Mathematics
Divisibility by 11 — Alternating digit sum method: subtract sum of odd-position digits from even-position digits. If result is 0 or divisible by 11, original number is divisible by 11. Example: 121 → (1+1)−2=0, divisible.
BODMAS Trap Awareness — Division and Multiplication have equal priority (left to right), as do Addition and Subtraction. Don't automatically do all multiplication before division. Example: 20÷5×2 = (20÷5)×2 = 8, not 20÷(5×2).
Percentage-Fraction Shortcuts — Memorize: 12.5%=1/8, 16.67%=1/6, 33.33%=1/3, 66.67%=2/3, 87.5%=7/8. Instantly convert percentages to fractions for faster mental calculation in percentage problems.
Time-Distance "DIST" — Distance = Speed × Time. Remember "DIST" where I=multiplication sign. Rearrange: Speed = D/T, Time = D/S. Cover the unknown in D/S×T triangle diagram.
Compound Interest Shortcut — For 2 years: CI−SI = (SI²)/(100×P). The extra interest is simple interest on first year's interest. For quick CI vs SI difference questions.
LCM×HCF Formula — For two numbers: Product of numbers = LCM × HCF. If three values given, find fourth instantly. Example: numbers 12,18 → 12×18 = LCM(36)×HCF(6).
Algebra: (a+b)² Identity — Remember "Square-Twice-Square": a²+2ab+b². Similarly (a−b)²=a²−2ab+b². The middle term is always TWICE the product, commonly forgotten in expansions.
Ratio Multiplication Trick — To compare ratios like A:B=2:3 and B:C=4:5, make B equal. Multiply first by 4, second by 3: A:B:C=8:12:15. Equalize common terms for combined ratios.
Average Addition Formula — When new number added: New Average = Old Average + (Difference/New Total). If 1 person added, divide difference by new count. Saves recalculation time.
Profit Percentage Quick — Profit% = (Profit/CP)×100, Loss% = (Loss/CP)×100. Always divide by COST PRICE, never selling price, unless "Loss on SP" explicitly stated. Common trap in exams.
Mensuration: Circle 2πr — Circumference = 2πr, Area = πr². Remember "Circumference has 2, Area is square." Perimeter formulas have dimension 1, area formulas have dimension 2 (squared terms).
Time-Work: M₁D₁W₂ = M₂D₂W₁ — Men₁×Days₁×Work₂ = Men₂×Days₂×Work₁. Cross-multiply for work-efficiency problems. Add hours: M₁D₁H₁W₂=M₂D₂H₂W₁ for detailed questions.
Logical Reasoning and Mental Ability
Blood Relations: "Mother's Brother" — Maternal uncle = Mama, Paternal uncle = Chacha. Mother's side = maternal, Father's side = paternal. Draw family tree instantly for complex relations; saves confusion.
Direction Sense: NESW Clock — Visualize clock: North=12, East=3, South=6, West=9. Right turn=clockwise, Left=anticlockwise. 90° right from North→East. Helps in quick angle-turn calculations.
Calendar: Odd Days Method — Ordinary year=1 odd day, Leap year=2 odd days. Century years divisible by 400 are leap. Count odd days from reference year to find day of week quickly.
Coding: Position Value A=1 — A=1, B=2...Z=26. For letter-number coding, remember positions. Reverse: Z=26, Y=25...A=1. EJOTY pattern: every 5th letter (E=5, J=10, O=15, T=20, Y=25).
Syllogism: "All-Some-No" Rules — "All A are B" + "All B are C" = "All A are C" (definite). But "Some A are B" gives no definite universal conclusion. At least 1 premise must be universal for universal conclusion.
Clock Angle Formula — Angle = |30H − 6M + M/2|, where H=hour, M=minutes. Hour hand moves 0.5° per minute. At 3:15, angle = |90−90+7.5| = 7.5°. Quick calculation for clock problems.
Dice Opposite Faces — On standard dice: 1-6, 2-5, 3-4 are opposite pairs. Total of opposite faces = 7. If 1,2,3 visible, hidden faces are 6,5,4 respectively.
Alphanumeric Series: +Prime — Common patterns: add prime numbers (2,3,5,7,11), Fibonacci (each = sum of previous two), or alternating operations. Check differences between consecutive terms first.
Ranking: Total = Sum − 1 — If A is 7th from left, 11th from right, Total = 7+11−1 = 17. Subtract 1 because A counted twice. Quick formula for position-based ranking questions.
General Knowledge and General Science
VIBGYOR — Visible light spectrum order: Violet, Indigo, Blue, Green, Yellow, Orange, Red. Wavelength increases, frequency decreases from V to R. Rainbow color sequence from inside to outside.
Vitamin Deficiency ABCD — A=Night blindness, B1=Beriberi, B12=Anemia, C=Scurvy, D=Rickets, E=Sterility, K=Blood clotting issues. Remember by disease initials matching vitamin where possible.
Bharat Ratna Chronology — First recipients (1954): C. Rajagopalachari, Sarvepalli Radhakrishnan, CV Raman. Latest years crucial for current affairs. Sachin Tendulkar first sportsperson (2014). Maximum 3/year allowed.
Budget Terms: "FRED" — Fiscal deficit, Revenue deficit, Effective revenue deficit, Deficit financing. Fiscal deficit = Revenue+Capital deficit. Revenue deficit = Revenue expenditure minus Revenue receipts. Remember hierarchy for budget questions.
Monsoon Months: JJAS — June, July, August, September. Southwest monsoon season in India. Accounts for 75% annual rainfall. Retreat begins September-October. Northeast monsoon: October-December (Tamil Nadu).
Ancient India Dynasties — HaMaGuVa: Harsha (606-647), Maurya (322-185 BCE), Gupta (320-550 CE), Vardhana. Chronological order trick. Add Kushana (1st-3rd century CE) between Maurya-Gupta for completeness.
Freedom Struggle Dates: "42-8-5" — 1942 Quit India, 1947−42=5 years to independence. 1857 First War. 1885 INC founded (57+28=85). 1905 Bengal Partition (85+20). Build timeline from these anchors.
Banking: SLR vs CRR — SLR (Statutory Liquidity Ratio) = banks keep liquid assets (gold, securities). CRR (Cash Reserve Ratio) = cash with RBI only. SLR has flexibility, CRR is pure cash reserve. SLR>CRR typically.
Rajasthan — General Knowledge
Rajasthan Folk Dances: "GhKaChaTe" — Ghoomar (women's, Udaipur), Kalbeliya (snake charmers), Chari (Ajmer water pots), Terah Taali (seated, 13 cymbals), Gair (men's