 Cr2O7^2– + 14H+ + 6e– → 2Cr3+ + 7H2O +1.33 O3 + H2O + 2e– → O2 + 2OH– +1.24 O2 + 4H+ + 4e– → 2H2O +1.23 ClO4– + 2H+ +2e– → ClO3– + H2O +1.23 MnO2 + 4H+ + 2e– → Mn2+ + 2H2O +1.23 Pt2+ + 2e– → Pt +1.20 Br2 + 2e– → 2Br– +1.09 Pu4+ + e– → Pu3+ +0.97 NO3– + 4H+ + 3e– → NO + 2H2O +0.96 2Hg2+ + 2e– → Hg2^2+ +0.92 ClO– + H2O + 2e– → Cl– + 2OH– +0.89 Hg2+ + 2e– → Hg +0.86 NO3– + 2H+ + e– → NO2 + H2O +0.80 Ag+ + e– → Ag +0.80 Hg2^2+ +2e– → 2Hg +0.79 Fe3+ + e– → Fe2+ +0.77 BrO– + H2O + 2e– → Br– + 2OH– +0.76 Hg2SO4 +2e– → 2Hg + SO4^2– +0.62 MnO4^2– + 2H2O + 2e– → MnO2 + 4OH– +0.60 MnO4– + e– → MnO4^2– +0.56 I2 + 2e– → 2I– +0.54 I3– + 2e– → 3I– +0.53 Cu+ + e– → Cu +0.52 NiOOH + H2O + e– → Ni(OH)2 + OH– +0.49 Ag2CrO4 + 2e– → 2Ag + CrO4^2– +0.45 O2 + 2H2O + 4e– → 4OH– +0.40 ClO4– + H2O + 2e– → ClO3– + 2OH– +0.36 [Fe(CN)6]^3– + e– → [Fe(CN)6]^4– +0.36 Cu2+ + 2e– → Cu +0.34 Hg2Cl2 + 2e– → 2Hg + 2Cl– +0.27 AgCl + e– → Ag + Cl– +0.27 Bi3+ + 3e– → Bi +0.20 SO4^2– + 4H+ + 2e– → H2SO3 + H2O +0.17 Cu2+ + e– → Cu+ +0.16 Sn4+ + 2e– → Sn2+ +0.15 AgBr + e– → Ag + Br– +0.07 Ti4+ + e– → Ti3+ 0.00 2H+ + 2e– → H2 0.0 by definition Fe3+ + 3e– → Fe –0.04 O2 + H2O + 2e– → HO2– + OH– –0.08 Pb2+ + 2e– → Pb –0.13 In+ + e– → In –0.14 Sn2+ + 2e– → Sn –0.14 AgI + e– → Ag + I– –0.15 Ni2+ + 2e– → Ni –0.23 V3+ + e– → V2+ –0.26 Co2+ + 2e– → Co –0.28 In3+ + 3e– → In –0.34 Tl+ + e– → Tl –0.34 PbSO4 + 2e– → Pb + SO4^2– –0.36 Ti3+ + e– → Ti2+ –0.37 Cd2+ + 2e– → Cd –0.40 In2+ + e– → In+ –0.40 Cr3+ + e– → Cr2+ –0.41 Fe2+ + 2e– → Fe –0.44 In3+ + 2e– → In+ –0.44 S + 2e– → S2– –0.48 In3+ + e– → In2+ –0.49 U4+ + e– → U3+ –0.61 Cr3+ + 3e– → Cr –0.74 Zn2+ + 2e– → Zn –0.76 Cd(OH)2 + 2e– → Cd + 2OH– –0.81 2H2O + 2e– → H2 + 2OH– –0.83 Cr2+ + 2e– → Cr –0.91 Mn2+ + 2e– → Mn –1.18 V2+ + 2e– → V –1.19 Ti2+ + 2e– → Ti –1.63 Al3+ + 3e– → Al –1.66 U3+ + 3e– → U –1.79 Sc3+ + 3e– → Sc –2.09 Mg2+ + 2e– → Mg –2.36 Ce3+ + 3e– → Ce –2.48 La3+ + 3e– → La –2.52 Na+ + e– → Na –2.71 Ca2+ + 2e– → Ca –2.87 Sr2+ + 2e– → Sr –2.89 Ba2+ + 2e– → Ba –2.91 Ra2+ + 2e– → Ra –2.92 Cs+ + e– → Cs –2.92 Rb+ + e– → Rb –2.93 K+ +e– → K –2.93 Li+ + e– → Li –3.05
Conceptual Diagram: Electrochemical Series
Decreasing E° from strong oxidants to reductants.
