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[ IMPORTANT TABLES ]

MATHEMATICAL SYMBOLS

Description Symbol

Less than <

Less than Equal to

Equal to =

Not equal to

Plus (Addition) +

Minus (Subtraction) -

Plus or Minus

Minus or Plus

Times (Multiplication)

Multiplication (Computing) *

Division

Identically Equal to

Approximately Equal to

Greater than >

Greater than Equal to

Proportional to

Approaches to

Magnitude of x or

Absolute value of x

 

2   

 

Factorial n n

Common Logarithm

Natural Logarithm or

Napier’s Logarithm

Summation

Angle

Right Angle

Triangle

Square

Parallelogram || gm

Circle

Parallel to ||

Perpendicular to

Congruent to

Similar to

Implies

Implied by

If and only if (iff)

Belongs to

Does not Belong to

Number of element of Set A n(A)

Universal Set U or E

 

3   

 

Empty Set (Null Set)

Union of Sets

Intersection of Sets

Conjunction

MATHEMATICAL SYMBOLS FOR GREEK ALPHABETS

Alphabet Symbol Symbol

Alpha A

Beta B

Chi X

Delta

Epsilon E

Eta H

Gamma

Iota i

Kappa

Lambda

Mu

Nu

Omega

Phi

Pi

 

4   

 

Psi

Rho

Sigma

Tau

Theta

Xi

Zeta

ROMAN NUMERALS AND THEIR EQUIVALENT

The symbols used are

I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000

Roman Numerals Equivalent

I                                                1 

                                         II                                                2 

                                        III                                                3 

                                        IV                                                4 

                                         V                                                 5 

                                        VI                                                6 

                                       VII                                                7 

                                      VIII                                               8 

                                         IX                                               9 

                                          X                                              10 

 

5   

 

                                         XI                                              11 

                                        XII                                              12 

                                       XIII                                             13 

                                       XIV                                             14 

                                        XV                                              15 

                                       XVI                                              16 

                                      XVII                                              17 

                                     XVIII                                              18 

                                        XIX                                              19 

                                          XX                                                20 

                                        XXX                                               30 

                                           XL                                               40 

                                              L                                               50 

                                            LX                                               60 

                                          LXX                                               70 

                                        LXXX                                              80 

                                              XC                                             90 

                                                 C                                          100 

                                               CC                                          200 

                                             CCC                                          300 

                                               CD                                          400 

                                                 D                                           500 

 

6   

 

                                               DC                                           600 

                                             DCC                                           700 

                                           DCCC                                          800 

                                                CM                                         900 

                                                   M                                       1000  

                                                 MD                                      1500      

 

 

 

S.I. Units of Physical Quantities

Physical Unit Abbreviation

Quantity

Mass Kilogram kg

Length Metre m

Time Second s

Area Square Metre m2

Volume Cubic Metre m3

Acceleration Metre per second

per second m/s2 or ms-2

Force Newton N

Pressure Pascal Pa

Electric current Ampere A

Thermodynamic

 

7   

 

temperature Kelvin K

Luminous intensity Candela cd

Amount of substance Mole mol

Frequency Hertz Hz

Energy Joule J

Power Watt W

Electric charge Coulomb C

Electric potential

difference Volt V

Electric Resistance Ohm

Electric Conductance Siemens S

Electric capacitance Farad F

Magnetic flux Weber Wb

Inductance Henry H

Magnetic flux intensity Tesla T

Magnetic flux Lumen lm

Illumination Lux lx

Plane angle Radian rad

Solid angle Steradian sr

 

8   

 

Decimal Multiples and Submultiples used with SI units

Multiple Prefix Symbol

10 deca - da

100 hecto - h

1000 kilo - k

106 mega - M

109 giga - G

1012 tera - T

1015 peta - P

1018 exa - E

Submultiple Prefix Symbol

10-1 deci - d

 

9   

 

10-2 centi - c

10-3 milli - m

10-6 micro -

10-9 nano - n

10-12 pico - p

10-15 femto - f

10-18 atto - a

CONVERSION FORMULAE

(1) Length

To Convert From To Convert to Multiply By

Inches Centimetres 2.541

Centimetres Inches 0.3937

Yards Metres 0.9144

Metres Yards 1.0936

Miles Kilometres 1.6093

Kilometres Miles 0.6214

Metres Feet 3.281

Millimetres Inches 0.03937

 

