Free Railways Chapter-Wise Notes

Types of Motion

• Uniform Motion: Equal distance in equal time intervals (constant speed)
• Non-Uniform Motion: Unequal distance in equal time intervals (variable speed)
• Rectilinear Motion: Motion along a straight line
• Circular Motion: Motion along a circular path
• Oscillatory Motion: Back-and-forth motion (pendulum, strings)
• Distance: Total path length (scalar) | Displacement: Shortest path (vector)

Newton's Laws of Motion

• 1st Law (Law of Inertia): A body at rest stays at rest and a body in motion stays in uniform motion unless acted upon by an external force. Inertia ∝ Mass.
• 2nd Law: F = ma. Force equals mass times acceleration. SI unit of Force = Newton (N). 1 N = 1 kg·m/s²
• 3rd Law: Every action has an equal and opposite reaction. Forces act on different bodies.

Key Formulas — Equations of Motion

Equation	Formula	Meaning
First	v = u + at	Final velocity
Second	s = ut + ½at²	Displacement
Third	v² = u² + 2as	Velocity–displacement

Physical Quantities and Units

Quantity	Formula	SI Unit
Speed	Distance ÷ Time	m/s
Velocity	Displacement ÷ Time	m/s (vector)
Acceleration	(v − u) ÷ t	m/s²
Momentum	Mass × Velocity	kg·m/s
Force	Mass × Acceleration	Newton (N)
Work	Force × Displacement × cos θ	Joule (J)
Power	Work ÷ Time	Watt (W)
Energy	Capacity to do work	Joule (J)
Pressure	Force ÷ Area	Pascal (Pa)
Density	Mass ÷ Volume	kg/m³

Gravitational Force

• g = 9.8 m/s² ≈ 10 m/s² (use 10 in MCQs for speed)
• Weight = Mass × g (unit: Newton)
• g is maximum at poles, minimum at equator
• g decreases as we go up or deep inside earth
• Moon's g = 1/6th of Earth's g ≈ 1.6 m/s²

Energy

• Kinetic Energy (KE): KE = ½mv² — energy due to motion
• Potential Energy (PE): PE = mgh — energy due to position
• Law of Conservation of Energy: Energy can neither be created nor destroyed, only transformed
• 1 kWh = 3.6 × 10⁶ J (unit of electrical energy on bills)

Simple Machines

• Lever: Load × Load arm = Effort × Effort arm (1st, 2nd, 3rd class)
• Pulley: Fixed (changes direction), Movable (MA = 2), Compound
• Inclined Plane, Wheel & Axle, Screw, Wedge — all reduce effort
• Mechanical Advantage (MA) = Load ÷ Effort

Light

• Speed of light = 3 × 10⁸ m/s (in vacuum)
• Light travels in a straight line (rectilinear propagation)
• Reflection: Angle of incidence = Angle of reflection
• Refraction: Bending of light when it passes from one medium to another. Speed changes, frequency unchanged.
• Total Internal Reflection: When angle exceeds critical angle — used in optical fibres, diamonds
• VIBGYOR = Violet, Indigo, Blue, Green, Yellow, Orange, Red (spectrum of white light)
• Red light has longest wavelength; Violet has shortest wavelength
• Sky appears blue: Rayleigh scattering (blue scattered most)
• Sun appears red at sunrise/sunset: red scattered least, travels longer path

Mirrors and Lenses

Type	Nature	Use
Concave Mirror	Converging	Shaving mirror, headlights, solar cooker, ENT doctor
Convex Mirror	Diverging	Vehicle rear-view mirror (wider field)
Convex Lens	Converging	Magnifying glass, camera, eye (hypermetropia correction)
Concave Lens	Diverging	Myopia (near-sightedness) correction

Eye Defects

Defect	Problem	Corrective Lens
Myopia (short-sight)	Cannot see far objects	Concave lens
Hypermetropia (long-sight)	Cannot see near objects	Convex lens
Presbyopia	Old age, both defects	Bifocal lens
Astigmatism	Irregular eye curvature	Cylindrical lens

Sound

• Sound is a longitudinal mechanical wave — needs a medium to travel
• Speed: Solids > Liquids > Gases
• Speed of sound in air ≈ 343 m/s at 20°C; in water ≈ 1500 m/s; in steel ≈ 5000 m/s
• Frequency: Number of oscillations per second (Hz)
• Pitch: Perceived frequency — high pitch = high frequency
• Amplitude: Maximum displacement — determines loudness
• Infrasound: < 20 Hz (elephants, whales) | Ultrasound: > 20,000 Hz (bats, sonar)
• Echo: Reflected sound heard after at least 0.1 sec; minimum distance from wall = 17.2 m
• Reverberation: Persistence of sound due to multiple reflections
• Decibel (dB): Unit of loudness. Normal conversation ≈ 60 dB; threshold of pain ≈ 120 dB

Heat and Temperature

• Temperature: Degree of hotness/coldness | Heat: Form of energy (Joule)
• SI unit of temperature: Kelvin (K) | Practical unit: °C (Celsius)
• °C = (°F − 32) × 5/9 | K = °C + 273
• Absolute zero = 0 K = −273°C (lowest possible temperature)
• Conduction: Heat transfer through solids (molecule-to-molecule)
• Convection: Heat transfer through liquids/gases (mass movement)
• Radiation: Heat transfer without medium (electromagnetic waves)
• Latent heat: Heat absorbed/released during change of state (temperature remains constant)
• Specific heat of water = 4200 J/kg·K (highest — reason for moderate coastal climate)

Electric Current

• Current (I): Rate of flow of charge. I = Q/t | Unit: Ampere (A)
• Voltage/EMF (V): Potential difference | Unit: Volt (V)
• Resistance (R): Opposition to current flow | Unit: Ohm (Ω)
• Ohm's Law: V = IR (valid for constant temperature and physical state)
• Power (P): P = VI = I²R = V²/R | Unit: Watt (W)
• Energy consumed: E = P × t | Unit: Joule or kWh (1 kWh = 1 unit of electricity)

Series and Parallel Circuits

Property	Series	Parallel
Current	Same through all	Divides
Voltage	Divides	Same across all
Resistance	R = R₁+R₂+R₃	1/R = 1/R₁+1/R₂
Home wiring	Not used	Used (independent switching)

Conductors, Insulators, Semiconductors

• Conductors: Allow free flow of electrons — copper, silver, aluminium, gold
• Insulators: Resist electron flow — rubber, glass, wood, plastic
• Semiconductors: Conductivity between conductors and insulators — Silicon (Si), Germanium (Ge)
• Resistance increases with temperature in conductors; decreases in semiconductors

Magnetism

• Magnets have two poles: North and South. Like poles repel, unlike poles attract
• A freely suspended magnet aligns in North–South direction (compass principle)
• Earth is a giant magnet with geographic north = magnetic south
• Electromagnet: Magnet produced by electric current through a coil (temporary)
• Solenoid: Coil of wire acting as a bar magnet when current flows
• Faraday's Law: Changing magnetic flux induces EMF — basis of generators, transformers
• Transformer: Increases (step-up) or decreases (step-down) AC voltage
• SI unit of magnetic field: Tesla (T)

