KPTCL AE/JE cheat sheet

Transformer EMF equation: E = 4.44 f N Φm; the 4.44 constant equals 2π/√2 and applies to sinusoidal flux only.

Three-phase power: P = √3 VL IL cos φ for balanced loads; delta line current is √3 times phase current, star line voltage is √3 times phase voltage.

Synchronous speed Ns = 120f/P rpm; slip s = (Ns − Nr)/Ns, and rotor frequency = s·f.

For a DC shunt generator, terminal voltage V = E − Ia·Ra; shunt field current is V/Rsh and armature current = load current + field current.

Thevenin resistance is found by killing all independent sources (voltage sources shorted, current sources opened); dependent sources stay active.

Resonance in a series RLC circuit occurs at f = 1/(2π√(LC)); at resonance impedance is purely resistive and equals R.

Per-unit quantity = actual value ÷ base value; base impedance Zbase = (kVbase)²/MVAbase for three-phase systems.

A 1-phase induction motor is not self-starting because the pulsating field splits into equal forward and backward rotating fields; a capacitor provides the phase split.

Slump test (IS 1199) measures workability; typical ranges: 25–75 mm for normal RCC, 75–125 mm for heavily reinforced sections.

M25 concrete means characteristic compressive strength of 25 N/mm² at 28 days measured on 150 mm cubes; target mean strength = fck + 1.65·standard deviation.

Flexural formula: M/I = σ/y = E/R; section modulus Z = I/ymax and bending stress σ = M/Z.

For a simply supported beam with central point load W and span L: maximum BM = WL/4 and maximum deflection = WL³/(48EI).

Density of water = 1000 kg/m³ = 9.81 kN/m³; hydrostatic pressure at depth h is ρgh and acts at h/3 above the base on a vertical surface.

Degree of saturation S = (w·G)/e; dry unit weight γd = γ/(1 + w) and γd = (G·γw)/(1 + e).

One bag of cement = 50 kg = 0.035 m³ volume; nominal concrete mix 1:2:4 refers to cement:sand:coarse aggregate by volume.

Levelling: reduced level of a point = height of instrument − staff reading; height of instrument = known RL + backsight reading.

Carnot efficiency η = 1 − TL/TH (absolute temperatures); no real engine between the same reservoirs can exceed it.

Otto cycle efficiency η = 1 − 1/r^(γ−1), where r is compression ratio; Diesel cycle efficiency also depends on cut-off ratio ρ.

First law for a closed system: Q − W = ΔU; for steady flow: q − w = Δh + ΔKE + ΔPE.

Continuity equation A1V1 = A2V2 for incompressible flow; Bernoulli's equation p/ρg + V²/2g + z = constant along a streamline.

Reynolds number Re = ρVD/μ; laminar pipe flow below Re ≈ 2000, turbulent above ≈ 4000, transition in between.

Stress σ = F/A and strain ε = ΔL/L; Young's modulus E = σ/ε in the elastic region, and Hooke's law holds up to the proportional limit.

Torsion of a circular shaft: τ/r = T/J = Gθ/L; maximum shear stress occurs at the outer surface.

For a single-stage impulse turbine, maximum blade efficiency occurs when blade speed ratio u/V1 = cos α / 2.

In an ideal op-amp, virtual short means V+ = V− and input currents are zero; inverting gain = −Rf/Rin, non-inverting gain = 1 + Rf/Rin.

Barkhausen criterion for oscillation: loop gain magnitude = 1 and total phase shift = 0° or 360° at the oscillation frequency.

For a BJT, IC = βIB and IE = (β + 1)IB; the transistor is in saturation when VCE ≈ 0.2 V and both junctions are forward biased.

Nyquist rate = 2 × highest signal frequency; sampling below this causes aliasing, which an anti-aliasing low-pass filter prevents.

Shannon capacity C = B·log2(1 + S/N); doubling bandwidth or increasing SNR in dB raises capacity.

AM bandwidth = 2fm; FM uses Carson's rule BW ≈ 2(Δf + fm), and FM has better noise immunity than AM.

A 4:1 multiplexer needs 2 select lines; a 3-to-8 decoder has 3 inputs and 8 outputs with one active output per code.

De Morgan's laws: (A·B)' = A' + B' and (A + B)' = A'·B'; NAND and NOR gates are each functionally complete.

Karnataka was formed on 1 November 1956 under the States Reorganisation Act, initially named Mysore State and renamed Karnataka on 1 November 1973.

Karnataka has 31 districts; Bengaluru is the capital, and the state legislature is bicameral (Legislative Assembly and Legislative Council).

