RRB JE Mechanical cheat sheet

Divisibility: a number is divisible by 3 or 9 if its digit sum is divisible by 3 or 9; by 4 if the last two digits form a multiple of 4; by 8 if the last three digits form a multiple of 8; by 11 if the alternating digit sum is 0 or a multiple of 11.

For two positive integers, HCF × LCM = product of the numbers. For fractions, HCF = HCF of numerators ÷ LCM of denominators and LCM = LCM of numerators ÷ HCF of denominators.

Successive percentage changes of a% and b% give a net change of a + b + ab/100 percent. A 20% rise followed by a 10% fall is a net 8% rise, not 10%.

Simple interest SI = PRT/100. Compound interest CI = P[(1 + r/100)^n − 1]. For two years, CI − SI = P(r/100)^2.

If A alone finishes work in x days and B in y days, together they take xy/(x + y) days. Efficiency is inversely proportional to the number of days taken.

For two equal distances covered at speeds x and y, average speed = 2xy/(x + y). Relative speed is x − y in the same direction and x + y in opposite directions.

Mensuration: circle area = πr² and circumference = 2πr; sphere volume = (4/3)πr³ and surface area = 4πr²; cylinder curved surface = 2πrh and total surface = 2πr(h + r).

Trigonometric values: sin 30° = 1/2, cos 30° = √3/2, tan 45° = 1, sin 60° = √3/2. Identities: sin²θ + cos²θ = 1 and 1 + tan²θ = sec²θ.

For ax² + bx + c = 0, sum of roots = −b/a and product of roots = c/a. The discriminant b² − 4ac is positive for real distinct roots, zero for equal roots and negative for complex roots.

Alphabet positions: A = 1 to Z = 26; reverse positions give Z = 1 to A = 26. The EJOTY anchors are E = 5, J = 10, O = 15, T = 20 and Y = 25.

Analogy questions require identifying the exact relation first: cause-effect, part-whole, worker-tool, synonym-antonym or number operation. Apply the same relation, in the same order, to the target pair.

Number series: check successive differences, then ratios, then squares, cubes and alternating or two-tier patterns before assuming a random rule.

Coding-decoding: compare the positions of letters in the code and the original word. A constant shift is a Caesar code; a reversing or alternating shift indicates a position-based rule.

Blood relations: draw a family tree. Vertical lines show parent-child generations and horizontal lines show siblings or spouse; compare the generation levels before deciding the relation.

Direction sense: fix the N-E-S-W axes and track facing direction. A left or right turn depends on the direction currently faced; net displacement is found using Pythagoras when the path is perpendicular.

Syllogism: All A are B does not imply All B are A. Some A are B always implies Some B are A. Test conclusions with a Venn diagram showing the minimum overlap required by the premises.

Mirror image reverses left and right while keeping top and bottom unchanged. Water image reverses top and bottom while keeping left and right unchanged.

Clock: angle between hands = |30H − 5.5M| degrees, where H is the hour and M the minutes. If the result exceeds 180°, subtract it from 360° for the smaller angle.

The Constitution of India was adopted on 26 November 1949 and came into force on 26 January 1950. Dr B. R. Ambedkar chaired the Drafting Committee.

Fundamental Rights are in Part III, Articles 12–35. Directive Principles of State Policy are in Part IV, Articles 36–51. Fundamental Duties are in Article 51A, added by the 42nd Amendment in 1976.

India has 28 states and 8 Union Territories after the 2019 Jammu and Kashmir reorganisation and the 2020 merger of Dadra and Nagar Haveli with Daman and Diu. Telangana became the 29th state in 2014.

The Reserve Bank of India was established on 1 April 1935 under the RBI Act 1934, nationalised in 1949 and shifted its central office to Mumbai in 1937.

India's first passenger train ran on 16 April 1853 from Bori Bunder, Mumbai, to Thane, covering about 34 km with three locomotives and about 400 passengers.