Household Appliances and their Working Principle

Appliance	Principle
Electric bulb (tungsten)	Heating effect of current
Electric heater / iron	Heating effect (Joule heating)
Fan / Motor	Magnetic effect of current
Transformer	Electromagnetic induction
Fuse / MCB	Heating / Magnetic effect — safety device

Acids

• pH < 7 | Sour taste | Turns blue litmus RED | Proton donors
• HCl = Hydrochloric acid — stomach acid (gastric juice), muriatic acid
• H₂SO₄ = Sulphuric acid — "King of Acids", battery acid, most widely used industrial acid
• HNO₃ = Nitric acid — used in explosives, fertilisers; "Aqua regia" = HNO₃ + HCl (3:1) dissolves gold/platinum
• CH₃COOH = Acetic/Ethanoic acid — vinegar (5% solution), pickling
• H₂CO₃ = Carbonic acid — fizzy drinks (soda water)
• H₃PO₄ = Phosphoric acid — fertilisers, soft drinks
• Citric acid — lemon, orange (natural acid)
• Formic/Methanoic acid — ant sting, nettle sting
• Lactic acid — sour milk, curd, muscles during exercise
• Oxalic acid — tomato, spinach (removes rust stains)

Bases and Alkalis

• pH > 7 | Bitter taste | Turns red litmus BLUE | Proton acceptors
• All alkalis are bases but all bases are not alkalis (alkalis = water-soluble bases)
• NaOH = Sodium hydroxide (Caustic soda) — soap making, paper, drain cleaner
• KOH = Potassium hydroxide (Caustic potash) — soft soaps, liquid soaps
• Ca(OH)₂ = Calcium hydroxide (Slaked lime) — white washing, water treatment, antacid
• NH₃ = Ammonia — fertilisers, cleaning agents, refrigerant
• Mg(OH)₂ = Milk of Magnesia — antacid (treats acidity/heartburn)
• Al(OH)₃ = Aluminium hydroxide — antacid, fire retardant
• NaHCO₃ = Sodium bicarbonate (Baking soda) — baking, fire extinguisher, antacid
• Na₂CO₃ = Sodium carbonate (Washing soda) — glass making, soap, water softening
• CaO = Calcium oxide (Quicklime / Burnt lime) — reacts with water violently (exothermic)

Important pH Values

Substance	pH	Nature
Battery acid (H₂SO₄)	0–1	Strong acid
Gastric juice (HCl)	1–2	Strong acid
Lemon juice	2–3	Acid
Vinegar	2.5–3.5	Weak acid
Cola/soft drinks	2.5–3.5	Acid
Coffee	5	Weak acid
Milk	6.4–6.8	Slightly acidic
Pure water	7	Neutral
Blood	7.35–7.45	Slightly basic
Sea water	8	Basic
Baking soda	8–9	Mild base
Milk of Magnesia	10	Base
Bleach/Ammonia	11–12	Strong base
Caustic soda (NaOH)	13–14	Strong base

Types of Chemical Reactions

Type	Definition	Example
Combination	A + B → AB	CaO + H₂O → Ca(OH)₂
Decomposition	AB → A + B	2H₂O → 2H₂ + O₂ (electrolysis)
Displacement	A + BC → AC + B	Zn + CuSO₄ → ZnSO₄ + Cu
Double Displacement	AB + CD → AD + CB	NaCl + AgNO₃ → NaNO₃ + AgCl↓
Oxidation	Loss of electrons / gain of O₂	Rusting of iron
Reduction	Gain of electrons / loss of O₂	Fe₂O₃ + CO → Fe + CO₂
Neutralisation	Acid + Base → Salt + Water	HCl + NaOH → NaCl + H₂O

Metals and Non-Metals

• Metals: Good conductors, lustrous, malleable, ductile, sonorous. React with acids to produce H₂ gas.
• Most reactive metals: K > Na > Ca > Mg > Al > Zn > Fe > Pb > Cu > Hg > Ag > Au (reactivity series)
• Gold and Platinum — least reactive (noble metals)
• Sodium and Potassium — stored in kerosene (react violently with water)
• Non-Metals: Poor conductors (except graphite), non-lustrous, brittle
• Diamond (hardest natural substance) and Graphite — allotropes of Carbon
• Alloys: Brass (Cu+Zn), Bronze (Cu+Sn), Stainless Steel (Fe+Cr+Ni), Duralumin (Al+Cu+Mn+Mg)

States of Matter

State	Shape	Volume	Particle Distance
Solid	Fixed	Fixed	Very close
Liquid	Variable (takes container)	Fixed	Close
Gas	Variable	Variable	Very far apart
Plasma	Variable	Variable	Ionised gas (Sun, stars)

Changes of State

• Solid → Liquid: Melting (heat absorbed) | Liquid → Solid: Freezing
• Liquid → Gas: Vaporisation/Boiling | Gas → Liquid: Condensation
• Solid → Gas directly: Sublimation (dry ice CO₂, iodine, naphthalene, camphor)
• Gas → Solid: Deposition

Mixtures vs Compounds

Feature	Mixture	Compound
Composition	Variable	Fixed (by mass)
Separation	Physical methods	Chemical methods only
Properties	Retain individual properties	New properties formed
Examples	Air, sea water, alloys	H₂O, NaCl, CO₂

Periodic Table — Important Facts

• Total elements in modern periodic table: 118
• Periods: 7 horizontal rows | Groups: 18 vertical columns
• Modern Periodic Law (Moseley): Properties of elements are periodic function of their atomic number
• Atomic number = number of protons = number of electrons (in neutral atom)
• Noble gases (Group 18): He, Ne, Ar, Kr, Xe, Rn — chemically inert, outermost shell complete
• Alkali metals (Group 1): Li, Na, K, Rb, Cs, Fr — most reactive metals
• Halogens (Group 17): F, Cl, Br, I, At — most reactive non-metals
• Transition metals: d-block elements (Fe, Cu, Zn, Ni, Co, Mn etc.) — variable valency

Important Elements & Their Symbols

Element	Symbol	Key Use / Fact
Hydrogen	H	Lightest element, fuel cell, universe's most abundant
Carbon	C	Basis of organic chemistry; diamond, graphite, fullerene
Nitrogen	N	78% of atmosphere; fertilisers, explosives
Oxygen	O	21% of atmosphere; respiration, combustion
Sodium	Na (Natrium)	Common salt (NaCl), baking soda
Iron	Fe (Ferrum)	Steel production, haemoglobin
Gold	Au (Aurum)	Least reactive, coinage, jewellery
Silver	Ag (Argentum)	Best conductor of electricity
Copper	Cu (Cuprum)	Electrical wires, utensils
Lead	Pb (Plumbum)	Batteries, radiation shielding
Mercury	Hg (Hydrargyrum)	Only liquid metal at room temperature; thermometers
Tungsten	W (Wolfram)	Highest melting point; electric bulb filament
Uranium	U	Nuclear fuel; radioactive

