RRB JE CBT 2 Civil cheat sheet

Concrete mix design by IS 10262 uses target mean strength f'ck = fck + 1.65s, where s is the assumed standard deviation (4.0 N/mm² for M20–M25, 5.0 for M30–M50).

Water-cement ratio governs both strength and durability; IS 456 limits w/c to 0.50 for mild exposure, 0.45 for moderate, 0.40 for severe, 0.35 for very severe and extreme exposure.

Slump ranges (IS 456): 25–75 mm for lightly reinforced, 50–100 mm for beams/slabs, 75–125 mm for heavily reinforced sections; use a superplasticizer rather than excess water to raise workability.

Bending moment coefficients for continuous beams (IS 456 Table 12): near middle of end span +1/12, at support next to end support −1/10, at middle of interior span +1/16, at other interior supports −1/12 (all × wl²).

Shear design: nominal shear stress τv = Vu/(bd); maximum shear stress τc,max (IS 456 Table 20) is 2.5, 2.8, 3.1, 3.5 N/mm² for M15, M20, M25, M30 and above respectively.

Development length Ld = φσs/(4τbd); for plain bars in tension τbd = 1.6 N/mm² for M20 and above, increased by 60% for deformed bars in tension and a further 25% for bars in compression.

Effective span of a simply supported beam = clear span + effective depth, or clear span + half the sum of support widths, whichever is smaller; effective cover is measured to the centre of the main bar.

Brick classification (IS 1077): first class has compressive strength ≥ 10 N/mm², water absorption ≤ 20% (first class ≤ 20%, second class ≤ 22%); standard brick size 190×90×90 mm with 10 mm mortar gives a 200×100×100 mm module.

Levelling: rise = backsight − foresight; reduce level of a point = height of instrument − intermediate or fore sight; arithmetic check ΣBS − ΣFS = last RL − first RL.

Indian Railways zones: 18 zones plus the Kolkata Metro; the first railway line in India ran from Bombay (Bori Bunder) to Thane in 1853, a distance of 34 km.

Constitutional facts: the Preamble was amended by the 42nd Amendment (1976) adding 'socialist', 'secular' and 'integrity'; Fundamental Duties were added by the 42nd Amendment on the recommendation of the Swaran Singh Committee.

Articles to remember: Article 14 (equality before law), Article 21 (life and personal liberty), Article 32 (writs, called the heart and soul of the Constitution by Ambedkar), Article 356 (President's Rule), Article 370 (abrogated in 2019).

Indian geography: the Tropic of Cancer passes through 8 states; the Western Ghats are older than the Himalayas; the Deccan Plateau is bounded by the Satpura range to the north and the Western and Eastern Ghats on the flanks.

Railway production units: Chittaranjan Locomotive Works (electric locomotives), Diesel Locomotive Works Varanasi, Integral Coach Factory Perambur, Rail Wheel Factory Yelahanka, Rail Coach Factory Kapurthala.

Research organisations: DRDO (defence), ISRO (space, founded 1969, HQ Bengaluru), BARC (atomic energy, Mumbai), CSIR (scientific and industrial research), ICAR (agricultural research).

Economic terms: repo rate is the rate at which RBI lends to banks; reverse repo absorbs liquidity; CRR is the cash reserve ratio; SLR is the statutory liquidity ratio; fiscal deficit = total expenditure − total receipts excluding borrowings.

Awards and institutions: Bharat Ratna is the highest civilian award (instituted 1954); the RBI was established in 1935 and nationalised in 1949; NITI Aayog replaced the Planning Commission in 2015.

Newton's second law F = ma; momentum p = mv; impulse = change in momentum; for a body on an incline, the component along the plane is mg sinθ and the normal reaction is mg cosθ.

Work-energy theorem: work done = change in kinetic energy; kinetic energy = ½mv²; potential energy near the surface = mgh; power = work/time = F·v.

Hooke's law: stress = Young's modulus × strain; for a wire, extension ΔL = FL/(AE). Young's modulus is defined only for the elastic region of the stress-strain curve.

Ohm's law V = IR; series resistance R = R1 + R2; parallel 1/R = 1/R1 + 1/R2; electrical power P = VI = I²R = V²/R; energy in kWh = power in kW × time in hours.

Optics: mirror formula 1/f = 1/v + 1/u, lens formula 1/f = 1/v − 1/u; power of a lens in dioptres = 1/f (metres); a convex lens has positive power and converges light.

Thermodynamics: first law ΔQ = ΔU + ΔW; work in an isothermal process = nRT ln(V2/V1); the efficiency of a Carnot engine = 1 − T2/T1 with temperatures in kelvin.

Periodic trends: atomic radius decreases left to right across a period and increases down a group; ionisation energy and electronegativity increase across a period; metallic character increases down a group.

Chemical basics: pH = −log[H⁺]; one mole contains 6.022×10²³ particles; molarity = moles of solute per litre of solution; oxidation is loss of electrons, reduction is gain (OIL RIG).

