DRDO CEPTAM Tech-A cheat sheet

Percentage change of two successive changes a% then b% equals a + b + ab/100; a rise of 20% then fall of 20% gives a net 4% decrease.

Simple interest SI = PRT/100; compound interest CI = P(1 + R/100)^T − P, and CI exceeds SI by P(R/100)^2 for T = 2.

Speed conversion: 1 km/h = 5/18 m/s; 1 m/s = 18/5 km/h. For equal distances at speeds x and y, average speed = 2xy/(x + y).

Train crossing a pole takes length/speed; crossing a platform of length L takes (train length + L)/speed; same-direction relative speed is the difference of speeds.

Work: if A does a job in a days and B in b days, together they take ab/(a + b) days; combined rate is 1/a + 1/b per day.

Boats: downstream speed = boat + stream, upstream = boat − stream; boat speed = (down + up)/2, stream speed = (down − up)/2.

Profit and loss: SP = CP(1 + profit%/100); successive discounts d1 and d2 give net discount d1 + d2 − d1d2/100.

Permutation vs combination: nPr = n!/(n − r)! (order matters), nCr = n!/[r!(n − r)!] (order does not matter); nC0 = nCn = 1.

Ratio and mixture: alligation gives ratio of quantities = (mean − cheaper) : (dearer − mean); for a two-part mixture the mean price lies between the two component prices.

Letter positions: A = 1 to Z = 26; reverse position = 27 − forward position, so E = 5 forward and 22 reverse.

Coding-decoding: check for constant shift, reversal, position-sum, or alternating shifts before assuming a single rule; verify the rule on every given pair.

Blood relations: draw a family tree using + for male and − for female; vertical lines show parent-child, horizontal lines show spouse or sibling.

Direction sense: net displacement after perpendicular moves uses Pythagoras; final facing direction rotates 90° per right/left turn.

Series completion: test differences, then ratios, then squares/cubes, then alternating or prime-based patterns; two interleaved series are common.

Syllogism: a conclusion follows only if true in every possible Venn arrangement; 'some A are B' does not imply 'some B are not A'.

Clock: angle between hands = |30H − 5.5M| degrees; hands coincide 11 times in 12 hours and are opposite 11 times in 12 hours.

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

SI base units: length metre, mass kilogram, time second, electric current ampere, temperature kelvin, amount mole, luminous intensity candela.

Newton's laws: F = ma; every action has an equal and opposite reaction; a body stays at rest or uniform motion unless a net external force acts.

Ohm's law V = IR; electrical power P = VI = I²R = V²/R; energy consumed in kWh = watts × hours / 1000.

Photosynthesis converts CO2 and water into glucose and oxygen using chlorophyll and light; it occurs in chloroplasts.

Human blood groups follow the ABO and Rh systems; O negative is the universal donor for red cells and AB positive the universal recipient.

Fundamental duties and the Directive Principles are non-justiciable; Fundamental Rights (Part III) are enforceable through writs under Article 32/226.

Indian Constitution came into force on 26 January 1950; Dr B. R. Ambedkar chaired the Drafting Committee of the Constituent Assembly.

Acids turn blue litmus red and have pH below 7; bases turn red litmus blue and have pH above 7; pH 7 is neutral at 25 °C.

DRDO is India's defence research and development agency, headquartered in New Delhi, established in 1958.

Subject-verb agreement: singular subject takes singular verb; 'each, every, either, neither, everyone' are grammatically singular.

Articles: 'a' before consonant sounds, 'an' before vowel sounds (an hour, a university); 'the' for specific or unique references.

Tenses: present perfect (has/have + past participle) links past action to present; past perfect (had + participle) marks the earlier of two past actions.

Active to passive: object becomes subject, verb becomes be + past participle, agent follows 'by'; tense of the original is preserved.

Direct to indirect speech: shift tense one step back, change pronouns to the reporter's perspective, and adjust time/place words (now → then, today → that day).

Common confusions: affect (verb) vs effect (noun); principal (head/main) vs principle (rule); stationary (fixed) vs stationery (writing material).

Idioms: 'at the eleventh hour' means at the last moment; 'to burn the midnight oil' means to study or work late.

One-word substitutions: 'altruist' is a selfless person, 'philanthropist' a charitable donor, 'misanthrope' a hater of mankind.

Error spotting: check preposition after verbs (differ from, comply with, consist of, prefer to) and avoid double comparatives such as 'more better'.

Vernier calliper least count = 1 main scale division − 1 vernier scale division; for 0.02 mm, 49 main divisions equal 50 vernier divisions.

