NPCIL Scientific Assistant cheat sheet

Newton's second law: F = ma; momentum p = mv; impulse J = FΔt = Δp.

Work-energy theorem: W_net = ΔK = ½mv² − ½mu²; power P = Fv cosθ.

Kinematic equations for constant acceleration: v = u + at; s = ut + ½at²; v² = u² + 2as.

Ohm's law: V = IR; resistors in series R_eq = R₁ + R₂ + …; in parallel 1/R_eq = 1/R₁ + 1/R₂ + ….

Lens/mirror formula: 1/f = 1/v − 1/u (sign convention); magnification m = v/u.

Photoelectric effect: E = hf = hc/λ; work function φ = hf₀; stopping potential eV₀ = hf − φ.

Half-life: N = N₀(1/2)^(t/T½); decay constant λ = ln2 / T½; activity A = λN.

Ideal gas law: PV = nRT; average kinetic energy per molecule = (3/2)kT.

Coulomb's law: F = k q₁q₂/r², k ≈ 9×10⁹ N·m²/C²; electric field E = F/q.

Mole concept: 1 mol = 6.022×10²³ particles; molar mass in g/mol; n = m/M.

Molarity M = moles solute / liters solution; molality m = moles solute / kg solvent.

pH = −log[H⁺]; pOH = −log[OH⁻]; pH + pOH = 14 at 25 °C.

Ideal gas equation: PV = nRT; R = 0.0821 L·atm/(mol·K) or 8.314 J/(mol·K).

Balancing redox: balance atoms other than O and H, then O with H₂O, H with H⁺, charge with e⁻.

Le Chatelier's principle: increasing pressure shifts equilibrium toward fewer gas moles.

Periodic trends: atomic radius decreases across a period, increases down a group; electronegativity increases across, decreases down.

First law of thermodynamics: ΔU = q + w; for ideal gas w = −PΔV at constant pressure.

Quadratic formula: x = [−b ± √(b² − 4ac)] / (2a); discriminant D = b² − 4ac determines root nature.

Sum of n terms of AP: S_n = n/2 [2a + (n−1)d]; GP: S_n = a(1 − rⁿ)/(1 − r), r ≠ 1.

Derivative rules: d/dx(xⁿ) = nxⁿ⁻¹; product rule (uv)' = u'v + uv'; chain rule dy/dx = dy/du · du/dx.

Integral: ∫xⁿ dx = xⁿ⁺¹/(n+1) + C, n ≠ −1; ∫eˣ dx = eˣ + C; ∫1/x dx = ln|x| + C.

Trigonometric identities: sin²θ + cos²θ = 1; sin2θ = 2 sinθ cosθ; cos2θ = 1 − 2sin²θ.

Binomial theorem: (a+b)ⁿ = Σ C(n,k) aⁿ⁻ᵏ bᵏ; general term T_{k+1} = C(n,k) aⁿ⁻ᵏ bᵏ.

Probability: P(A∪B) = P(A) + P(B) − P(A∩B); P(A|B) = P(A∩B)/P(B).

Logarithm rules: log(ab) = log a + log b; log(a/b) = log a − log b; log aⁿ = n log a.

Area under curve y = f(x) from a to b: ∫ₐᵇ f(x) dx; volume of revolution V = π∫ₐᵇ y² dx.

Subject-verb agreement: singular subject takes singular verb; compound subjects joined by 'and' take plural verb.

Articles: 'a' before consonant sounds, 'an' before vowel sounds; 'the' for specific or unique items.

Tenses: present perfect (has/have + past participle) for past actions with present relevance.

Active to passive: object becomes subject; verb becomes be + past participle; agent introduced by 'by'.

Direct to indirect speech: change pronouns, tense backshift, and time/place words (now → then, here → there).

Comprehension strategy: identify main idea, supporting details, inference, and tone; eliminate options not supported by passage.

Common error: 'one of the + plural noun + singular verb' (e.g., One of the boys is absent).

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

Synonyms/antonyms: use context clues; prefix/suffix meanings (un-, -less, -ful) help deduce meaning.

Indian Constitution: adopted 26 Nov 1949, enforced 26 Jan 1950; Dr. B.R. Ambedkar chaired Drafting Committee.

Fundamental Rights are in Part III (Articles 12–35); Fundamental Duties in Part IVA (Article 51A).

NPCIL was incorporated in 1987 under the Companies Act; operates India's nuclear power reactors.

India's three-stage nuclear programme: PHWR (natural U), Fast Breeder (Pu), Thorium-based reactors.

Important Indian nuclear plants: Tarapur (Maharashtra), Rawatbhata (Rajasthan), Kalpakkam (Tamil Nadu), Kudankulam (Tamil Nadu), Kakrapar (Gujarat).

National awards: Bharat Ratna (highest civilian), Padma Vibhushan, Padma Bhushan, Padma Shri.

Indian space organisation ISRO founded 1969; headquarters Bengaluru; Chandrayaan-3 landed near lunar south pole in 2023.

World organisations: UN HQ New York; IAEA HQ Vienna; WHO HQ Geneva; UNESCO HQ Paris.

Indian currency symbol ₹ designed by D. Udaya Kumar; adopted in 2010.

IAEA safeguards verify nuclear material not diverted for weapons; India has an Additional Protocol with IAEA.

Nuclear Suppliers Group (NSG) controls nuclear exports; India received a waiver in 2008.

