SJVN JFE & FE cheat sheet

Three-phase power: P = √3·V_L·I_L·cosφ; reactive power Q = √3·V_L·I_L·sinφ; apparent power S = √3·V_L·I_L.

Transformer EMF equation: E = 4.44·f·N·Φ_max; turns ratio a = N1/N2 = V1/V2, and current ratio I1/I2 = N2/N1 for an ideal transformer.

Synchronous speed N_s = 120f/P; slip s = (N_s − N_r)/N_s; rotor frequency f_r = s·f.

DC machine EMF: E = (P·Φ·N·Z)/(60·A), where A = number of parallel paths (2 for lap, 2P for wave winding).

Per-unit quantity = actual value ÷ base value; base impedance Z_base = V_base²/S_base, and per-unit impedance changes with the square of the voltage-base ratio.

Induction motor torque is proportional to slip at low slip and peaks at the breakdown slip; a wound-rotor motor uses external rotor resistance to raise starting torque.

Power system stability: steady-state stability limit of a lossless line is P_max = E·V/X; equal-area criterion decides transient stability.

Mechanical: bending stress σ = M·y/I; torsion τ = T·r/J; Euler buckling load P_cr = π²EI/(L_e)².

Civil concrete mix design: nominal grades M20 = 1:1.5:3, M25 = 1:1:2; water-cement ratio governs strength and durability, lower w/c giving higher strength.

Percentage change rule: a% increase followed by b% decrease gives net change = a − b − (ab/100) percent.

Compound interest: A = P(1 + r/n)^(nt); for two years the CI exceeds SI by P(r/100)².

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

Trains and boats: relative speed adds when moving opposite and subtracts when moving in the same direction; downstream speed = boat + stream.

Number series: check successive differences, then ratios, then alternating or two interleaved series before assuming a polynomial rule.

Coding-decoding: convert letters to positions 1–26 and test constant shifts, reversal (Atbash: position p maps to 27 − p), or positional arithmetic.

Syllogism: two particular premises give no universal conclusion; a conclusion is valid only if true in every Venn diagram satisfying the premises.

Blood relations: draw a family tree with gender markers; vertical lines for generations, horizontal lines for siblings and spouses.

Permutation vs combination: arrangements of r from n use nPr = n!/(n−r)!; selections use nCr = n!/(r!(n−r)!).

Indian power sector: SJVN Ltd is a central public sector enterprise under the Ministry of Power, incorporated in 1988, headquartered at Shimla, Himachal Pradesh.

SJVN's flagship project is the 1,500 MW Nathpa Jhakri Hydro Power Station on the Satluj river in Himachal Pradesh.

Constitutional articles: Article 14 equality before law, Article 19 freedoms, Article 21 life and personal liberty, Article 356 President's rule, Article 370 dealt with Jammu and Kashmir.

Fundamental duties appear in Article 51A, added by the 42nd Amendment Act, 1976; the Fundamental Rights are in Part III.

Subject-verb agreement: a collective noun takes a singular verb when acting as one unit; 'one of the + plural noun' takes a singular verb.

Articles: 'a' before consonant sounds, 'an' before vowel sounds (an hour, a university); 'the' with superlatives, rivers, and unique entities.

Tenses: present perfect (has/have + past participle) for past action with present relevance; simple past with a definite past time marker.

Prepositions: 'since' with a point of time, 'for' with a duration; 'between' for two, 'among' for more than two.

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