BHEL Supervisor Trainee cheat sheet

Mechanical: for a simply supported beam with central point load W and span L, maximum bending moment = WL/4 and maximum deflection = WL³/(48EI); for uniformly distributed load w per unit length, M(max) = wL²/8 and δ(max) = 5wL⁴/(384EI).

Mechanical: thermal stress in a fully constrained bar = α·ΔT·E; it is independent of bar length and cross-section, since free expansion α·ΔT·L is fully suppressed.

Electrical: for a three-phase balanced load, P = √3·V_L·I_L·cos φ; delta connection gives I_L = √3·I_phase and V_L = V_phase, star connection gives V_L = √3·V_phase and I_L = I_phase.

Electrical: transformer EMF equation E = 4.44·f·N·Φ_max; the 4.44 constant arises from the RMS value of a sinusoidal flux wave (form factor 1.11 × 2π/√2).

Electronics: ideal op-amp rules - no current into inputs (infinite input impedance) and zero differential input voltage (infinite open-loop gain); inverting gain = −R_f/R_in, non-inverting gain = 1 + R_f/R_in.

Civil: for M20 concrete and Fe415 steel, design stress values are f_ck = 20 N/mm², f_y = 415 N/mm²; working-stress method modular ratio m = 280/(3σ_cbc) governs composite-section analysis.

Chemical: conversion X = (moles fed − moles leaving)/moles fed; for a first-order batch reactor, −ln(1 − X) = k·t, so time to 90% conversion equals 2.303/k.

Metallurgy: the iron–carbon diagram has eutectoid at 0.76% C and 723 °C (pearlite), eutectic at 4.3% C and 1147 °C (ledeburite); quenching forms martensite, a supersaturated body-centred tetragonal phase.

Percentage change shortcut: successive changes of a% and b% give a net change of a + b + ab/100 percent; a 20% rise then 20% fall leaves a net 4% decrease.

Profit and loss: if an article is sold at a loss of x%, the cost price = SP × 100/(100 − x); two articles sold at equal price with equal percentage gain and loss always give a net loss of (x/100)² percent.

Simple interest SI = P·R·T/100; compound interest CI = P[(1 + R/100)^T − 1]; for 2 years the CI − SI difference equals P(R/100)².

Time–speed–distance: if speed ratio is a:b, time ratio for fixed distance is b:a; a train of length L crossing a platform of length P at speed v takes (L + P)/v seconds.

Mixtures and alligation: ratio of quantities = (mean price − cheaper price) : (dearer price − mean price); repeated replacement of x litres from V litres leaves V(1 − x/V)^n of the original liquid.

Averages: if every value is increased by k, the average rises by k; if all values are multiplied by k, the average is multiplied by k. Average of first n natural numbers = (n + 1)/2.

Work and time: if A does work in a days and B in b days, together they take ab/(a + b) days; efficiency is inversely proportional to time taken.

Permutation and combination: nPr = n!/(n − r)! and nCr = n!/[r!(n − r)!]; nCr = nC(n − r), and the number of diagonals of an n-sided polygon is n(n − 3)/2.

Number series checks run in order: difference, then ratio, then alternating/prime-square patterns, then two interleaved series at odd and even positions.

Coding–decoding: letter positions A = 1 … Z = 26; opposite-letter pairs sum to 27 (A–Z, B–Y, C–X), which resolves reversal-based codes quickly.

Blood relations: draw a family tree using fixed symbols - vertical line for parent–child, horizontal line for siblings/spouse - and mark gender before answering.

Syllogism: a conclusion follows only if it is true in every possible Venn diagram of the premises; 'some A are B' and 'no A is B' cannot both be true, but 'some A are not B' is compatible with 'all A are B' only when A is non-empty.

Seating arrangement: fix the definite clue first, then apply left/right and facing-direction reversals; in a circle facing the centre, 'left' means clockwise.

Direction sense: use a coordinate grid; net displacement after turns is the vector sum, and the shortest distance is the hypotenuse from the start point.

Analogy and classification: test the relation as cause–effect, part–whole, worker–tool, or unit–quantity before choosing an option; odd-one-out is decided by a single shared attribute.

Clocks and calendars: hands coincide 11 times in 12 hours; angle between hands = |30H − 5.5M| degrees; in a non-leap year 1 January and 31 December fall on the same weekday.

Constitutional facts: the Constitution was adopted on 26 November 1949 and came into force on 26 January 1950; the Preamble was amended by the 42nd Amendment Act, 1976, which added 'socialist', 'secular' and 'integrity'.

Fundamental Rights occupy Part III (Articles 12–35); the Right to Constitutional Remedies (Article 32) was called the 'heart and soul of the Constitution' by Dr B. R. Ambedkar.

Indian polity offices: the President is elected by an electoral college under Article 54; the Comptroller and Auditor General is appointed under Article 148 and holds office for six years or up to 65 years of age.