Key Definitions & Terms
Standard Potential
E° reduction (V). Ex: F2 +2.87. Relevance: Redox strength. Detailed: At 298K, 1M, 1 atm.
Reduction Half-Reaction
Gain electrons. Ex: Cu2+ +2e- → Cu. Relevance: E° table. Detailed: Positive strong oxidant.
Electrochemical Order
Decreasing E°. Relevance: Table. Detailed: Oxidants top.
60+ Questions & Answers - Based on Appendix III
10 1 mark, 10 4 marks, 10 6 marks. Answers point-wise in black text.
Part A: 1 Mark Questions (10 Qs - Short)
3. Standard E° for H2 is?
Part B: 4 Marks Questions (10 Qs - Medium, Exactly 5 Lines Each)
1. What is electrochemical series?
Part C: 6 Marks Questions (10 Qs - Long, Exactly 8 Lines Each)
1. How to calculate cell potential.
6 Marks Answer:
Identify cathode (higher E°).
Anode lower E°.
E_cell = E_cath - E_anod.
Positive spontaneous.
Ex: Zn (-0.76) anode, Cu (+0.34) cathode.
E = 0.34 - (-0.76) = 1.10 V.
At 298K standard.
Use for battery design.
Key Formulas & Tables
Key Formula: E_cell = E°_reduction (cathode) - E°_reduction (anode)
Reduction half-reaction E°/V
Derivations & Calculations
Derivation: Spontaneity
ΔG = -nFE.
Positive E spontaneous.
Ex: For Zn/Cu.
Solved Examples & Problems
Example: Zn/Cu cell E°
1.10 V.
Activities & Applications
Activity: Predict Reaction
Step 1: Choose half-reactions.
Step 2: Compare E°.
Step 3: Determine direction.
Observation: Spontaneity.
Precaution: Standard conditions.
Key Concepts
Standard Potential
Steps: Table lookup. Ex: Redox. Pitfall: Sign error. Interlink: Electrochemistry.
Interactive Quiz (10 Q)
Quick Revision Notes & Mnemonics
Decreasing E° order.
Mnemonic: FONCl BrIS CH (for common halogens and others).
Key Terms & Formulas
Term Description Example Usage
E° Standard potential +2.87 V F2 Redox
Key Processes & Tables
Process: Cell E° Calc
Step 1: Cathode higher.
Step 2: Subtract.
Step 3: Positive check.
Logarithms
Overview & Key Concepts
Content : Logarithms for calculations, laws, base 10, characteristic, mantissa, tables, examples.Importance : Easy multiplication, division, powers. Used in pH, kinetics.Applications : Numerical problems in Chemistry. Real-world: Scientific calc.
Introduction
Sometimes, a numerical expression may involve multiplication, division or rational powers of large numbers. For such calculations, logarithms are very useful. They help us in making difficult calculations easy. In Chemistry, logarithm values are required in solving problems of chemical kinetics, thermodynamics, electrochemistry, etc. We shall first introduce this concept, and discuss the laws, which will have to be followed in working with logarithms, and then apply this technique to a number of problems to show how it makes difficult calculations simple.
Laws of Logarithms
First Law: log_a (mn) = log_a m + log_a n
Second Law: log_a (m/n) = log_a m - log_a n
Third Law: log_a (m^n) = n log_a m
Logarithms to Base 10
Because number 10 is the base of writing numbers, it is very convenient to use logarithms to the base 10. Some examples are: log10 10 = 1, log10 100 = 2, log10 0.01 = –2, etc.
Standard Form
n = m × 10^p, where 1 ≤ m < 10. log n = p + log m, p characteristic, log m mantissa.
Logarithms Table
N 0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9
10 0000 0043 0086 0128 0170 0212 0253 0294 0334 0374 4 8 12 17 21 25 29 33 37 11 0414 0453 0492 0531 0569 0607 0645 0682 0719 0755 4 7 11 15 18 22 26 29 33 50 6990 6998 7007 7016 7024 7033 7042 7050 7059 7067 1 2 3 3 4 5 6 7 8 51 7076 7084 7093 7101 7110 7118 7126 7135 7143 7152 1 2 3 3 4 5 6 7 8 52 7160 7168 7177 7185 7193 7202 7210 7218 7226 7235 1 2 2 3 4 5 6 7 7 99 9956 9961 9965 9969 9974 9978 9983 9987 9991 9996 0 1 1 2 2 3 3 3 4
Antilogarithms Table
N 0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9
.00 1000 1002 1005 1007 1009 1012 1014 1016 1019 1021 0 0 1 1 1 1 2 2 2 .01 1023 1026 1028 1030 1033 1035 1038 1040 1042 1045 0 0 1 1 1 1 2 2 2 .99 9772 9795 9817 9840 9863 9886 9908 9931 9954 9977 2 5 7 9 11 14 16 18 20
Conceptual Diagram: Log Laws
Multiply → Add logs; Division → Subtract.