Karnataka's state animal is the elephant, state bird the Indian roller (neelakanta), state tree sandalwood, and state flower lotus.

Karnataka rivers: Krishna and its tributaries (Bhima, Tungabhadra, Ghataprabha, Malaprabha) flow east; Cauvery rises at Talakaveri in Kodagu.

Jog Falls on the Sharavathi river in Shivamogga district is one of India's highest plunge waterfalls; the Sharavathi valley hosts major hydel stations.

National institutions in Karnataka include ISRO headquarters and ISTRAC in Bengaluru, DRDO labs, and the Indian Institute of Science (founded 1909).

The Constitution of India came into force on 26 January 1950; the President is the constitutional head and the Prime Minister heads the real executive.

Karnataka's major industries include IT services, aerospace, biotech, and coffee; Karnataka is India's largest coffee-producing state.

Subject-verb agreement: a singular subject takes a singular verb; phrases between subject and verb do not change the verb number.

Use 'fewer' with countable nouns and 'less' with uncountable nouns; 'amount' pairs with uncountable, 'number' with countable.

Active to passive: object becomes subject, verb becomes be + past participle, and the agent is introduced by 'by'.

Reported speech shifts tense one step back (present to past) unless the reporting verb is in the present or the statement is a universal truth.

Choose 'who' for subject position, 'whom' for object position, and 'whose' for possession in relative clauses.

Idiom meaning check: 'to bite the bullet' = to endure a difficult situation bravely; 'once in a blue moon' = very rarely.

For cloze and error-spotting, test each option against the preposition or article required by the surrounding word, not by sound alone.

Antonym/synonym questions: confirm the part of speech first, then match the sense of the word in context, not its most common meaning.

Kannada script derives from the Kadamba/Brahmi lineage and has 49 letters in the standard alphabet: 14 vowels (swaragalu) and 35 consonants (vyanjanagalu).

Kannada is a Dravidian language; the earliest available literary work is Kavirajamarga (c. 850 CE) attributed to Srivijaya under Rashtrakuta patronage.

Pampa, Ranna, and Ponna are the three gems (ratnatrayaru) of Kannada literature; Pampa's Vikramarjuna Vijaya is a classic.

Kannada cases (vibhaktis) number eight, including nominative, accusative, instrumental, dative, ablative, genitive, locative, and vocative.

Kannada is an agglutinative, subject-object-verb (SOV) language; verbs agree with the subject in person, number, and gender.

Jnanpith awardees writing in Kannada include Kuvempu, D. R. Bendre, Shivaram Karanth, Masti Venkatesha Iyengar, V. K. Gokak, U. R. Ananthamurthy, Girish Karnad, and Chandrashekhara Kambara.

Kannada Rajyotsava is celebrated on 1 November, marking the unification of Kannada-speaking areas in 1956.

Sandhi in Kannada joins words with sound changes; common types include swara sandhi and vyanjana sandhi, as in 'mane + alli' becoming 'maneyalli'.

Percentage change = (new − old)/old × 100; successive changes of a% and b% give net change a + b + ab/100.

Simple interest SI = PRT/100; compound interest amount A = P(1 + R/100)^T, and CI = A − P.

Speed = distance/time; for a train crossing a platform, total distance = train length + platform length.

Work: if A alone takes x days and B alone y days, together they take xy/(x + y) days.

Profit% = (SP − CP)/CP × 100; if an article is sold at a discount d% on marked price, SP = MP(1 − d/100).

Average = sum of observations ÷ number of observations; for an arithmetic progression, average = (first + last)/2.

nPr = n!/(n − r)! and nCr = n!/[r!(n − r)!]; nCr = nC(n−r).

Ratio and mixture: alligation rule gives ratio of quantities = (mean − cheaper) : (dearer − mean).

In a series of numbers, check differences, then ratios, then alternating sub-series before assuming a polynomial pattern.

Coding-decoding: map letter positions A = 1 to Z = 26 and test shifts; also check reverse alphabet positions (A = 26, Z = 1).

Blood relations: draw a family tree with gender symbols; 'maternal uncle' is mother's brother, 'paternal aunt' is father's sister.

Direction sense: net displacement uses Pythagoras when movements are perpendicular; final facing direction depends on cumulative turns.

Syllogism: a conclusion is valid only if it holds in every possible Venn diagram of the premises; 'some' and 'no' statements need careful overlap checks.

Seating arrangement: fix the most constrained person first, then place others relative to that anchor.

Odd-one-out: identify the shared property (prime, perfect square, cube, divisibility) before choosing the exception.

Calendar: a normal year shifts the day of the week by 1, a leap year by 2; 100 years shift by 5 odd days, 400 years by 0.