Paris Agreement (2015) aims to limit global warming to well below 2 °C, preferably 1.5 °C.

India's net-zero target year is 2070, announced at COP26 Glasgow.

Nuclear Liability Act (2010) in India: operator liable up to ₹1,500 crore; supplier liability limited.

AERB (Atomic Energy Regulatory Board) is India's nuclear safety regulator, headquartered in Mumbai.

Department of Atomic Energy (DAE) founded in 1954; oversees BARC, NPCIL, and other units.

Global nuclear capacity: about 440 operable power reactors worldwide; USA, France, China, Russia are major producers.

Indian government schemes: PM-KUSUM for solar pumps; UJALA for LED bulbs; both promote energy efficiency.

Number series: check differences, ratios, squares/cubes, or alternating patterns before assuming a rule.

Coding-decoding: letter positions A=1 … Z=26; reverse position = 27 − position; apply shift consistently.

Blood relations: draw a family tree; use + for male, − for female; vertical for generations, horizontal for siblings/spouses.

Syllogism: use Venn diagrams; 'All A are B' does not imply 'All B are A'; 'Some' means at least one.

Direction sense: fix north up; right turn = 90° clockwise; left turn = 90° counterclockwise; track net displacement.

Seating arrangement: for circular arrangement facing center, left = clockwise, right = counterclockwise.

Analogy: identify relationship type (part-whole, cause-effect, synonym, worker-tool) before choosing option.

Series completion: look for two interleaved series when single pattern fails.

Statement-assumption: assumption is unstated but necessary for statement; do not add outside knowledge.

Percentage: x% of y = (x/100)y; percentage change = (new − old)/old × 100.

Profit/loss: profit% = (SP − CP)/CP × 100; discount% = (MP − SP)/MP × 100.

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

Time-speed-distance: distance = speed × time; average speed = total distance / total time (not average of speeds).

Work: if A can do work in x days, 1 day's work = 1/x; combined rate = 1/x + 1/y.

Ratio and proportion: if a:b = c:d then ad = bc; divide a quantity in ratio m:n as (m/(m+n)) × total.

Averages: average = sum / count; if each item increases by k, average increases by k.

Permutation/combination: nPr = n!/(n−r)!; nCr = n!/(r!(n−r)!); nC0 = 1.

Mensuration: area circle = πr²; volume cylinder = πr²h; surface area sphere = 4πr².

CPU components: ALU (arithmetic/logic), control unit, registers; clock speed in GHz.

Memory hierarchy: registers > cache > RAM > secondary storage; RAM is volatile, ROM non-volatile.

OS functions: process management, memory management, file system, device I/O, security.

Number systems: binary base 2, octal 8, decimal 10, hexadecimal 16; convert by repeated division or grouping bits.

MS Word shortcut: Ctrl+C copy, Ctrl+V paste, Ctrl+Z undo, Ctrl+S save; Excel: =SUM(A1:A10).

Networking: IP address identifies device; IPv4 32-bit, IPv6 128-bit; DNS resolves domain names to IP.

Cyber safety: use strong unique passwords, enable 2FA, avoid clicking unknown links, keep software updated.

File extensions: .docx Word, .xlsx Excel, .pptx PowerPoint, .pdf portable document, .exe executable.

Database basics: table = rows (records) + columns (fields); primary key uniquely identifies a record.

ALARA principle: keep radiation exposure As Low As Reasonably Achievable, considering economic and social factors.

Three basic protection measures: time (minimize), distance (maximize, dose ∝ 1/r²), shielding (lead, concrete, water).

Dose limits (ICRP/IAEA): occupational 20 mSv/year averaged over 5 years (max 50 mSv in any one year); public 1 mSv/year.

Radiation units: absorbed dose gray (Gy) = J/kg; equivalent dose sievert (Sv) = Gy × radiation weighting factor.

Personal dosimeters: TLD (thermoluminescent), film badge, OSL; worn at chest level; record cumulative dose.

Contamination control: use PPE, frisk hands/feet, change gloves; separate clean and active zones.

Radiation warning symbol: magenta trefoil on yellow background; indicates ionizing radiation hazard.

Emergency: evacuate, secure area, report to radiation safety officer; do not eat/drink in controlled areas.

Half-value layer (HVL): thickness of material that reduces radiation intensity to half; use to design shielding.

Nuclear fission: heavy nucleus (U-235) splits into lighter nuclei, releasing energy and 2–3 neutrons; chain reaction sustained by k ≥ 1.

Moderator slows neutrons (heavy water, light water, graphite); control rods absorb neutrons (boron, cadmium).

Pressurized Heavy Water Reactor (PHWR): uses natural uranium fuel and heavy water moderator/coolant; common in India.

Defence-in-depth: multiple independent barriers (fuel cladding, pressure boundary, containment) prevent release.

Industrial safety: use PPE (helmet, goggles, gloves, safety shoes); follow lockout/tagout for maintenance.

Fire safety: PASS technique for extinguishers - Pull, Aim, Squeeze, Sweep; know classes A, B, C, D, K.

Hazard communication: SDS (Safety Data Sheet) gives chemical properties, hazards, first-aid, and handling.

Emergency preparedness: know evacuation routes, assembly points, and alarm signals at the site.

Radiation monitoring: area monitors and survey meters (Geiger-Müller, ionization chamber) check dose rates.