Circulatory System

• Heart has 4 chambers: 2 Atria (upper) + 2 Ventricles (lower)
• Left ventricle — pumps oxygenated blood to body; Right ventricle — to lungs
• Normal heart rate: 72 beats/minute | Blood pressure: 120/80 mmHg (normal)
• RBC (Red Blood Cells): Carry O₂ via Haemoglobin (iron-containing protein); no nucleus; 120-day lifespan
• WBC (White Blood Cells): Immunity and infection-fighting; nucleus present; Types: Neutrophils, Lymphocytes, Monocytes, Eosinophils, Basophils
• Platelets (Thrombocytes): Blood clotting; 7–10 day lifespan
• Blood pH = 7.35–7.45 (slightly alkaline)
• Blood groups: A, B, AB, O (ABO system) + Rh factor
• Universal Donor: O− | Universal Recipient: AB+

Digestive System

• Alimentary canal: Mouth → Oesophagus → Stomach → Small intestine → Large intestine → Rectum → Anus
• Largest gland: Liver — produces bile (emulsifies fats), stores glycogen, detoxifies blood
• Pancreas: Produces insulin (lowers blood sugar) and glucagon (raises blood sugar); also digestive enzymes
• Small intestine: 6–7 m long — main site of digestion and absorption (villi increase surface area)
• Large intestine: Absorbs water; 1.5 m long
• Salivary amylase (ptyalin): Digests starch in mouth
• Pepsin (stomach, acidic): Digests proteins | Lipase: Digests fats

Respiratory System

• Organs: Nose → Pharynx → Larynx → Trachea → Bronchi → Bronchioles → Alveoli (lungs)
• Alveoli: Site of gas exchange; ~300–500 million in both lungs
• Inhale: O₂ (21%) | Exhale: CO₂ (4%), O₂ (17%), N₂ (78%), water vapour
• Normal breathing rate: 12–18 breaths/minute
• Diaphragm: Muscular sheet below lungs; controls breathing

Nervous System

• CNS: Brain + Spinal cord
• PNS: All nerves outside CNS
• Basic unit: Neuron (nerve cell)
• Brain parts: Cerebrum (thinking, voluntary), Cerebellum (balance, coordination), Medulla oblongata (breathing, heartbeat)
• Reflex action: Automatic response through spinal cord (no brain involvement) — knee jerk, blinking
• Largest nerve: Sciatic nerve | Largest brain part: Cerebrum | Smallest bone: Stapes (ear)

Endocrine System — Important Hormones

Gland	Hormone	Function
Pituitary (Master gland)	GH, FSH, LH, ADH, TSH	Controls all other glands; growth
Thyroid	Thyroxine	Metabolic rate; deficiency → Goitre
Parathyroid	Parathormone (PTH)	Calcium balance
Adrenal	Adrenaline	"Fight or flight" response
Pancreas (Islets of Langerhans)	Insulin, Glucagon	Blood sugar regulation
Testes	Testosterone	Male sex characteristics
Ovaries	Oestrogen, Progesterone	Female sex characteristics
Pineal	Melatonin	Sleep cycle regulation

Vitamins — Complete Table

Vitamin	Chemical Name	Source	Deficiency Disease
A	Retinol	Carrot, milk, liver, egg yolk	Night blindness, Xerophthalmia
B1	Thiamine	Cereals, yeast, pulses	Beriberi (nervous system damage)
B2	Riboflavin	Milk, eggs, green vegetables	Ariboflavinosis (cracks at lips)
B3	Niacin	Meat, fish, cereals	Pellagra (4 Ds: Dermatitis, Diarrhoea, Dementia, Death)
B6	Pyridoxine	Meat, fish, potatoes	Anaemia, Dermatitis
B9	Folic acid	Leafy vegetables, legumes	Megaloblastic anaemia, neural tube defects in pregnancy
B12	Cobalamin	Meat, dairy products, eggs	Pernicious anaemia
C	Ascorbic acid	Citrus fruits, amla, guava	Scurvy (bleeding gums, joint pain)
D	Calciferol	Sunlight, fish liver oil, egg yolk	Rickets (children), Osteomalacia (adults)
E	Tocopherol	Vegetable oils, nuts, green veg	Muscle weakness, reproductive problems
K	Phylloquinone	Green leafy vegetables, soybean	Excessive bleeding (blood clotting failure)

Minerals and their Functions

Mineral	Source	Function / Deficiency
Calcium (Ca)	Milk, dairy, leafy veg	Bones, teeth, clotting. Deficiency → Osteoporosis
Iron (Fe)	Spinach, meat, liver, jaggery	Haemoglobin synthesis. Deficiency → Iron-deficiency anaemia
Iodine (I)	Sea fish, iodised salt	Thyroxine synthesis. Deficiency → Goitre, Cretinism
Phosphorus (P)	Milk, meat, nuts	Bones, teeth, ATP energy
Sodium (Na)	Table salt	Fluid balance, nerve impulses
Potassium (K)	Banana, potato, nuts	Heart rhythm, muscle function
Zinc (Zn)	Meat, nuts, seeds	Immune function, wound healing
Fluoride (F)	Water, toothpaste	Tooth enamel protection. Excess → Fluorosis

Common Diseases — Causative Agents

Disease	Caused By	Affected Organ/System
Malaria	Plasmodium (Protozoa) via female Anopheles mosquito	Liver, RBC
Dengue	Dengue virus via female Aedes mosquito	Platelets, blood
Tuberculosis (TB)	Mycobacterium tuberculosis (Bacteria)	Lungs
Typhoid	Salmonella typhi (Bacteria)	Intestine
Cholera	Vibrio cholerae (Bacteria)	Intestine
Pneumonia	Streptococcus pneumoniae (Bacteria)	Lungs
Influenza (Flu)	Influenza virus	Respiratory system
HIV/AIDS	HIV Virus (Retrovirus)	Immune system (CD4 T cells)
Rabies	Rabies virus (Rhabdovirus)	Brain, nervous system
Hepatitis B	Hepatitis B virus (HBV)	Liver
Ringworm	Fungi (Tinea)	Skin
Amoebiasis	Entamoeba histolytica (Protozoa)	Large intestine
Polio	Poliovirus	Spinal cord, brain stem
COVID-19	SARS-CoV-2 virus (Coronavirus)	Respiratory system

Photosynthesis

• Process: 6CO₂ + 6H₂O + Light energy → C₆H₁₂O₆ (glucose) + 6O₂
• Site: Chloroplasts (containing chlorophyll — green pigment)
• Raw materials: CO₂ (from air via stomata) + H₂O (from roots) + Sunlight
• Chlorophyll absorbs red and blue light most; reflects green (hence plants look green)
• Two stages: Light reactions (in thylakoids) + Dark reactions/Calvin cycle (in stroma)

Plant Hormones

Hormone	Function
Auxin	Cell elongation, phototropism, apical dominance
Gibberellin	Stem elongation, seed germination, fruit development
Cytokinin	Cell division, delays senescence (ageing)
Abscisic acid (ABA)	"Stress hormone" — causes stomata closure, seed dormancy
Ethylene	Fruit ripening, leaf fall (abscission)

Ecology — Key Terms

• Ecosystem: Biotic (living) + Abiotic (non-living) components interacting together
• Food chain: Producers → Primary consumers → Secondary consumers → Tertiary consumers
• Food web: Interconnected food chains
• Producers: Green plants (autotrophs) | Consumers: Animals (heterotrophs)
• Decomposers: Bacteria, Fungi — break down dead matter; return nutrients to soil
• 10% Law: Only 10% energy transfers from one trophic level to the next
• Pyramid of Numbers: Decreases from producers to top carnivores (usually)