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(2) Area

Square Inches Square Centimetres 6.4516

Square Centimetres Square Inches 0.1550

Square Feet Square Metres 0.093

Square Metres Square Feet 10.7639

Square Yards Square Metres 0.8361

Square Metres Square Yards 1.1960

Square Miles Square Kilometres 2.5899

Square Kilometres Square Miles 0.38602

Square Miles Acres 640

Acres Square Miles 0.001563

Square Metres Acres 0.0002471

Acres Square Metres 4046.86

Acres Hectares 0.4047

(3) Volume

Cubic Inches Cubic Centimetres 0.061

Cubic Centimetres Cubic Inches 16.387

Cubic Feet Cubic Metres 0.02832

Cubic Metres Cubic Feet 35.3144

Cubic Yards Cubic Metres 0.7646

Cubic Metres Cubic Yards 1.3081

Gallons Litres 4.5461

Litres Gallons 0.22

(4) Mass

 

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Pounds Kilograms 0.4536

Kilograms Pounds 2.2046

Pounds Tonnes 0.0004536

Tonnes Pounds 2204.623

Tons Kilogram 1016.047

Tolas Grams 11.6638

Grams Tolas 0.857

Ounces Grams 28.349

Grams Ounces 0.0353

Seers Kilograms 0.9331

Kilograms Seers 1.0717

Maunds Quintals 0.03732

Coefficients of Linear Expansion of Some Common Solid Substances

S.N. Substance Coefficient of Linear Expansion

per

1. Pyrex glass 3 × 10-6 2. Soft glass 9 × 10-6 3. Platinum 9 × 10-6 4. Concrete 11 × 10-6 5. Steel 11 × 10-6 6. Iron 12 × 10-6 7. Gold 14 × 10-6 8. Copper 17 × 10-6 9. Bronze 18 × 10-6 10. Brass 19 × 10-6

 

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11. Silver 19 × 10-6 12. Tin 21 × 10-6 13. Aluminium 26 × 10-6 14. Lead 29 × 10-6 15. Rubber 80 × 10-6

Coefficient of Cubical Expansion of Various Liquids

S.N. Liquid Coefficient of cubical expansion

per

1. Benzene 12.1 × 10-4 2. Alcohol 11.0 × 10-4 3. Turpentine 10.5 × 10-4 4. Water 3.7 × 10-4 5. Mercury 1.8 × 10-4

Specific Heats of Some Common Substances in S.I. Units

Substance Specific Heat J/Kg/

Gold 130

Mercury 138

Silver 234

Brass 372

Copper 390

Bronze 400

 

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Steel 447

Steam 460

Iron 480

Glass 677

Aluminium 899

Wood 1755

Kerosene 2090

Ice 2130

Alcohol 2590

Water 4180

VALUES OF FUNDAMENTAL CONSTANTS

Constant Symbol App. Value

Acceleration due to gravity g 9.8 ms-1

Atmospheric pressure at sea level atm 1.01 × 105 Nm-2

Absolute zero K -273.15

Atomic mass unit u 1.67 × 10-27 kg

= 931 MeV

 

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Avogadro’s number N 6.023 × 1023 /mol

Boltzman’s constant k 1.38 × 10-23 J/k

Bohr Magneton 9.27 × 10-24 Am2

Electronic charge e 1.6 × 10-19 C

Electronic radius re 2.8 × 10-15 m

Electron rest mass me 9.1 × 10-31 kg

Gravitational constant G 6.67 × 10-11 Mm2 kg-2

Neutron rest mass mn 1.675 × 10-27 kg

Permittivity of free space 8.85 × 10-12 C2N-1m-2

Permeability of free space 4 × 10-7 Tm A-1

(Wb A-1m-1)

Plank’s constant h 6.63 × 10-34 Js

Proton rest mass mp 1.673 × 10-27 kg

Rydberg constant RH 1.097 × 107m-1

Speed of light C 3 × 108 ms-1

Specific charge e/m 1.76 × 1011 C kg-1

Stefen’s constant 5.67 10-8 Wm-2 k-4

Universal gas constant R 8.31 J mol-1 K-1

Specific Gravity of Some Common Materials

Material Specific Gravity

Aluminium 2.70

Bakelite 1.35

Brass 8.5

Bronze (Phosphor) 8.9

 