Micrometer least count = pitch / number of circular scale divisions; a 0.5 mm pitch with a 50-division thimble gives 0.01 mm.

Limits and fits: clearance fit always has positive clearance, interference fit always has negative clearance, transition fit may give either.

Drill speed for HSS: N (rpm) = 1000 × cutting speed / (π × drill diameter); cutting speed is in m/min.

Taps: taper tap starts the thread, plug tap continues, bottoming tap finishes to the blind hole bottom; drill size ≈ major diameter − pitch.

Files cut on the forward stroke only; grades are rough, bastard, second cut and smooth, in increasing order of fineness.

Scraping is a hand operation to produce bearing spots on mating surfaces; blue marking compound shows high spots.

Soldering joins below 450 °C, brazing above 450 °C; both rely on capillary action of filler metal without melting the base metal.

ISO tolerance letter case: capital letters denote holes, lowercase letters denote shafts; IT grades 01 to 18 indicate tolerance magnitude.

Ohm's law V = IR; series resistances add (R = R1 + R2 + …), parallel resistances add as reciprocals (1/R = 1/R1 + 1/R2 + …).

Three-phase power P = √3 × VL × IL × cos φ for a balanced load; single-phase P = V × I × cos φ.

Star connection: line current equals phase current, line voltage = √3 × phase voltage. Delta: line voltage equals phase voltage, line current = √3 × phase current.

Transformer EMF equation E = 4.44 f N Φm; turns ratio V1/V2 = N1/N2 = I2/I1 for an ideal transformer.

DC motor back EMF Eb = V − IaRa; torque is proportional to flux × armature current; speed rises when field flux falls.

Fuse rating is chosen above normal current but below cable capacity; earthing provides a low-resistance path to protect persons from shock.

Insulation resistance is measured with a megger; a minimum of 1 MΩ is commonly required for low-voltage installations.

Power factor correction uses capacitors in parallel; kWh is measured by an energy meter, and 1 HP ≈ 746 W.

Induction motor synchronous speed Ns = 120f/P; slip s = (Ns − N)/Ns and rotor frequency = s × supply frequency.

Oxy-acetylene flame types: neutral (ratio about 1:1), oxidising (excess oxygen, for brass), carburising (excess acetylene, for high-carbon steel).

Arc welding electrode polarity: DCEN concentrates heat at the workpiece for deeper penetration; DCEP concentrates heat at the electrode.

Welding defects: porosity from gas entrapment, slag inclusion from poor cleaning, undercut from excessive current, and lack of fusion from low current.

Cutting speed on a lathe V = πDN/1000 m/min; feed is in mm/rev and depth of cut in mm; material removal rate ≈ V × feed × depth.

Taper turning by compound rest suits steep short tapers; the tailstock offset method suits long shallow tapers between centres.

Lathe operations: facing reduces length, turning reduces diameter, knurling forms a rough grip, and boring enlarges an existing internal hole.

Milling: up-milling cutter rotates against the feed, down-milling with the feed; down-milling gives a better finish on rigid machines.

Drilling and reaming: reaming removes little material (about 0.2–0.5 mm) to improve hole accuracy and surface finish.

Carbide tools run at much higher cutting speeds than HSS; HSS retains hardness up to about 600 °C, carbide well beyond that.

Diode: forward biased when anode is positive relative to cathode; silicon barrier potential ≈ 0.7 V, germanium ≈ 0.3 V.

Half-wave rectifier output frequency equals supply frequency; full-wave and bridge rectifiers give twice the supply frequency.

BJT regions: cutoff (both junctions off), active (base-emitter forward, base-collector reverse), saturation (both forward); β = IC/IB.

Op-amp ideal properties: infinite open-loop gain and input impedance, zero output impedance; inverting gain = −Rf/Rin, non-inverting gain = 1 + Rf/Rin.

Boolean algebra: A + A'B = A + B, De Morgan's laws (A·B)' = A' + B' and (A + B)' = A'·B'.

Number systems: binary 1011 = decimal 11 = hex B; 1 byte = 8 bits, 1 KB = 1024 bytes, 1 MB = 1024 KB.

Instrumentation: RTD (Pt-100) measures temperature by resistance change, thermocouple by Seebeck EMF, and strain gauge by piezoresistive change.

Wheatstone bridge balances when R1/R2 = R3/R4; a transducer converts a physical quantity into an electrical signal.

Computer basics: RAM is volatile, ROM is non-volatile; cache is faster than RAM, and an operating system manages hardware, memory and processes.