Environmental Issues

Issue	Cause	Effect
Global Warming	Greenhouse gases (CO₂, CH₄, N₂O, CFC)	Rising temperature, glacial melting, sea level rise
Ozone depletion	CFCs (chlorofluorocarbons)	More UV radiation → skin cancer, cataract
Acid Rain	SO₂ and NOₓ (from industries, vehicles)	Damages buildings, kills aquatic life (pH below 5.6)
Eutrophication	Excess nitrates/phosphates in water bodies	Algal bloom, O₂ depletion, death of aquatic life

Greenhouse Gases (GHG) and their Sources

• CO₂: Fossil fuel burning, deforestation (largest contributor)
• CH₄ (Methane): Livestock (cattle), paddy fields, landfills
• N₂O: Fertilisers, vehicle exhaust
• CFCs: Refrigerators, air conditioners, aerosols (banned by Montreal Protocol 1987)
• Water vapour: Most abundant GHG naturally

Types of Numbers

• Natural Numbers (N): 1, 2, 3, 4, … (counting numbers)
• Whole Numbers (W): 0, 1, 2, 3, … (natural + 0)
• Integers (Z): …−3, −2, −1, 0, 1, 2, 3… (positive + negative + 0)
• Rational Numbers: Can be expressed as p/q where q ≠ 0 (fractions, terminating decimals)
• Irrational Numbers: Cannot be expressed as p/q — √2, √3, π, e
• Real Numbers: Rational + Irrational
• Prime numbers: Exactly 2 factors (1 and itself) — 2, 3, 5, 7, 11, 13, 17, 19, 23, 29…
• 2 is the only even prime number
• Composite numbers: More than 2 factors — 4, 6, 8, 9…
• 1 is neither prime nor composite

Divisibility Rules

Divisor	Rule
2	Last digit is 0, 2, 4, 6 or 8 (even)
3	Sum of digits divisible by 3
4	Last two digits divisible by 4
5	Last digit is 0 or 5
6	Divisible by both 2 and 3
7	Double last digit, subtract from rest; repeat till single/two digits
8	Last three digits divisible by 8
9	Sum of digits divisible by 9
10	Last digit is 0
11	(Sum of odd-position digits) − (Sum of even-position digits) = 0 or multiple of 11

LCM and HCF

• HCF (GCD): Highest Common Factor — largest number dividing all given numbers
• LCM: Least Common Multiple — smallest number divisible by all given numbers
• HCF × LCM = Product of two numbers (for two numbers only)
• HCF ≤ LCM always | HCF is always a factor of LCM

BODMAS / PEMDAS Rule

Order of operations: Brackets → Of (powers/roots) → Division → Multiplication → Addition → Subtraction

Percentage

• Percentage = (Value / Total) × 100
• x% of y = y% of x
• If A is r% more than B, then B is less than A by: [r/(100+r)] × 100 %
• If A is r% less than B, then B is more than A by: [r/(100−r)] × 100 %

Fraction–Percentage Equivalents (Must Memorise)

Fraction	Percentage	Fraction	Percentage
1/1	100%	1/6	16.67%
1/2	50%	1/7	14.28%
1/3	33.33%	1/8	12.5%
1/4	25%	1/9	11.11%
1/5	20%	1/10	10%

Profit and Loss

• Profit = SP − CP (when SP > CP)
• Loss = CP − SP (when CP > SP)
• Profit% = (Profit / CP) × 100
• Loss% = (Loss / CP) × 100
• SP = CP × (100 + Profit%) / 100
• SP = CP × (100 − Loss%) / 100
• CP = SP × 100 / (100 + Profit%) when profit
• CP = SP × 100 / (100 − Loss%) when loss
• Discount: Discount = Marked Price − Selling Price
• Discount% = (Discount / Marked Price) × 100
• SP = MP × (100 − Discount%) / 100

Simple Interest (SI)

• SI = (P × R × T) / 100
• Amount (A) = P + SI
• P = Principal | R = Rate of interest per annum | T = Time in years
• P = (SI × 100) / (R × T)
• R = (SI × 100) / (P × T)
• T = (SI × 100) / (P × R)

Compound Interest (CI)

• A = P × (1 + R/100)ⁿ
• CI = A − P = P [(1 + R/100)ⁿ − 1]
• n = number of compounding periods
• If compounded half-yearly: A = P × (1 + R/200)²ⁿ
• If compounded quarterly: A = P × (1 + R/400)⁴ⁿ
• Difference between CI and SI for 2 years = P × (R/100)²
• Difference between CI and SI for 3 years = P(R/100)² × (R/100 + 3)

Basic Formulas

• Speed = Distance / Time
• Distance = Speed × Time
• Time = Distance / Speed
• To convert km/h to m/s: multiply by 5/18
• To convert m/s to km/h: multiply by 18/5

Average Speed

• If same distance at two speeds u and v: Average speed = 2uv/(u+v) [Harmonic Mean]
• If same time at two speeds: Average speed = (u+v)/2 [Arithmetic Mean]

Train Problems

• Train crossing a pole/person: Time = Length of Train / Speed of Train
• Train crossing a platform/bridge: Time = (Length of Train + Length of Platform) / Speed
• Two trains same direction: Relative speed = |S₁ − S₂| | Time = (L₁ + L₂) / |S₁ − S₂|
• Two trains opposite direction: Relative speed = S₁ + S₂ | Time = (L₁ + L₂) / (S₁ + S₂)

Boat and Stream

• Downstream speed = u + v (u = boat speed, v = stream speed)
• Upstream speed = u − v
• Speed of boat = (Downstream + Upstream) / 2
• Speed of stream = (Downstream − Upstream) / 2

2D Shapes — Area and Perimeter

Shape	Area	Perimeter
Square (side a)	a²	4a
Rectangle (l × b)	l × b	2(l + b)
Triangle (b, h)	½ × b × h	a + b + c
Equilateral Triangle (a)	(√3/4)a²	3a
Circle (r)	πr²	2πr
Semi-circle	½πr²	πr + 2r
Parallelogram	base × height	2(a + b)
Trapezium	½ × (a + b) × h	sum of all sides
Rhombus (d₁, d₂)	½ × d₁ × d₂	4a

3D Shapes — Volume and Surface Area

Shape	Volume	Total Surface Area
Cube (a)	a³	6a²
Cuboid (l,b,h)	l×b×h	2(lb+bh+lh)
Cylinder (r,h)	πr²h	2πr(r+h)
Cone (r,h,l)	⅓πr²h	πr(r+l), l=slant height
Sphere (r)	4/3 πr³	4πr²
Hemisphere (r)	⅔πr³	3πr²

Pythagorean Triplets (Common)

• 3, 4, 5 | 5, 12, 13 | 8, 15, 17 | 7, 24, 25 | 9, 40, 41
• Multiples also valid: 6, 8, 10 | 10, 24, 26 etc.
• Pythagoras theorem: a² + b² = c² (right angle triangle)