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Copper 8.9

Diamond 3.5

Diesel Oil 0.9

Gold 19.3

Ice 0.91

Iron 7.8

Lead 11.4

Mica 2.8

Milk 1.03

Monel Metal 8.9

Nickel 9.0

Platinum 21.4

Sea water 1.03

Silver 10.5

Steel 7.8

Sugar 1.7

Tin 7.3

Water 1.0

Zinc 7.1

Latent Heat of Fusion of Some Common Materials

S.N. Material Latent Heat of

Fusion in × 105 J/kg

1. Aluminium 3.21 2. Brass 2.0 3. Copper 1.80

 

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4. Ice 3.34 5. Lead 0.25 6. Mercuty 0.12 7. Nickel 3.05 8. Nepthalene 1.46 9. Silver 0.92 10. Zinc 1.13

Latent Heat of Vaporization of Some Common Materials

S.N. Substance Latent Heat in × 105 J/kg

1. Aluminium 108.7 2. Ammonia 13.1 3. Alcohol 8.5 4. Chlorine 2.8 5. Ether 3.9 6. Gold 17.0 7. Hydrogen 4.5 8. Kerosene 2.5 9. Mercury 2.8 10. Nitrogen 2.0 11. Sulphuric acid 5.1 12. Sulpher dioxide 3.8 13. Water 22.5

Boiling Points of Some Common Substances

S.N. Substance Boiling Temperature

1. Air -194 2. Alcohol 80 3. Aluminium 2200

 

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4. Ammonia -33 5. Carbon Dioxide -43 6. Chlorine -34 7. Copper 2570 8. Ether 35 9. Gold 2970 10. Iron 3000 11. Kerosene 290 12. Lead 1750 13. Mercury 360 14. Nickel 2730 15. Platinum 4300 16. Silver 2170 17. Sulphuric acid 340 18. Tin 2270 19. Water 100 20. Zinc 900

Melting Points of Some Common Substances

S.N. Substance Melting Point

1. Aluminium 660 2. Brass 1070

 

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3. Bronze (Phos.) 1000 4. Copper 1080 5. Glass 1215 6. Gold 1060 7. Ice 0 8. Iron (Pure) 1540 9. Lead 325 10. Mercury -39 11. Nickel 1455 12. Rubber 120 13. Silver 960 14. Steel 1400 15. Sugar 160 16. Tin 230 17. Zinc 415 18. Nephthalene 80

Water Vapour in Saturated Air

S.N. Temperature of Mass of water required

air ( ) to saturate 1 m3 of air

1. 10 9.3 gm 2. 15 12.7 gm 3. 20 17.1 gm 4. 25 22.8 gm 5. 30 30.0 gm 6. 35 39.2 gm 7. 40 51.0 gm

Power Rating of Some Common Electrical Appliances

S.N. Appliance Useful Power Rating

 

19   

 

1. 4 ft Tube light 40 W 2. Bulb 60 W, 100 W 3. Radio Set 80 W 4. T.V. Set 120 W 5. Electric fan 100 W 6. Refrigerator 150 W 7. Electric Iron 750 W 8. Electric heater 1000 W 9. Immerson heater 1500 W

“Conductivity or Various materials”

(as percent copper)

Copper = 5,80,000 mho/cm.

S.N. Material Conductivity (g)

1. Aluminium 62 2. Brass 25 3. Bronze (Phos.) 38 4. Copper (annealed) 100 5. Gold 71 6. Lead 7.8 7. Mercury 1.8 8. Nickel 22 9. Silver 105 10. Tin 15

International Electrical Units

 

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(Conversion from absolute standard units)

S. No. Absolute International

1. Ampere 1.000165 amperes 2. Coulomb 1.000165 coulombs 3. Farad 1.000495 farads 4. Henry 0.999505 henry 5. Joule 0.999835 Joule 6. Ohm 0.999505 ohm 7. Volt 0.999670 volt 8. Watt 0.999835 watt

Hysterisis Coefficients for Various Materials

S. No. Material Coefficient

1. Iron Cast 0.013 2. Iron, Sheet 0.004 3. Steel, Cast 0.005 4. Steel, forged 0.020 5. Steel, low-carbon Sheet 0.003 6. Steel, 50% nickel 0.00015 7. Steel, Silicon 0.0009