Common compounds and their formulas: quicklime CaO, slaked lime Ca(OH)₂, washing soda Na₂CO₃·10H₂O, baking soda NaHCO₃, plaster of Paris CaSO₄·½H₂O, blue vitriol CuSO₄·5H₂O.

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

Number systems: binary uses base 2, octal base 8, decimal base 10, hexadecimal base 16; hexadecimal digits 10–15 are written A–F.

Logic gates: AND outputs 1 only when all inputs are 1; OR outputs 1 when any input is 1; NAND and NOR are universal gates because any other gate can be built from them.

Shortcut keys: Ctrl+C copy, Ctrl+V paste, Ctrl+X cut, Ctrl+Z undo, Ctrl+Y redo, Ctrl+S save, Ctrl+P print, Alt+F4 close the active window, F5 refresh.

Software categories: an operating system (Windows, Linux, macOS) manages hardware and provides services to programs; application software (MS Word, Excel, AutoCAD) performs user tasks.

MS Excel: a formula begins with '='; $A$1 is an absolute reference, A1 a relative reference; SUM, AVERAGE, MAX, MIN and IF are common functions; a cell range is written A1:B10.

Networking: an IP address identifies a device on a network; IPv4 is 32-bit and IPv6 is 128-bit; HTTP/HTTPS are web protocols, FTP transfers files, SMTP sends mail and POP3/IMAP receive it.

Computer generations: first generation used vacuum tubes, second transistors, third integrated circuits, fourth microprocessors, fifth artificial intelligence; ENIAC was a first-generation machine.

File extensions: .docx Word document, .xlsx Excel workbook, .pptx PowerPoint, .pdf portable document, .dwg AutoCAD drawing, .exe executable, .jpg/.png images.

Air pollutants and standards: particulate matter is classified by aerodynamic diameter as PM10 (≤10 µm) and PM2.5 (≤2.5 µm); PM2.5 penetrates deeper into the lungs and is more harmful.

Major air pollutants: carbon monoxide (incomplete combustion), sulphur dioxide and nitrogen oxides (acid rain precursors), ozone at ground level (photochemical smog), and lead.

BOD is the oxygen consumed by microorganisms to oxidise organic matter in a water sample, usually measured over 5 days at 20 °C (BOD5); COD measures chemical oxidation and is always higher than BOD for the same sample.

Water quality: dissolved oxygen below about 4 mg/L stresses aquatic life; pH of normal water is about 6.5–8.5; eutrophication is nutrient enrichment causing algal blooms and oxygen depletion.

Noise units and limits: sound is measured in decibels (dB), an A-weighted scale (dB(A)) is used for environmental noise; industrial zone daytime limit under Indian ambient noise standards is 75 dB(A).

The 3R hierarchy is Reduce > Reuse > Recycle; composting and vermicomposting are aerobic biological treatment methods for organic solid waste.

Greenhouse gases and their main sources: CO₂ (fossil fuel burning), CH₄ (livestock, paddy fields, landfills), N₂O (fertilisers), plus fluorinated gases; CO₂ has the largest share of anthropogenic emissions.

Pollution control devices: electrostatic precipitators and fabric filters remove particulates; catalytic converters reduce CO, HC and NOx in vehicle exhaust; scrubbers remove SO₂ from flue gas.

Environmental law and bodies: the Environment (Protection) Act 1986, Water Act 1974, Air Act 1981, and the CPCB (Central Pollution Control Board) with SPCBs at state level.

Scaling: if a map or drawing has a scale of 1:50, a measured 40 mm on the drawing represents 2.0 m on the ground; convert units before applying the scale factor.

Surveying computations: for a chain line, the perpendicular offset from a right angle can be checked by the 3-4-5 rule (a triangle with sides 3, 4 and 5 units is right-angled).

Quantity estimation: volume of a rectangular footing = length × breadth × depth; volume of a trapezoidal trench = ((top width + bottom width)/2) × depth × length.

Slope and gradient: gradient = vertical rise / horizontal distance; a 1 in 40 slope over 20 m gives a rise of 0.5 m; convert percentages to ratios by dividing 100 by the percentage.

Material quantities: dry volume of mortar or concrete is about 1.30–1.54 times the wet volume; cement bags per cubic metre of 1:2:4 concrete are computed from the dry-volume method.

Steel and weight: unit weight of steel = d²/162 kg/m for bar diameter d in mm; a 12 mm bar therefore weighs about 0.89 kg/m.

Drawing conventions: first-angle projection places the top view below the front view; third-angle projection places the top view above the front view; hidden edges are shown by dashed lines.

Measurement units: 1 hectare = 10,000 m²; 1 m³ = 1,000 litres; 1 acre ≈ 4,047 m²; 1 quintal = 100 kg; 1 km/h = 5/18 m/s.

Work and rate problems: if A finishes a job in x days and B in y days, together they take xy/(x + y) days; the same rate logic applies to labour-output problems in construction estimates.