Angles and Lines

• Sum of angles of triangle = 180°
• Sum of angles of quadrilateral = 360°
• Sum of interior angles of polygon = (n − 2) × 180°
• Exterior angle = sum of two non-adjacent interior angles
• Vertically opposite angles are equal
• Alternate interior angles are equal (parallel lines cut by transversal)

Historical Milestones

• First train in India: 16 April 1853 — Bori Bunder (Mumbai) to Thane, 34 km, operated by Great Indian Peninsular Railway (GIPR)
• Engines: Sahib, Sindh, Sultan (the three engines)
• First electric train: 3 February 1925 — Bombay VT to Kurla (GIPR)
• Indian Railways nationalized: 1951 (merged into single entity)
• Railway Budget merged with Union Budget: 2017
• World's 4th largest railway network by route length (after USA, Russia, China)
• Headquarters: Rail Bhavan, New Delhi
• Total Railway Zones: 18 (increased from 17 when South Coast Railway was added)

Key Records & Firsts

Record	Detail
Longest railway platform	Hubballi Junction, Karnataka — 1,507 m (World record)
Second longest platform	Gorakhpur, UP — 1,366 m
Fastest train (operational)	Vande Bharat Express — design speed 180 km/h; operational ~160 km/h
Highest railway station	Ghum (West Bengal) — 2,258 m (Darjeeling Himalayan Railway)
Highest broad gauge station	Kazigund (J&K) — 1,722 m
Longest railway tunnel	Pir Panjal Tunnel (J&K) — 11.215 km
Longest railway bridge	Vembanad Rail Bridge (Kerala) — 4.62 km
First Metro Rail	Kolkata Metro — 1984
Longest train route	Vivek Express — Dibrugarh to Kanyakumari — 4,273 km (82 hrs)
Highest railway bridge	Chenab Bridge (J&K) — 359 m above river (taller than Eiffel Tower)
First train with AC coach	Frontier Mail (1928)
First luxury train	Palace on Wheels (1982, Rajasthan)

All 18 Railway Zones & Headquarters

Zone	Abbreviation	Headquarters
Northern Railway	NR	New Delhi
North Eastern Railway	NER	Gorakhpur
North East Frontier Railway	NFR	Maligaon (Guwahati)
Eastern Railway	ER	Kolkata
South Eastern Railway	SER	Kolkata
South Central Railway	SCR	Secunderabad
Southern Railway	SR	Chennai
Central Railway	CR	Mumbai (CST)
Western Railway	WR	Mumbai (Churchgate)
South Western Railway	SWR	Hubballi
North Western Railway	NWR	Jaipur
West Central Railway	WCR	Jabalpur
North Central Railway	NCR	Prayagraj
East Central Railway	ECR	Hajipur
East Coast Railway	ECoR	Bhubaneswar
South East Central Railway	SECR	Bilaspur
Metro Railway Kolkata	MR	Kolkata
South Coast Railway	SCoR	Visakhapatnam

Gauge Types

Gauge	Width	Usage
Broad Gauge (BG)	1676 mm (5 ft 6 in)	Main network — most of India
Metre Gauge (MG)	1000 mm (3 ft 3 in)	Being converted to BG
Narrow Gauge (NG)	762 mm or 610 mm	Hilly regions — Darjeeling, Matheran

Important Trains

Train	Route	Significance
Rajdhani Express	Delhi to state capitals	Fully AC; fastest long-distance
Shatabdi Express	Delhi to nearby cities (day travel)	AC Chair Car; high-speed
Vande Bharat	Multiple routes across India	Semi-high speed, Made-in-India
Duronto Express	Major city to major city	Non-stop point-to-point
Vivek Express	Dibrugarh–Kanyakumari	Longest route (4,273 km)
Palace on Wheels	Delhi + Rajasthan circuit	First luxury tourist train (1982)
Deccan Queen	Mumbai–Pune	Oldest electric train still running (1930)

January

Date	Day
1 Jan	New Year's Day | Global Family Day
10 Jan	World Hindi Day
12 Jan	National Youth Day (Swami Vivekananda's Birthday)
15 Jan	Army Day
23 Jan	Netaji Subhas Chandra Bose Jayanti (Parakram Diwas)
24 Jan	National Girl Child Day
25 Jan	National Voters' Day | National Tourism Day
26 Jan	Republic Day (India) | International Customs Day
28 Jan	Lala Lajpat Rai Jayanti | Data Protection Day
30 Jan	Martyrs' Day (Mahatma Gandhi's death anniversary) | World Leprosy Day

February

Date	Day
4 Feb	World Cancer Day
14 Feb	Valentine's Day | Saint Valentine's Day
20 Feb	World Day of Social Justice
21 Feb	International Mother Language Day
28 Feb	National Science Day (CV Raman discovered Raman Effect — 1928)

March

Date	Day
1 Mar	World Civil Defence Day | Zero Discrimination Day
4 Mar	National Safety Day
8 Mar	International Women's Day
15 Mar	World Consumer Rights Day
20 Mar	World Sparrow Day | International Day of Happiness
21 Mar	World Forestry Day | World Poetry Day
22 Mar	World Water Day
23 Mar	World Meteorological Day | Bhagat Singh, Sukhdev, Rajguru's Martyrdom Day
24 Mar	World Tuberculosis Day
27 Mar	World Theatre Day

April

Date	Day
1 Apr	April Fool's Day | Odisha Day
2 Apr	World Autism Awareness Day
7 Apr	World Health Day (WHO founded 1948)
14 Apr	Ambedkar Jayanti | Tamil New Year (Puthandu)
17 Apr	World Haemophilia Day
18 Apr	World Heritage Day
19 Apr	World Liver Day
22 Apr	Earth Day (first observed 1970)
23 Apr	World Book and Copyright Day
25 Apr	World Malaria Day
29 Apr	International Dance Day

May

Date	Day
1 May	International Labour Day (Workers' Day) | Maharashtra/Gujarat Day
3 May	World Press Freedom Day
4 May	Coal Miners' Day
8 May	World Red Cross Day | World Thalassemia Day
11 May	National Technology Day (India — Pokhran nuclear test 1998)
12 May	International Nurses Day (Florence Nightingale's Birthday)
15 May	International Family Day
17 May	World Telecommunication Day
21 May	Anti-Terrorism Day (India — Rajiv Gandhi assassination 1991)
22 May	International Day for Biological Diversity
31 May	World No Tobacco Day

June

Date	Day
1 Jun	World Milk Day | International Children's Day
5 Jun	World Environment Day
8 Jun	World Ocean Day
12 Jun	World Anti-Child Labour Day
14 Jun	World Blood Donor Day
15 Jun	World Elder Abuse Awareness Day
21 Jun	International Yoga Day (declared by UN 2015; India's initiative)
23 Jun	Olympic Day | UN Public Service Day
26 Jun	International Day against Drug Abuse and Illicit Trafficking

July

Date	Day
1 Jul	Doctor's Day (India — Bidhan Chandra Roy's Birthday) | GST Day (2017)
11 Jul	World Population Day
26 Jul	Kargil Vijay Diwas (1999)
28 Jul	World Nature Conservation Day | World Hepatitis Day