Indian Standard Time is based on longitude 82.5°E and equals UTC + 5:30. India follows one time zone although sunrise in the northeast is about two hours earlier than in Gujarat.

The Tropic of Cancer passes through eight Indian states: Gujarat, Rajasthan, Madhya Pradesh, Chhattisgarh, Jharkhand, West Bengal, Tripura and Mizoram.

Kangchenjunga (8,586 m) is the highest peak entirely within India. The first President of India was Dr Rajendra Prasad and the first woman President was Pratibha Patil.

SI units: force in newton, energy and work in joule, power in watt, pressure in pascal, frequency in hertz and electric charge in coulomb.

Newton's laws: first law defines inertia; second law gives F = ma or F = dp/dt; third law states that every action has an equal and opposite reaction on a different body.

The cell is the structural and functional unit of life. Mitochondria are the powerhouse producing ATP; chloroplasts carry out photosynthesis; ribosomes synthesise proteins.

Photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ in the presence of chlorophyll and sunlight. Respiration is the reverse energy-releasing process.

Normal arterial blood pH is about 7.35–7.45. Normal adult blood pressure is about 120/80 mmHg, where 120 mmHg is systolic and 80 mmHg diastolic.

Acids turn blue litmus red and have pH below 7; bases turn red litmus blue and have pH above 7; neutral solutions have pH 7 at 25°C.

Ohm's law: V = IR at constant temperature. Electric power P = VI = I²R = V²/R. Resistance in series adds directly; in parallel the reciprocal sum is used.

Speed of light in vacuum is about 3 × 10⁸ m/s. Speed of sound in air at 20°C is about 343 m/s and is faster in solids than in gases.

O negative red cells are the universal donor for red-cell transfusion; AB positive is the universal recipient for red cells. AB positive plasma is universal donor plasma.

Newton's second law: F = dp/dt = ma when mass is constant. Impulse equals change in momentum, J = FΔt = Δp.

Work-energy theorem: net work done equals change in kinetic energy. Kinetic energy = ½mv²; gravitational potential energy = mgh near the Earth's surface.

First law of thermodynamics for a closed system: ΔQ = ΔU + W. Adiabatic means Q = 0; isothermal means ΔU = 0 for an ideal gas; isochoric means W = 0.

Ideal gas equation: PV = nRT with R = 8.314 J mol⁻¹ K⁻¹. One mole of an ideal gas occupies 22.4 litres at STP.

Coulomb's law: F = kq₁q₂/r². Electric field E = F/q. Electric potential energy between two charges is kq₁q₂/r.

pH = −log₁₀[H⁺]. Each pH unit represents a tenfold change in hydrogen-ion concentration. A buffer resists pH change on adding small amounts of acid or base.

Periodic trends: atomic radius decreases left to right across a period and increases down a group. Electronegativity and ionisation energy generally increase across a period.

Le Chatelier's principle: increasing pressure shifts equilibrium toward the side with fewer gas moles; increasing temperature shifts equilibrium in the endothermic direction.

Mole concept: one mole = 6.022 × 10²³ particles. Molarity = moles of solute per litre of solution; molality = moles of solute per kilogram of solvent.

CPU components: arithmetic logic unit, control unit and registers. RAM is volatile read/write working memory; ROM is non-volatile and mainly read-only firmware memory.

Memory units: 1 byte = 8 bits; 1 KB = 1024 bytes; 1 MB = 1024 KB; 1 GB = 1024 MB; 1 TB = 1024 GB.

Windows shortcuts: Ctrl+C copy, Ctrl+X cut, Ctrl+V paste, Ctrl+Z undo, Ctrl+Y redo, Ctrl+S save, Ctrl+P print, Ctrl+A select all.

Spreadsheet: =SUM(A1:A5) adds a range; $A$1 is an absolute reference that does not change when copied; F2 edits the active cell in Excel.