Geography: the Tropic of Cancer passes through eight Indian states; the Standard Meridian of India is 82°30′ E, giving IST = UTC + 5:30.

Economy: the Reserve Bank of India was established on 1 April 1935 and nationalised in 1949; repo rate is the rate at which RBI lends to banks against government securities.

Science basics: SI unit of force is the newton, of pressure the pascal, of power the watt; the speed of light in vacuum is about 3 × 10⁸ m/s.

National institutions: ISRO is headquartered at Bengaluru, BHEL at New Delhi, and the Atomic Energy Commission was constituted in 1948 with Homi J. Bhabha as its first chairman.

Awards and days: the Bharat Ratna is India's highest civilian award, instituted in 1954; National Safety Day is observed on 4 March, and Engineers' Day on 15 September (birth anniversary of M. Visvesvaraya).

Subject–verb agreement: a singular subject takes a singular verb; with 'either…or' and 'neither…nor' the verb agrees with the nearer subject; 'each', 'every', 'everyone' and 'nobody' are singular.

Articles: 'a' before consonant sounds, 'an' before vowel sounds (an hour, a university); 'the' is used for superlatives, unique objects, rivers, ranges and ordinal numbers.

Prepositions of time: 'in' for months, years and long periods; 'on' for days and dates; 'at' for clock times and fixed points (at noon, at night).

Tenses: present perfect (has/have + past participle) is used for past actions with present relevance and with 'since'/'for'; simple past is used with a definite past time marker.

Active to passive: object becomes subject, verb becomes be + past participle, and the agent is introduced by 'by'; tense of the auxiliary must match the original tense.

Direct to indirect speech: present tense in the reported clause shifts one step back (present → past), 'this' → 'that', 'today' → 'that day', and 'now' → 'then'.

Common error traps: 'one of the boys is' (singular verb), 'furniture/information/advice' are uncountable (no plural -s), and 'discuss about' is wrong because 'discuss' is transitive.

Vocabulary: synonym pairs to know - 'abate' (reduce), 'lucid' (clear), 'frugal' (thrifty), 'obstinate' (stubborn); antonym pairs - 'benevolent'/'malevolent', 'transparent'/'opaque'.

Tolerance and fits: clearance fit has minimum clearance ≥ 0, interference fit always has negative clearance, transition fit may give either; hole basis system (H) is preferred because holes are harder to machine to size than shafts.

Limits: tolerance = upper limit − lower limit; fundamental deviation fixes the position of the tolerance zone relative to the nominal size, while grade (IT01–IT16) fixes its width.

Measurement: least count of a vernier calliper = 1 MSD − 1 VSD; for a micrometer, least count = pitch/number of circular scale divisions (typically 0.5 mm/50 = 0.01 mm).

Welding symbols and joints: butt joints use square, V, U or J grooves; fillet welds are shown by a triangle on the reference line; a tail of the symbol carries process or specification notes.

Electrical trade practice: earth continuity resistance is measured with an earth tester; insulation resistance is measured by a megger at 500 V for LV installations, and acceptable values are in the megohm range.

Bearings and lubrication: deep-groove ball bearings carry radial and moderate axial loads; in a hydrodynamic journal bearing, oil pressure is generated by shaft rotation in a converging wedge, not by an external pump.

Power plant practice: boiler feedwater is treated to control hardness, dissolved oxygen and pH; blowdown controls dissolved solids, and economiser recovers heat from flue gas before the air preheater.

Drawing reading: first-angle projection places the top view below the front view and the left-side view to the right; in third-angle projection the views are placed on the same side as the observer.

Permit to work: a work permit must state the job, isolation points, validity time and authorised signatories; the permit is issued by the area authority and accepted by the executing agency before work starts, and is closed only after the site is verified safe.

Lockout–tagout: isolate the energy source, lock it, attach a tag naming the holder, and verify zero energy by test; only the person who applied the lock may remove it, except under a documented emergency procedure.

Electrical safety: for low-voltage systems the safe approach distance is 0.3 m and for 11 kV it is 1.5 m (IE Rules); earth the circuit on all phases and test with a voltage detector after isolation.

Confined space entry: test the atmosphere for oxygen (19.5–23.5% by volume), flammable gas and toxic gas before entry; forced ventilation and a standby observer at the entrance are mandatory.

Hot work: gas cutting and welding near flammable material require a fire watch, removal or shielding of combustibles, and a fire extinguisher at the site; hot work is stopped if flammable gas exceeds 10% of LEL.

Personal protective equipment hierarchy: elimination, substitution, engineering control, administrative control, then PPE as the last line of defence; a safety helmet, safety shoes and eye protection are minimum site PPE.

Working at height: fall protection (full-body harness with lanyard to an independent anchor) is required above 1.8 m; scaffolds must be inspected and tagged before use, and guard rails are set at about 1 m height.

First aid and reporting: artificial respiration is given at about 12–15 breaths per minute; every accident, including a near miss, is recorded, and the statutory accident report is submitted to the factory inspector within the prescribed time.