August

Date	Day
6 Aug	Hiroshima Day (1945 — US atomic bomb)
9 Aug	Nagasaki Day | Quit India Day (1942) | International Day of Indigenous Peoples
12 Aug	International Youth Day
15 Aug	Independence Day (India — 1947) | National Day of India
19 Aug	World Humanitarian Day
20 Aug	Sadbhavana Diwas (Rajiv Gandhi's Birthday)
29 Aug	National Sports Day (Major Dhyan Chand's Birthday)
30 Aug	International Day of Victims of Enforced Disappearances

September

Date	Day
5 Sep	Teachers' Day (India — Dr. S. Radhakrishnan's Birthday)
8 Sep	International Literacy Day
14 Sep	Hindi Diwas (Hindi adopted as official language 1949)
15 Sep	Engineers' Day (M. Visvesvaraya's Birthday)
16 Sep	World Ozone Day (Montreal Protocol 1987)
21 Sep	International Day of Peace | World Alzheimer's Day
27 Sep	World Tourism Day

October

Date	Day
1 Oct	International Day of Older Persons | World Vegetarian Day
2 Oct	Gandhi Jayanti | World Non-Violence Day
4 Oct	World Animal Day | World Habitat Day
5 Oct	World Teachers' Day (UNESCO)
8 Oct	Indian Air Force Day (1932)
9 Oct	World Post Day
10 Oct	World Mental Health Day
16 Oct	World Food Day (FAO founded 1945)
24 Oct	United Nations Day (UN founded 1945) | World Development Information Day
31 Oct	National Unity Day (Sardar Patel's Birthday — "Statue of Unity") | Halloween

November

Date	Day
5 Nov	World Tsunami Awareness Day
9 Nov	Legal Services Day (India)
11 Nov	National Education Day (Maulana Abul Kalam Azad's Birthday)
14 Nov	Children's Day India (Nehru Jayanti) | World Diabetes Day
17 Nov	National Epilepsy Day | International Student's Day
19 Nov	National Integration Day | World Toilet Day
20 Nov	Universal Children's Day (UN)
21 Nov	World Television Day
26 Nov	Constitution Day (Samvidhan Diwas) — adopted 1949

December

Date	Day
1 Dec	World AIDS Day
2 Dec	National Pollution Control Day | International Day for Abolition of Slavery
3 Dec	World Disability Day
4 Dec	Indian Navy Day
5 Dec	World Soil Day
7 Dec	Indian Armed Forces Flag Day
9 Dec	International Anti-Corruption Day
10 Dec	Human Rights Day (Universal Declaration adopted 1948)
11 Dec	International Mountain Day | UNICEF Day
14 Dec	National Energy Conservation Day
16 Dec	Vijay Diwas (1971 war — Bangladesh Liberation)
18 Dec	Minority Rights Day | International Migrants Day
22 Dec	National Mathematics Day (Ramanujan's Birthday)
23 Dec	Kisan Diwas (Chaudhary Charan Singh's Birthday)
24 Dec	National Consumer Rights Day
25 Dec	Christmas Day | Good Governance Day (Atal Bihari Vajpayee's Birthday)

Bharat Ratna

• India's highest civilian honour | Established: 1954
• First recipients (1954): C. Rajagopalachari, S. Radhakrishnan, C.V. Raman
• First woman: Indira Gandhi (1971)
• First posthumous: Lal Bahadur Shastri (1966)
• First non-Indian: Khan Abdul Ghaffar Khan (1987) — Pakistan
• Maximum 3 awards per year

Padma Awards

Award	Significance
Padma Vibhushan	Exceptional and distinguished service (2nd highest civilian)
Padma Bhushan	Distinguished service of high order (3rd highest)
Padma Shri	Distinguished service in any field (4th highest)

Sports Awards

Award	Field	Prize Money
Rajiv Gandhi Khel Ratna (now Major Dhyan Chand)	Sports (highest)	₹25 lakh
Arjuna Award	Outstanding sports performance	₹15 lakh
Dronacharya Award	Sports Coaches	₹15 lakh
Dhyan Chand Award	Lifetime achievement in sports	₹10 lakh

Literary & Arts Awards

Award	Field	Given By
Sahitya Akademi Award	Literature (24 languages)	Sahitya Akademi
Sangeet Natak Akademi	Music, Dance, Drama	Sangeet Natak Akademi
Dada Saheb Phalke Award	Indian Cinema (highest)	Govt of India / BIFF
Jnanpith Award	Indian literature (highest)	Bharatiya Jnanpith
Booker Prize	Fiction in English	Booker Prize Foundation (UK)
Nobel Prize	Various — Physics, Chemistry, Medicine, Literature, Peace, Economics	Swedish/Norwegian Academy

Indian Nobel Prize Winners

Name	Year	Prize
Rabindranath Tagore	1913	Literature (Gitanjali)
C.V. Raman	1930	Physics (Raman Effect)
Har Gobind Khorana	1968	Medicine
Mother Teresa	1979	Peace
S. Chandrasekhar	1983	Physics
Amartya Sen	1998	Economics
V.S. Naipaul	2001	Literature
Venkatraman Ramakrishnan	2009	Chemistry
Kailash Satyarthi	2014	Peace
Abhijit Banerjee	2019	Economics

India at a Glance

• Area: 3,287,263 km² — 7th largest country in the world
• Population: ~1.44 billion (2nd most populous, surpassed China in 2023)
• Total States: 28 | Union Territories: 8
• Northernmost point: Siachen Glacier, J&K | Southernmost: Indira Point, Great Nicobar
• Easternmost: Kibithu, Arunachal Pradesh | Westernmost: Ghuar Mota, Gujarat
• Longest coastline state: Gujarat (1,600 km)
• Tropic of Cancer (23.5°N) passes through: Gujarat, Rajasthan, MP, Chhattisgarh, Jharkhand, West Bengal, Tripura, Mizoram
• Standard Meridian of India: 82.5°E (passes through Mirzapur, UP)
• IST = UTC + 5:30 hours

Longest, Largest, Highest in India

Superlative	Answer	State
Longest river (by length)	Ganga	UP, Bihar, WB
Largest river (by volume)	Brahmaputra	Arunachal, Assam
Largest lake	Vembanad Lake	Kerala
Highest mountain	Kangchenjunga (8,586 m)	Sikkim/Nepal border
Highest waterfall	Kunchikal Falls (455 m)	Karnataka
Largest state (area)	Rajasthan	—
Smallest state (area)	Goa	—
Most populous state	Uttar Pradesh	—
Least populous state	Sikkim	—
Longest national highway	NH-44 (Srinagar–Kanyakumari) — 3,745 km	Multiple
Largest desert	Thar Desert (Great Indian Desert)	Rajasthan
Largest forest cover	Madhya Pradesh	—
Largest delta	Sundarbans Delta	West Bengal
Largest island	Andaman Island	Andaman & Nicobar

Important Rivers and their Origins

River	Origin	Drains into
Ganga	Gangotri Glacier	Bay of Bengal
Yamuna	Yamunotri Glacier	Ganga (at Prayagraj — Triveni Sangam)
Brahmaputra	Angsi Glacier, Tibet	Bay of Bengal
Indus	Sengge Zangbo, Tibet	Arabian Sea
Godavari	Trimbakeshwar, Maharashtra	Bay of Bengal (longest Peninsular river)
Krishna	Mahabaleshwar, Maharashtra	Bay of Bengal
Kaveri	Talacauvery, Coorg, Karnataka	Bay of Bengal
Narmada	Amarkantak Plateau, MP	Arabian Sea (flows west)
Tapti/Tapi	Betul, MP	Arabian Sea (flows west)
Mahanadi	Chhattisgarh	Bay of Bengal