Operating-system functions: process management, memory management, file management and device management. Examples are Windows, Linux and macOS.

IPv4 addresses are 32-bit and written as four dotted decimal octets; IPv6 addresses are 128-bit. HTTP uses port 80 and HTTPS uses port 443.

Malware types include virus, worm, Trojan and ransomware. A firewall filters incoming and outgoing network traffic by rules; antivirus software detects known malicious patterns.

Computer generations: first vacuum tubes, second transistors, third integrated circuits, fourth microprocessors, fifth artificial intelligence and parallel processing.

Email: To is the main recipient, CC is visible to all recipients, BCC is hidden. SMTP sends mail; POP3 and IMAP retrieve mail from a server.

Major pollution types are air, water, soil, noise, thermal and radioactive pollution. Pollutants may be primary (emitted directly) or secondary (formed in the atmosphere).

Principal greenhouse gases are CO₂, CH₄, N₂O and CFCs. CO₂ contributes the largest share by volume from fossil-fuel burning and deforestation.

The stratospheric ozone layer absorbs harmful UV-B and UV-C radiation. CFCs release chlorine that destroys ozone; the Montreal Protocol of 1987 controls ozone-depleting substances.

Common air pollutants are PM2.5, PM10, SO₂, NOx and CO. The National Air Quality Index runs from Good through Moderate, Poor, Very Poor to Severe.

Water pollution indicators: BOD, COD and dissolved oxygen. Higher BOD means more biodegradable organic pollution and lower dissolved oxygen available to aquatic life.

Noise is measured in decibels on a logarithmic scale. CPCB limits are about 55 dB(A) daytime and 45 dB(A) night for residential areas, and 75 dB(A) daytime for industrial areas.

Key Indian laws: Water Act 1974, Air Act 1981, Forest Conservation Act 1980 and Environment Protection Act 1986. The EPA was enacted after the Bhopal gas tragedy.

Environmental Impact Assessment operates under the EPA 1986 through EIA notifications. Projects are categorised A or B and appraised by the MoEFCC or State Expert Appraisal Committee respectively.

Renewable sources include solar, wind, hydro and biomass; non-renewable sources include coal, petroleum and natural gas. Sustainable development meets present needs without compromising future generations.

First law for a closed system: Q − W = ΔU. For a steady-flow control volume, h₁ + V₁²/2 + gz₁ + q = h₂ + V₂²/2 + gz₂ + w.

Air-standard Otto efficiency = 1 − 1/r^(γ−1), where r is compression ratio and γ = cp/cv. Diesel efficiency = 1 − [1/(r^(γ−1))] × [(ρ^γ − 1)/(γ(ρ − 1))], where ρ is cut-off ratio.

Direct stress σ = F/A; strain ε = ΔL/L; Young's modulus E = σ/ε. Hooke's law applies within the elastic limit; Poisson's ratio = lateral strain / longitudinal strain.

Bernoulli's equation for steady, incompressible, frictionless flow along a streamline: P/ρg + V²/2g + z = constant. It represents energy per unit weight.

Reynolds number Re = ρVD/μ = VD/ν. In pipe flow, Re below about 2000 is laminar, 2000–4000 is transitional and above 4000 is turbulent.

Gear train velocity ratio = speed of driver / speed of driven = product of teeth on driven gears / product of teeth on driving gears. Module m = pitch-circle diameter / number of teeth.

Refrigeration COP = refrigerating effect / work input. Carnot COP = T_L/(T_H − T_L) for temperatures in kelvin; actual COP is always lower than Carnot COP.

Casting allowances include shrinkage, draft and machining allowance. Pattern is larger than the casting by the shrinkage allowance. Welding electrode E6013 indicates 60 ksi tensile strength, all-position use and rutile coating.

Rankine cycle is the ideal cycle for steam power plants; Brayton cycle is used for gas turbines. Boiler efficiency = heat output in steam / heat input from fuel × 100%.