 

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Dielectric Strength for Various Materials

S.No. Material Dielectric strength Kv/mm

1. Air 3.2 2. Bakelite 6.20 3. Glass 12-20 4. Marble 3 5. Mica 20-60 6. Paper 10-20 7. Rubber 16-30 8. Water 15 9. Wood 1-3

Dielectric constant (k) for Various Materials

S. No. Materials Dielectric constant

1. Air 1.00 2. Bakelite 5 3. Glass 5.4 – 9.1 4. Ice 86 5. Mica 2.5 – 6.6 6. Paper 1.7 – 3.8 7. Polythylene 2.4 8. Rubber, hard 1.9 – 7.4 9. Slate 6.6 – 7.4 10. Vaccum 1.000 11. Water, distilled 80 12. Wood 2.5 – 8.0

 

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Absolute Viscocity of Various Liquids

S. No. Liquid Viscosity (Absolute)[C.P.]

1. Acetic acid 1.15 2. Carbon tetrachloride 0.86 3. Castor oil 600 4. Ether 0.25 5. Glycerine 700 6. Kerosene 1.8 7. Mercury 1.6 8. Methyl alcohol 0.56 9. Phenol 8.0 10. Sodium chloride (20%) 2.0 11. Turpentine 3 12. Water 1.0

Viscosity (kinematic) of Various Liquids

S. No. Liquids Viscosity (kinematic)(cst)

1. Acetic acid 1.1 2. Benzene 0.70 3. Carbon tetrachloride 0.60 4. Ether 0.312 5. Ethyl alcohol 1.49 6. Gasoline 0.435 7. Kerosene 2.25 8. Mercury 0.117 9. Turpentine 1.6 10. Water 1.0

 

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Conduction Coefficient of Various Materials

S. No. Materials Conduction coefficient

(W/mk)

1. Air 0.025 2. Aluminium 205 3. Brass 108 4. Brick, Alumina 0.84 5. Charcoal 0.09 6. Coal 0.13 7. Copper 383 8. Cork 0.04 9. Fibre glass 0.21 10. Glass 0.87 11. Gold 292 12. Ice 2.2 13. Iron, Cast 45

Pure 67

14. Kerosene 0.15 15. Lead 34.15 16. Leather 0.18 17. Mercury 8.3 18. Mica 0.36 19. Monel 30 20. Nickel 90 21. Nylon 0.25 22. Phosphor bronze 108 23. Porcelain 1.8 24. Silver 418 25. Tin 65 26. Water 0.6

 

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Radiation Factor for Various Materials

S. No. Materials Radiation Factor

1. Aluminium, dull 0.22 2. Asbestos board 0.95 3. Black body 1.00 4. Brass, dull 0.25

polished 0.03

5. Copper, dull 0.25

polished 0.04

6. Glass 0.92 7. Gold, polished 0.02 8. Ice 0.97 9. Lead, dull 0.25

polished 0.07

10. Mercury 0.12 11. Monel 0.03 12. Peper 0.86 13. Platinum 0.04 14. Rubber 0.91 15. Silver, polished 0.025 16. Steel, Galvanized 0.25

polished 0.07

17. Tin, clean 0.08

polished 0.03

18. Water 0.96 19. Wood 0.87

 

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Heat Value of Various Materials

S. No. Materials Heat – Value

( × 103 kJ/kg)

1. Ammonia 22.5 2. Blast furnace gas 2.8 3. Carbon 33.7 4. Charcoal 30.2 5. Coal 32.5 6. Coke 30.2 7. Coke oven gas 44.1 8. Diesel oil 46.5 9. Ether 51.1 10. Gasoline 49.5 11. Kerosene 46 12. Natural gas 53 13. Producer gas 5.6 14. Sawdust 10.5 15. Wood, yellow pine 15.1

Elastic Limit (Compression) of Various Materials

S. No. Materials Elastic Limit (Kg/cm2)

(Compression)

1. Aluminium, cast 630 2. Brass 1750

 

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3. Bronze 1400 4. Copper 560 5. Iron, cast 1400 6. Steel, cold-rolled 4200