Constitution — Basic Facts

• Drafted by: Constituent Assembly under Dr. B.R. Ambedkar (Chairman, Drafting Committee)
• Adopted: 26 November 1949 (Constitution Day / Samvidhan Diwas)
• Enforced/Implemented: 26 January 1950 (Republic Day)
• Originally: 395 Articles, 8 Schedules, 22 Parts | Currently: ~448 Articles, 12 Schedules, 25 Parts
• Longest written constitution in the world
• Preamble adopted: November 26, 1949. Key words: Sovereign, Socialist, Secular, Democratic, Republic
• India borrowed from: UK (Parliamentary system, Rule of Law), USA (Fundamental Rights, Judicial Review), Ireland (DPSP), Canada (Federal structure), USSR (DPSP), France (Liberty, Equality, Fraternity), Germany (Emergency provisions), South Africa (Amendment process), Japan (Procedure established by law)

Fundamental Rights (Part III, Articles 12–35)

Right	Articles
Right to Equality	14–18
Right to Freedom	19–22
Right against Exploitation	23–24
Right to Freedom of Religion	25–28
Cultural and Educational Rights	29–30
Right to Constitutional Remedies	32 (Heart and Soul — Ambedkar)

Important Constitutional Articles

Article	Provision
Article 1	India shall be a Union of States
Article 13	Laws inconsistent with Fundamental Rights void
Article 21	Right to Life and Personal Liberty
Article 32	Right to approach Supreme Court for FRs
Article 44	Uniform Civil Code (DPSP)
Article 51A	Fundamental Duties (added by 42nd Amendment 1976)
Article 112	Annual Financial Statement (Union Budget)
Article 123	Ordinance-making power of President
Article 226	Writ jurisdiction of High Courts
Article 324	Election Commission of India
Article 352	National Emergency
Article 356	President's Rule (State Emergency)
Article 360	Financial Emergency
Article 370	Special status to J&K (abrogated Aug 2019)

Constitutional Bodies

Body	Article	Head
Election Commission	324	Chief Election Commissioner
CAG (Comptroller & Auditor General)	148	CAG of India
UPSC	315	Chairman
Finance Commission	280	Chairman (appointed every 5 years)
Attorney General	76	Top Law Officer of India

What is a Computer?

• Computer = Electronic device that processes data (Input → Process → Output)
• Full form: Commonly Operated Machine Particularly Used for Technology, Education and Research
• Characteristics: Speed, Accuracy, Diligence, Storage, Automation, Versatility
• Father of Computer: Charles Babbage (Difference Engine, Analytical Engine)
• Father of Modern Computer: Alan Turing
• First programmer: Ada Lovelace
• First electronic computer: ENIAC (1946) — used vacuum tubes
• First Indian computer: TIFRAC (1960) at TIFR, Mumbai

Generations of Computers

Generation	Period	Technology	Example
1st	1940–1956	Vacuum Tubes	ENIAC, UNIVAC
2nd	1956–1963	Transistors	IBM 1401, UNIVAC 1107
3rd	1964–1971	Integrated Circuits (ICs)	IBM 360, ICL 2900
4th	1971–present	Microprocessors (VLSI)	IBM PC, Apple Macintosh
5th	Present–future	AI, ULSI, Quantum	AI systems, quantum computers

Types of Computers

• Supercomputer: Fastest, most powerful (PARAM — India's first supercomputer, 1991)
• Mainframe: Large organizations, many users simultaneously (IBM Z)
• Minicomputer: Mid-range (PDP-11)
• Microcomputer: Personal use — desktops, laptops, tablets
• Based on data handling: Analog, Digital, Hybrid

Input Devices

• Keyboard, Mouse, Touchpad, Joystick, Trackball, Light Pen
• Scanner, Webcam, Microphone, Barcode Reader
• OCR (Optical Character Recognition) — reads printed text
• OMR (Optical Mark Recognition) — reads pencil/pen marks (used in MCQ sheets)
• MICR (Magnetic Ink Character Recognition) — used in bank cheques
• Biometric: Fingerprint scanner, iris scanner, face recognition

Output Devices

• Monitor (VGA, HDMI), Printer (Inkjet, Laser, Dot-matrix, 3D), Plotter
• Speaker, Projector, Headphone
• Softcopy output: Monitor/screen | Hardcopy: Printer (permanent physical output)

Memory Types

Type	Full Form	Nature
RAM	Random Access Memory	Volatile — data lost when power off (primary memory)
ROM	Read Only Memory	Non-volatile — permanent (stores BIOS/firmware)
PROM	Programmable ROM	Written once, read many times
EPROM	Erasable PROM	Erased by UV light
EEPROM	Electrically Erasable PROM	Erased by electric signal (Flash memory)
Cache Memory	—	Fastest, between CPU and RAM (L1, L2, L3)
Virtual Memory	—	Hard disk used as RAM extension

Storage Units

Unit	Equivalent
1 Bit	Smallest unit (0 or 1)
1 Nibble	4 bits
1 Byte	8 bits
1 Kilobyte (KB)	1024 Bytes
1 Megabyte (MB)	1024 KB
1 Gigabyte (GB)	1024 MB
1 Terabyte (TB)	1024 GB
1 Petabyte (PB)	1024 TB
1 Exabyte	1024 PB

Software

• System Software: OS, device drivers, utilities — manages hardware
• Application Software: End-user programs — MS Word, Excel, browser
• Programming Software: Compilers, interpreters, assemblers, debuggers
• Operating Systems: Windows, Linux, macOS, Android, iOS, Ubuntu
• Android is based on Linux kernel. Developed by Google/Android Inc.

Internet Basics

• Internet = Global network of interconnected computers using TCP/IP protocol
• WWW (World Wide Web) invented by: Tim Berners-Lee (1989) — not the same as internet
• Internet started as ARPANET (1969) by US Department of Defense
• Internet came to India: 15 August 1995 (VSNL launched public internet)
• Protocol = Set of rules for data communication
• IP Address: Unique numerical address for each device (IPv4: 32-bit; IPv6: 128-bit)
• DNS (Domain Name System): Converts domain names to IP addresses
• HTTP = HyperText Transfer Protocol | HTTPS = Secure version (SSL/TLS encrypted)
• FTP = File Transfer Protocol | SMTP = Simple Mail Transfer Protocol | POP3/IMAP = email receiving

Types of Networks

Network	Full Form	Range
PAN	Personal Area Network	Few meters (Bluetooth, USB)
LAN	Local Area Network	Building/campus (Ethernet, WiFi)
MAN	Metropolitan Area Network	City-wide
WAN	Wide Area Network	Country/global (Internet is WAN)

Network Topologies

• Bus: All devices on single cable — failure of cable → whole network down
• Star: All devices connect to central hub/switch — most common in LANs
• Ring: Devices connected in a circle — data travels in one direction
• Mesh: Every device connected to every other — most reliable, most expensive