Key Definitions & Terms
Logarithm
Exponent base. Ex: log10 100=2. Relevance: Simplify calculations. Detailed: Laws add/subtract/multiply.
Characteristic
Integer part log. Ex: log 25.2=1.401. Relevance: Standard form. Detailed: p in m×10^p.
Mantissa
Fractional part log. Ex: 0.401 above. Relevance: Table lookup. Detailed: Always 0 to 1.
Base 10 Log
Common log. Ex: log10 10=1. Relevance: Decimal convenient. Detailed: Powers 10 easy.
Standard Form
n=m×10^p, 1≤m<10. Ex: 25.2=2.52×10^1. Relevance: Log calculation. Detailed: Decimal shift.
Mean Difference
Table section logs. Ex: For fine adjustment. Relevance: Accuracy. Detailed: Columns 1-9.
Antilog
Inverse log. Relevance: From log to number. Detailed: Use table reverse.
Negative Log
Bar notation. Ex: log 0.005= -2.3010 = 3.6990 bar -3. Relevance: Small numbers.
60+ Questions & Answers - Based on Appendix IV
10 1 mark, 10 4 marks, 10 6 marks. Answers point-wise in black text.
Part A: 1 Mark Questions (10 Qs - Short)
5. Characteristic log 25.2?
10. Standard form for 0.005?
Part B: 4 Marks Questions (10 Qs - Medium, Exactly 5 Lines Each)
Part C: 6 Marks Questions (10 Qs - Long, Exactly 8 Lines Each)
1. Explain characteristic and mantissa.
6 Marks Answer:
log n = p + log m, p integer characteristic.
log m mantissa 0 to 1.
Standard form n = m ×10^p, 1≤m<10.
Ex: log 0.005 = -3 + 0.699 = 0.699 bar -3.
p from exponent.
Mantissa from table.
Negative logs bar notation.
Use for small/large numbers.
Key Formulas & Tables
Key Formula: log (mn) = log m + log n, etc.
Derivations & Calculations
Proof First Law
Step 1: a^x = m, a^y = n.
Step 2: mn = a^{x+y}.
Step 3: log_a (mn) = x+y.
Solved Examples & Problems
Example 1: 6.3 × 1.29
log x = log6.3 + log1.29 = 0.7993 + 0.1106 = 0.9099, x = antilog 0.9099 = 8.127.
Example 2: (1.23)^3 / (11.2 × 23.5)
From page 8, x = 0.005183.
Example 3: (71.24)^5 × 56^7 / (2.3)^21
From page 9, x = 2967.
Illustration 1: log x = 1.0712
x = 11.79.
Illustration 2: log10 x = 2.1352
x = 1366.
Illustration: Find (1.23)^3 / 11.2 x 23.5
x = 0.005183.
Illustration: Find 11.2^3 / (1.23)^5
Let x = 11.2^3 / (1.23)^5, log x = 3 log11.2 - 5 log1.23 = 3.1476 - 0.4495 = 2.6981, x = 498.9.
Illustration: Find sqrt[3]{(7.124)^2 / 56}
log x = (2/3) log7.124 - (1/3) log56 = 0.6018 - 0.5827 = 0.0191, x = 1.045.
Activities & Applications
Activity: Calculate pH
Step 1: pH = -log[H+].
Step 2: Use table for log.
Step 3: Negative.
Observation: Acid/base.
Precaution: Small numbers.
Key Concepts
Log Laws
Steps: Apply to simplify. Ex: Multi add. Pitfall: Base mismatch. Interlink: pH.
Interactive Quiz (10 Q)
Quick Revision Notes & Mnemonics
Laws: Product add, quotient subtract, power multiply.
Mnemonic: Product Add, Quotient Subtract (PAQS).
Key Terms & Formulas
Term Description Example Usage
Logarithm Exponent log10 100=2 Calc
Key Processes & Tables
Process: Find log using table
Step 1: Standard form.
Step 2: Characteristic.
Step 3: Mantissa row/col/diff.
Step 4: Add.
