Mathematics
Divisibility by 11 — Alternating sum of digits must be 0 or divisible by 11. For 1234: (1+3)-(2+4)=−2, not divisible; for 121: (1+1)−2=0, divisible by 11.
BODMAS trap — Division and Multiplication have equal priority (left-to-right); Addition and Subtraction have equal priority (left-to-right). Don't blindly do all multiplication before division.
Percentage-to-fraction quick converts — 12.5%=1/8, 16.67%=1/6, 20%=1/5, 33.33%=1/3, 62.5%=5/8, 87.5%=7/8. Memorize these for instant calculation without calculator.
Profit-Loss-Discount triangle — SP = MP − Discount = CP + Profit. Always identify which two you have; the third follows. Marked Price (MP) is the tagged price.
CI minus SI for 2 years — Difference = P×(R/100)². For P=1000, R=10%, CI−SI = 1000×0.01 = ₹10. Quick way to find rate or principal.
Speed-Distance-Time triangle — Cover 'S' at top; D and T at bottom. D=S×T, S=D/T, T=D/S. Palm trick: hide what you want, see the formula.
Relative speed — Same direction: subtract speeds; Opposite direction: add speeds. For trains/runners crossing, always identify direction first before calculating time.
Time-Work inverse relationship — If A does work in 10 days, A's 1-day work = 1/10. If A+B together = 1/10+1/15 = 5/30 = 1/6, they finish in 6 days.
Pythagoras triplets — (3,4,5), (5,12,13), (8,15,17), (7,24,25). Multiples also work: (6,8,10), (9,12,15). Saves 30 seconds in geometry/mensuration problems.
Circle mensuration — Circumference = 2πr, Area = πr². For semicircle perimeter add diameter: πr+2r. For arc/sector, use angle/360 as multiplier.
Average = Sum/Count — If average of n numbers increases by x when new number is added, then new number = old average + (n+1)×x.
HCF-LCM product rule — For two numbers A and B: A×B = HCF×LCM. If three values given, find the fourth instantly.
General Intelligence and Reasoning
Alphabet positions (EJOTY) — E=5, J=10, O=15, T=20, Y=25. Every 5th letter. For others: count forward/backward from nearest EJOTY anchor.
Coding-Decoding pattern check — Test first with A→? and Z→? to identify shift/reverse. If A→Z, it's reverse alphabet (A=26, B=25...). Saves trial-error time.
Blood relations: gender trap — Brother/son/father/uncle/nephew are male; Sister/daughter/mother/aunt/niece are female. Cousin/parent/child/sibling can be either—question must specify.
Number series: difference method — Write differences between consecutive terms. If differences don't show pattern, take differences of differences (second-order). Most RRB series break at level 1 or 2.
Syllogism: Venn diagram shortcut — For "All A are B; No B are C" → draw circles. All/No/Some statements translate directly. "No" means non-overlapping circles.
Direction sense: NEWS clockwork — North-East-South-West goes clockwise. Right turn from North = East, Left turn = West. 45° turns give NE, SE, SW, NW.
Analogy odd-one-out — Check relationship type: synonym, antonym, part-whole, tool-worker, genus-species, increasing/decreasing order. Match the relationship pattern first.
Missing number: row-column-diagonal — In 3×3 matrices, check row sums, column sums, diagonal sums, or row products. RRB loves constant sum/product patterns.
General Awareness
Indian Presidents mnemonic (recent) — "RANI Prayed Kindly, More RAM" → RAmaswamy Venkataraman, Narayanan, Kalam, Pratibha Patil, Pranab Mukherjee, Ramnath Kovind, Murmu (Droupadi). Last 7 presidents in order.
Computer generations (5 generations) — Vacuum tubes (1940s), Transistors (1950s), ICs (1960s), Microprocessors (1970s), AI/Parallel (1980s+). Each generation roughly one decade apart.
VIRUS full form — Vital Information Resources Under Siege. Not an acronym officially, but helps remember it's an information/resource attacker.
Bharat Ratna recent (2019-24) — Pranab Mukherjee (2019), Bhupen Hazarika, Nanaji Deshmukh (posthumous, 2019), PV Narasimha Rao, Charan Singh (posthumous, 2024), Karpoori Thakur (posthumous, 2024). Track year-wise.
RAM vs ROM — RAM is Random Access (temporary, volatile, loses data on power-off); ROM is Read-Only (permanent, non-volatile, retains data). RAM=working memory, ROM=permanent storage.
UN Security Council permanent 5 — "FRUC-China" → France, Russia, UK, China, USA. These five have veto power; 10 rotating non-permanent members serve 2-year terms.
Space missions 2023-24 — Chandrayaan-3 (Moon landing, Aug 2023), Aditya-L1 (Sun mission, Sept 2023), Gaganyaan (upcoming manned mission). ISRO's recent headline missions for current affairs.