Cyber Security Terms

Term	Meaning
Virus	Malicious program that replicates and attaches to files
Worm	Self-replicating malware that spreads via network without host file
Trojan	Disguised as legitimate software; opens backdoor for hackers
Ransomware	Encrypts user data and demands ransom (e.g., WannaCry 2017)
Phishing	Fake emails/websites to steal credentials
Firewall	Security system that monitors/controls incoming and outgoing network traffic
Encryption	Converting data into coded format for security
Spyware	Secretly monitors and collects user information
Adware	Displays unwanted advertisements; often tracks browsing
Keylogger	Records keystrokes to steal passwords

MS Word

Shortcut	Action
Ctrl + A	Select All
Ctrl + B	Bold
Ctrl + C	Copy
Ctrl + V	Paste
Ctrl + X	Cut
Ctrl + Z	Undo
Ctrl + Y	Redo
Ctrl + F	Find
Ctrl + H	Find and Replace
Ctrl + P	Print
Ctrl + S	Save
Ctrl + N	New document
Ctrl + O	Open file
Ctrl + I	Italic
Ctrl + U	Underline
Ctrl + Home	Go to beginning of document
Ctrl + End	Go to end of document
F7	Spelling and Grammar check

MS Excel

• Formula starts with = (equals sign)
• SUM: =SUM(A1:A10) | AVERAGE: =AVERAGE(A1:A10)
• MAX: =MAX(range) | MIN: =MIN(range) | COUNT: =COUNT(range)
• Cell address: Column letter + Row number (e.g., A1, B5, C10)
• F2: Edit cell | F4: Repeat last action | Ctrl+`: Toggle formulas/values
• Chart shortcut: Select data → Alt+F1 inserts chart

File Extensions

Extension	File Type
.doc / .docx	MS Word document
.xls / .xlsx	MS Excel spreadsheet
.ppt / .pptx	MS PowerPoint presentation
.pdf	Portable Document Format (Adobe)
.jpg / .png / .gif	Image files
.mp3 / .wav	Audio files
.mp4 / .avi	Video files
.zip / .rar	Compressed archive files
.exe	Executable/installable program (Windows)
.html / .htm	Web page files
.txt	Plain text file

Analogy

• Find the relationship between a given pair; apply same relationship to find missing term
• Types: Word analogy, Number analogy, Letter analogy
• Examples: Doctor : Hospital :: Teacher : ? → School
• Common relationships: Tool-User, Place-Product, Part-Whole, Young one, Worker-Workplace, Quantity-Unit, Country-Capital, Animal-Sound, Animal-Home

Number Series Patterns

• Arithmetic: Constant difference — 2, 5, 8, 11, 14 (diff = 3)
• Geometric: Constant ratio — 3, 6, 12, 24, 48 (ratio = 2)
• Squares: 1, 4, 9, 16, 25, 36…
• Cubes: 1, 8, 27, 64, 125…
• Fibonacci: 1, 1, 2, 3, 5, 8, 13, 21… (each = sum of previous two)
• Alternating: Two interleaved series — check odd-position and even-position terms separately
• Mixed: Combination — add, then multiply, then subtract etc.

Alphabet Series

• Learn alphabet positions: A=1, B=2, C=3 … M=13, N=14 … Z=26
• EJOTY rule: E=5, J=10, O=15, T=20, Y=25 (multiples of 5)
• Mirror image of alphabet: A↔Z, B↔Y, C↔X, D↔W … N↔M

Classification (Odd One Out)

• Find which item does NOT belong to the same group/category as others
• Approach: Identify common feature in 3 items → 4th that lacks it = odd one
• Check multiple angles: alphabetical, numerical, category, shape, function

Coding-Decoding

• Letter substitution: Each letter replaced by another letter (shifted by fixed number)
• Caesar cipher: Shift letters by n positions forward or backward
• Reverse alphabet coding: A↔Z, B↔Y etc.
• Number coding: Letters coded as numbers (A=1, B=2… or reverse Z=1)
• Word coding: Each word replaced by another word consistently
• Always find the pattern from the given example, then apply to the unknown

Direction Sense

• Standard directions: N, S, E, W (cardinal) and NE, NW, SE, SW (intercardinal)
• Sun rises in East and sets in West
• If facing North: Right = East, Left = West, Back = South
• If facing South: Right = West, Left = East, Back = North
• Turning right = Clockwise | Turning left = Anticlockwise
• Shadow of person: In morning (sun in East) → shadow falls West. In evening (sun in West) → shadow falls East. At noon → shadow falls North in India (sun to South)
• Use Pythagoras theorem to find shortest (straight-line) distance after multiple movements

Blood Relations

Relation	Meaning
Father's / Mother's father	Grandfather (Paternal/Maternal)
Father's / Mother's mother	Grandmother
Father's brother	Uncle (Paternal)
Mother's brother	Maternal Uncle (Mama)
Father's sister	Aunt (Bua/Paternal)
Mother's sister	Maternal Aunt (Maasi)
Uncle's / Aunt's child	Cousin
Husband's / Wife's brother	Brother-in-law
Husband's / Wife's sister	Sister-in-law
Son's wife	Daughter-in-law
Daughter's husband	Son-in-law

Strategy for Blood Relation Problems

• Draw a family tree/diagram. Use squares for males, circles for females
• Always read carefully — the question often asks the relationship the other way
• Coded blood relations: First decode the code, then find the family relationship

Rankings and Arrangements

• If a person is Rth from top and Sth from bottom in a row: Total = R + S − 1
• Rank from bottom = Total − Rank from top + 1
• If two persons exchange positions: new rank of first = old rank of second and vice versa

Seating Arrangement Tips

• Linear: Left and Right are as per reader's orientation unless stated "facing you"
• Circular (facing centre): Right = clockwise direction from outside view
• Circular (facing outside): Right = anticlockwise from outside view
• Always start with fixed/definite clues first

Syllogism — Statement Types

Type	Form	Example
Universal Affirmative (A)	All S are P	All dogs are animals
Universal Negative (E)	No S is P	No cat is a dog
Particular Affirmative (I)	Some S are P	Some men are tall
Particular Negative (O)	Some S are not P	Some birds cannot fly

Syllogism — Mediate Inferences

• All A are B + All B are C → All A are C ✅
• All A are B + No B is C → No A is C ✅
• All A are B + Some B are C → Some A are C ✗ (not definite) — Only "Some A may be C"
• No A is B + All C are B → No C is A ✅
• Some A are B + All B are C → Some A are C ✅
• Some A are B + No B is C → Some A are not C ✅

Venn Diagram Approach

• Draw the most general/inclusive set first (largest circle)
• "All A are B" → Circle A inside Circle B
• "No A is B" → Circles A and B completely separate
• "Some A are B" → Circles A and B partially overlapping
• Check each conclusion against all possible diagrams — if true in ALL cases → definite conclusion

Statement-Assumption / Argument Questions

• Assumption: Something taken for granted, not explicitly stated but underlying the statement
• Conclusion: Something that logically follows from the statement
• Inference: Something that can be deduced from the given information
• Strong argument: Directly related to the topic, based on facts
• Weak argument: Minor point, assumptions, emotional, not directly relevant