Elastic Limit (Tension) of Various Materials

S. No. Materials Elastic limit (Tension)

kg / cm2

1. Aluminium 450 2. Aluminium/bronze 2810 3. Aluminium, wire, Annealed 1000 4. Brass 410 5. Brass wire, anmealed 1100 6. Bronze 1400 7. Bronze / Phosphor 1680 8. Copler 410 9. Copper wire, Annealed 700 10. German Silver 1300 11. Gold, cast 280 12. Iron 2500 13. Stainless steel 2450 14. Steel 2500 15. Zinc, cast 280

Modulus of Elasticity (Compression) of Various Materials

S.No. Material Modulus of Elasticity

(Compression)

1. Aluminium 7 × 105 kg / cm2 2. Brass 9 × 105 kg / cm2 3. Bronze 8.4 × 105 kg / cm2 4. Copper 11 × 105 kg / cm2

 

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5. Iron 14 × 105 kg / cm2 6. Marble 5.6 × 105 kg / cm2 7. Steel 21 × 105 kg / cm2

Modulus of Elasticity (Tension) of Various Materials

S.No. Material Modulus of Elasticity

(Tension)

1. Aluminium 7.3 × 105 kg / cm2 2. Brass 9 × 105 kg / cm2 3. Bronze 8.5 × 105 kg / cm2 4. Copper 11 × 105 kg / cm2 5. Gold 4.2 × 105 kg / cm2 6. Iron 17 × 105 kg / cm2 7. Lead 0.7 × 105 kg / cm2 8. Platinum 1.8 × 105 kg / cm2 9. Stainless steel 20 × 105 kg / cm2 10. Zinc 9 × 105 kg / cm2

Various Planets and Their Distance from Sun

S.No. Planet Radius Distance from Sun

× 103 km × 106 km

1. Mercury 2.4 57.9 2. Venus 6.1 108.2 3. Earth 6.3 149.6 4. Mars 3.4 227.9 5. Jupiter 71.4 778.3

 

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6. Saturn 60.0 1427 7. Uranus 23.4 2870 8. Neptune 22.3 4594 9. Pluto 3.2 5900

Conversion of Temperature from Degree Celsius to Degree Fahrenheit and Degree Fahrenheit to Degree Celsius

To From To

-45.56 -50 -58

-40 -40 -40

-37.22 -35 -31

-34.44 -30 -22

-31.67 -25 -13

-28.89 -20 -4

-26.11 -15 5

-23.33 -10 14

-22.78 -9 15.8

-22.22 -8 17.6

-21.67 -7 19.4

-21.11 -6 21.2

-20.56 -5 23

 

29   

 

-20 -4 24.8

-19.44 -3 26.6

-18.89 -2 28.4

-18.33 -1 30.2

-17.78 0 32

-17.22 1 33.8

-16.67 2 35.6

-16.11 3 37.4

-15.56 4 39.2

-15 5 41

-14.44 6 42.8

-13.89 7 44.6

-13.33 8 46.4

-12.78 9 48.2

-12.22 10 50

-9.44 15 59

-6.67 20 68

-3.89 25 77

-1.11 30 86

1.67 35 95

4.44 40 104

7.22 45 113

10 50 122

12.78 55 131

 

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15.56 60 140

18.33 65 149

21.11 70 158

23.89 75 167

26.67 80 176

29.44 85 185

32.22 90 194

35 95 203

37.78 100 212

43.33 110 230

48.89 120 248

54.44 130 266

60 140 284

65.56 150 302

71.11 160 320

76.67 170 338

82.22 180 356

87.78 190 374

93.33 200 392

107.22 225 437

121.11 250 482

135 275 527

148.89 300 572

204.44 400 752

 

31   

 

260 500 932

315.56 600 1112

371.11 700 1292

426.67 800 1472

482.22 900 1652

537.78 1000 1832

593.33 1100 2012

648.89 1200 2192

704.44 1300 2372

760 1400 2552

815.56 1500 2732

871.11 1600 2912

926.67 1700 3092

982.22 1800 3272

1037.78 1900 3452

1093.33 2000 3632

1148.89 2100 3812

1204.44 2200 3992

1260 2300 4172

1315.56 2400 4352

1371.11 2500 4532

1426.67 2600 4712

1493.33 2720 4928

1537.78 2800 5072

 

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1604.44 2920 5288

1648.89 3000 5432