Mathematics
Divisibility by 11 — Alternating digit sum (add odd positions, subtract even positions); if result is 0 or divisible by 11, number is divisible by 11. E.g., 121: (1+1)–2=0 ✓
Percentage-Fraction Conversions — Memorize: 12.5%=⅛, 16.67%=⅙, 25%=¼, 33.33%=⅓, 37.5%=⅜, 62.5%=⅝, 87.5%=⅞. Saves calculation time in competitive exams instantly.
BODMAS Trap Alert — Division and Multiplication have equal priority (left to right); Addition and Subtraction have equal priority (left to right). 6÷2×3=9, not 1.
Age Problems Key — "n years ago, sum of ages was X" → Subtract n per person from current ages. "After n years" → Add n per person. Track one person's age as variable.
LCM×HCF Formula — For two numbers: LCM × HCF = Product of the two numbers. Use to find missing value when three are given.
Profit/Loss Successive Change — Two successive changes of a% and b%: Net = a + b + (ab/100). For 10% increase then 10% decrease: 10+(-10)+(10×-10/100) = -1%.
Mixture Allegation Cross — Write cheaper and dearer values vertically, mean in middle. Cross-subtract to get ratio. CP ratio = (Dearer–Mean):(Mean–Cheaper). Visual cross method.
Simple Interest Shortcut — SI for n years = (P×R×n)/100. If tripled period, SI triples. Amount = P(1+Rn/100). For comparing rates, use direct proportion.
Compound Interest Doubling — Rule of 72: Years to double ≈ 72/Rate%. At 8%, money doubles in 9 years. At 12%, in 6 years.
Calendar: Odd Days — Leap year=2 odd days; Normal=1 odd day. Century non-leap unless divisible by 400. 1600,2000=leap; 1700,1800,1900=not leap. Count total odd days mod 7.
Clock Angle Formula — At time H:M, angle = |11M/2 – 30H| degrees. If >180°, take 360–angle. At 3:15, angle = |11×15/2 – 90| = 7.5°.
Pipe Filling Efficiency — If A fills in x hours, B in y hours, together = xy/(x+y) hours. Leak empties: subtract its rate as negative efficiency.
General Intelligence and Reasoning
Direction Clockwise Order — "Never Eat Soggy Waffles" for N-E-S-W clockwise. Or "NEWS" with E-W swapped from reading order. Right turn=clockwise 90°, Left=anticlockwise 90°, About=180°.
Opposite Directions Memory — N↔S, E↔W, NE↔SW, NW↔SE. If facing direction X and turn back/about-turn, final direction is opposite of X.
Alphabet Position Trick — A=1, Z=26. For reverse: A=26, Z=1. EJOTY: positions 5,10,15,20,25 (multiples of 5). Letters 1-9 and 19-26 are single consonant clusters.
Coding: Letter Shift Pattern — CAT→DBU means +1 shift. Find the constant (+n or -n) for each letter position. Check if shift varies by position.
Blood Relations Core — Mother's/Father's side: Maternal/Paternal. Sibling's child=Niece/Nephew. Parent's sibling=Uncle/Aunt. Spouse's parents=In-laws. Son's wife=Daughter-in-law.
Series: Difference of Differences — For 2,5,10,17,26: differences are 3,5,7,9 (arithmetic). Second-level differences constant=quadratic pattern. Check prime additions too.
Analogy Relationship Types — Tool:Worker, Part:Whole, Synonym:Antonym, Young:Adult, Male:Female, Genus:Species, Cause:Effect. Identify exact relationship type first before solving.
Venn Diagrams Quick Rule — Only A = Total A – (A∩B). Neither = Universal – (A∪B). Exactly one = (Only A) + (Only B). Use formula: n(A∪B) = n(A)+n(B)–n(A∩B).
General Science
Periodic Table Memory — "Happy Henry Lives Beside Boron Cottage" for H, He, Li, Be, B, C (first six elements). Groups: 1=Alkali, 2=Alkaline earth, 17=Halogens, 18=Noble gases.
pH Scale Quick — pH <7=Acidic, 7=Neutral, >7=Basic. Strong acids: HCl, H₂SO₄, HNO₃. Strong bases: NaOH, KOH. Stomach=pH 2, Blood=pH 7.4, Soap=pH 10.
Vitamin Deficiency Code — A=Night blindness, B1=Beri-beri, B12=Pernicious anemia, C=Scurvy, D=Rickets, E=Sterility, K=Blood clotting issues. "ABCD-K" for fat-soluble vitamins.
Human Body Cell Count — RBC lifespan=120 days, WBC=13-20 days. RBC (no nucleus in mammals), WBC (has nucleus). Normal RBC count: 5 million/mm³, WBC: 7000-10000/mm³.
Plant Tissues Mnemonic — "Me Para Collects Sclera": Meristematic, Parenchyma, Collenchyma, Sclerenchyma (simple permanent tissues). Xylem=water up, Phloem=food down (complex tissues).
Metal Reactivity Series — "Please Send Charlie's Monkeys And Zebras In Lead Heavily Covered": K, Na, Ca, Mg, Al, Zn, Fe, Pb, H, Cu, Ag, Au. Top=most reactive, bottom=least.
Atomic Structure Numbers — Atomic number=Protons=Electrons (neutral atom). Mass number=Protons+Neutrons. Isotopes=same protons, different neutrons. Valency: Group 1=1, 2=2, 13=3, 14=4, 15=3, 16=2, 17=1.
Human Diseases Pathogen — TB, Cholera, Typhoid=Bacteria. Malaria, Amoebic dysentery=Protozoa. Ringworm=Fungus. Polio, Dengue, AIDS, COVID=Virus. Vector for Malaria=Mosquito (Anopheles).
General Awareness and Current Affairs
Indian Presidents Chronology — "Rajendra Radhakrishnan Zakir FakhrUddin Giri Reddy Venkat Pratibha Pranab RamNath Draupadi": First 15 presidents' first names for quick recall in polity/history questions.
Bharat Ratna Winners (Key) — CVR (Raman), Nehru, Radhakrishnan (first 3, 1954). Recent: Pranab (2019), Nanaji Deshmukh, Bhupen Hazarika (2019 posthumous), Vajpayee (2015). Mother Teresa (1980, only naturalized citizen).
Railway Zones Headquarters — 18 zones: Northern=Delhi, Western=Mumbai, Southern=Chennai, Eastern=Kolkata, Central=Mumbai, NE Frontier=Guwahati. Metro Railway=Kolkata (smallest zone). Remember major 6-8 for