CBSE Class 12 kits Marks booster + cheatsheet: key concepts in 2 lines each, common traps 35 marks: Calculus, shared with Part II 10 marks: Algebra, Ch 3–4 Common traps that cost marks, listed 6 principal branches of inverse trig Every derivative rule with its condition Page 1 free about 8 min read , Full kit about 55 min read ₹159
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This chapter is part of the CBSE Class 12 Board Examination Board Examination Explore every chapter — summary, notes, extra questions & MCQ quizzes Preparing for CBSE Class 12 Board Examination? Students also sit JEE is set on the Class 11 and 12 Physics, Chemistry and Maths syllabus; students prepare for boards and JEE together.
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The Last Lesson
Start here
#2
Economics (Class 12) Practice Quiz | CBSE Class 12 Board Examination
#3
#4
Challenges of Nation Building
#5
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#7
Human Geography: Nature and Scope
#8
Bricks, Beads and Bones — The Harappan Civilisation
#9
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#11
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Inverse Trigonometric Functions
#18
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Journey to the End of the Earth
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#27
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#29
The Challenges of Cultural Diversity
#30
Patterns of Social Inequality and Exclusion
#31
Social Institutions: Continuity and Change
#32
The Demographic Structure of the Indian Society
#33
Introducing Indian Society
#34
#35
Security in the Contemporary World
#36
International Trade (India)
#37
Transport and Communication (India)
#38
Tertiary and Quaternary Activities
#39
#40
Kings, Farmers and Towns — Early States and Economies (c. 600 BCE-600 CE)
#41
Theory of Consumer Behaviour
#42
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#44
Nature and Significance of Management
#45
Dissolution of Partnership Firm
#46
Accounting for Partnership: Basic Concepts
#47
Three Dimensional Geometry
#48
Continuity and Differentiability
#49
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#51
Principles of Inheritance and Variation
#52
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#57
Accountancy (Class 12) Practice Quiz | CBSE Class 12 Board Examination
#58
Electrostatic Potential and Capacitance Fundamentals | CBSE Class 12 Board Examination
#59
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An Elementary School Classroom in a Slum
#61
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Social Influence and Group Processes
#63
Attitude and Social Cognition
#64
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Variations in Psychological Attributes
#68
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Mass Media and Communications
#70
Globalisation and Social Change
#71
Change and Development in Industrial Society
#72
Change and Development in Rural Society
#73
The Constitution and Social Change
#74
The Market as a Social Institution
#75
Recent Developments in Indian Politics
#76
The Crisis of Democratic Order
#77
Challenges to and Restoration of the Congress System
#78
India's External Relations
#79
Politics of Planned Development
#80
Era of One-party Dominance
#81
Environment and Natural Resources
#82
International Organisations
#83
#84
Contemporary Centres of Power
#85
Geographical Perspective on Selected Issues and Problems
#86
Planning and Sustainable Development in the Indian Context
#87
Mineral and Energy Resources
#88
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Land Resources and Agriculture
#90
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Population: Distribution, Density, Growth and Composition
#92
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The World Population: Distribution, Density and Growth
#95
Framing the Constitution — The Beginning of a New Era
#96
Mahatma Gandhi and the Nationalist Movement — Civil Disobedience and Beyond
#97
Rebels and the Raj — The Revolt of 1857 and its Representations
#98
Colonialism and the Countryside — Exploring Official Archives
#99
Peasants, Zamindars and the State — Agrarian Society and the Mughal Empire (c. sixteenth-seventeenth centuries)
#100
An Imperial Capital: Vijayanagara (c. fourteenth to sixteenth century)
#101
Bhakti-Sufi Traditions — Changes in Religious Beliefs and Devotional Texts (c. eighth to eighteenth century)
#102
Through the Eyes of Travellers — Perceptions of Society (c. tenth to seventeenth century)
#103
Thinkers, Beliefs and Buildings — Cultural Developments (c. 600 BCE-600 CE)
#104
Kinship, Caste and Class — Early Societies (c. 600 BCE-600 CE)
#105
Open Economy Macroeconomics
#106
Government Budget and the Economy
#107
Determination of Income and Employment
#108
National Income Accounting
#109
#110
The Theory of the Firm under Perfect Competition
#111
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#121
#122
Analysis of Financial Statements
#123
Financial Statements of a Company
#124
Issue and Redemption of Debentures
#125
Accounting for Share Capital
#126
Reconstitution of a Partnership Firm – Retirement/Death of a Partner
#127
Reconstitution of a Partnership Firm – Admission of a Partner
#128
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Application of Derivatives
#135
Biodiversity and its Conservation
#136
#137
Organisms and Populations
#138
Biotechnology and its Applications
#139
Biotechnology: Principles and Processes
#140
Microbes in Human Welfare
#141
#142
#143
Molecular Basis of Inheritance
#144
Sexual Reproduction in Flowering Plants
#145
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#147
Aldehydes, Ketones and Carboxylic Acids
#148
Alcohols, Phenols and Ethers
#149
Haloalkanes and Haloarenes
#150
#151
The d- and f-Block Elements
#152
#153
Semiconductor Electronics: Materials, Devices and Simple Circuits
#154
#155
#156
Dual Nature of Radiation and Matter
#157
#158
Ray Optics and Optical Instruments
#159
#160
#161
Electromagnetic Induction
#162
#163
Moving Charges and Magnetism
#164
Electrostatic Potential and Capacitance
#165
Electric Charges and Fields
#166
CBSE Class 12 — Genetics and Evolution
#167
CBSE Class 12 — Matrices and Determinants
#168
CBSE Class 12 — Solutions and Colligative Properties
#169
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CBSE Class 12 — Electrostatics and Electric Field
#171
Humanities Subjects Practice Quiz | CBSE Class 12 Board Examination
More on CBSE Class 12 Board Examination19 guides Complete Summary and Solutions for Database Concepts – NCERT Class XII Computer Science, Chapter 8 – File Systems, DBMS, Relational Models, Keys, SQL Introduction, Questions, Answers Complete Summary and Solutions for Consumer Education and Protection – NCERT Human Ecology and Family Sciences, Chapter 12 – Study Summary, Explanation, Questions, Answers Complete Summary and Solutions for Project Based Learning – NCERT Class XII Computer Science, Chapter 13 – Project Planning, Implementation, Presentation, Documentation, and Evaluation Complete Summary and Solutions for Querying and SQL Functions – NCERT Class XII Informatics Practices, Chapter 1 – Explanation, Questions, Answers अंतरा भाग 2 – कक्षा 12 के लिए हिंदी (ऐच्छिक) की पाठ्यपुस्तक story खंड – पाठ-16 अंतरा भाग 2 – कक्षा 12 के लिए हिंदी (ऐच्छिक) की पाठ्यपुस्तक काव्य खंड – तुलसीदास: (क) भरत-राम का प्रेम, (ख) पद अंतरा भाग 2 – कक्षा 12 के लिए हिंदी (ऐच्छिक) की पाठ्यपुस्तक story खंड – पाठ-17 अंतरा भाग 2 – कक्षा 12 के लिए हिंदी (ऐच्छिक) की पाठ्यपुस्तक काव्य खंड – मलिक मुहम्मद जायसी: बारहमासा अंतरा भाग 2 – कक्षा 12 के लिए हिंदी (ऐच्छिक) की पाठ्यपुस्तक story खंड – पाठ-15 अंतरा भाग 2 – कक्षा 12 के लिए हिंदी (ऐच्छिक) की पाठ्यपुस्तक काव्य खंड – विष्णु खरे: (क) सत्य, (ख) एक कम अंतरा भाग 2 – कक्षा 12 के लिए हिंदी (ऐच्छिक) की पाठ्यपुस्तक story खंड – पाठ-11 अंतरा भाग 2 – कक्षा 12 हिंदी (ऐच्छिक) काव्य खंड – जयशंकर प्रसाद: (क) देवसेना का गीत, (ख) कार्नेलिया का गीत – संपूर्ण सारांश, व्याख्या, प्रश्न और उत्तर अंतरा भाग 2 – कक्षा 12 के लिए हिंदी (ऐच्छिक) की पाठ्यपुस्तक काव्य खंड – विद्यापति: पद अंतरा भाग 2 – कक्षा 12 के लिए हिंदी (ऐच्छिक) पाठ्यपुस्तक story खंड – पाठ-12 अंतरा भाग 2 – कक्षा 12 के लिए हिंदी (ऐच्छिक) की पाठ्यपुस्तक काव्य खंड – सूर्यकांत त्रिपाठी ‘निराला’: (क) गीत गाने दो मुझे, (ख) सरोज-स्मृति अंतरा भाग 2 – कक्षा 12 के लिए हिंदी (ऐच्छिक) की पाठ्यपुस्तक story खंड – पाठ-10 अंतरा भाग 2 – कक्षा 12 के लिए हिंदी (ऐच्छिक) की पाठ्यपुस्तक काव्य खंड – कुकुआन: दोह अंतरा भाग 2 – कक्षा 12 के लिए हिंदी (ऐच्छिक) की पाठ्यपुस्तक story खंड – पाठ-14 अंतरा भाग 2 – कक्षा 12 के लिए हिंदी (ऐच्छिक) की पाठ्यपुस्तक काव्य खंड – केदारनाथ सिंह: (क) बनारस, (ख) दिशा Notebook backup + AI Save your notes. Revise with AI. Learn more → Share this article
