General Mathematics
Divisibility by 11 — Alternating sum rule: subtract and add digits alternately from right; if result is 0 or divisible by 11, number is too. Example: 121→1−2+1=0, divisible.
BODMAS Order — Brackets, Of (powers), Division, Multiplication, Addition, Subtraction. Remember: Division and Multiplication are equal priority (left to right), same for Addition and Subtraction.
Speed-Distance-Time Triangle — Cover 'S' in △; see D×T. Cover 'D'; see S÷T. Cover 'T'; see D÷S. Draw triangle with S on top, D and T at base.
Profit % Quick Formula — If CP=100, SP=110 means 10% profit. For reverse: SP given, CP unknown? CP = SP×100/(100+Profit%). Loss: use (100−Loss%).
Compound Interest Approximation — For 2 years at R%: CI ≈ Simple Interest + (R% of SI). Example: ₹1000 at 10% for 2yr, SI=₹200, extra=₹20, CI=₹220.
Geometry: Sum of Polygon Angles — (n−2)×180° where n=number of sides. Triangle (3): 180°, Quadrilateral (4): 360°, Pentagon (5): 540°.
LCM×HCF Trick — For two numbers: LCM × HCF = Product of the two numbers. Use when three values given, find fourth.
Percentage to Fraction — 12.5%=1/8, 16.66%=1/6, 20%=1/5, 25%=1/4, 33.33%=1/3, 50%=1/2. Memorize these for rapid calculation in competitive exams.
Average Addition Formula — When new number added: New Average = Old Average + (New number − Old Average)/(Total count after addition). Saves recalculation time.
Time-Work Inverse Rule — If A completes work in 'a' days and B in 'b' days, together they finish in (a×b)/(a+b) days. Remember: add reciprocals, flip result.
Pythagorean Triplets — Memorize: (3,4,5), (5,12,13), (8,15,17), (7,24,25). Multiples also work: (6,8,10), (9,12,15). Saves calculation in right-triangle problems.
Successive Percentage Change — For R1% then R2%: Combined % = R1+R2+(R1×R2)/100. Example: 10% increase then 20% increase = 10+20+2=32% total increase.
Mental Ability and Logical Reasoning
Direction Sense NESW Clock — Visualize analog clock: 12=N, 3=E, 6=S, 9=W. Right turn=clockwise 90°, Left turn=anticlockwise 90°, About turn=180°. Track cumulative rotation.
Blood Relations Gender Keys — Maternal side: Mama (uncle), Mausi (aunt). Paternal: Chacha/Tau (uncle), Bua (aunt). Son's wife=Daughter-in-law. Brother's wife=Sister-in-law (Bhabhi). Daughter's husband=Son-in-law (Damaad).
Coding Pattern Check — First check: Letter position shift (A=1, B=2...). Second: Reverse alphabet (A↔Z). Third: Previous/next letter. Fourth: Consonant-vowel swap pattern. Apply systematically.
Calendar Day Count — Odd days method: Divide days by 7, remainder=odd days. 1 odd day→next weekday, 2→skip one day. Memorize: 400yrs=0 odd days, 100yrs=5 odd days, 4yrs=5 odd days, 1yr=1(normal)/2(leap).
Series Missing Number — Check: +n pattern, ×n pattern, squares (n²), cubes (n³), prime numbers (2,3,5,7,11...), alternating operations. Test each systematically within 30 seconds.
Clock Angle Formula — Angle = |11M−60H|/2 degrees, where H=hour, M=minute. If >180°, take 360−angle. Right angle at 3:00, 9:00. Straight line at 6:00.
Syllogism "Some-All-No" Rule — "All A are B" + "All B are C" → "All A are C" (valid). "Some A are B" + "All B are C" → "Some A are C". "No A are B" + "All B are C" → "No A are C".
Mirror Image Left-Right Swap — Only horizontal flip occurs; vertical positions stay same. Letters like A, H, I, M, O, T, U, V, W, X, Y look identical. Asymmetric letters flip: b↔d, p↔q.
Cube Painted Faces Formula — N³ cube cut into unit cubes: 0 faces painted=(N−2)³, 1 face=(N−2)²×6, 2 faces=(N−2)×12, 3 faces=8 (corners only).
General Science
Acids-Bases pH Scale — pH<7=Acidic (HCl, H₂SO₄, lemon), pH=7=Neutral (water), pH>7=Basic (NaOH, soap, baking soda). Strong acid: pH 0-3, Weak: 4-6. Litmus: Red→acid, Blue→base.
Electromagnetic Spectrum Order — Radio Microwave Infrared Visible Ultraviolet X-ray Gamma. Mnemonic: Raman Meets Indian Very Urgently eXamining Genetics. Increasing frequency and energy left to right.
Human Blood Groups Compatibility — O− universal donor (gives to all), AB+ universal recipient (receives from all). A receives A/O, B receives B/O, AB receives all, O receives only O. Rh+ receives ±, Rh− receives only −.
Planet Order from Sun — Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune. Mnemonic: My Very Educated Mother Just Served Us Noodles.
Ohm's Law Triangle — V on top, I and R at base. V=I×R, I=V/R, R=V/I. Cover unknown, see formula. Voltage (Volts), Current (Amperes), Resistance (Ohms).
Cell Organelles Functions — Mitochondria=Powerhouse (ATP), Ribosomes=Protein factory, Golgi=Packaging/sorting, ER=Transport, Lysosomes=Suicide bags (digestion), Chloroplast=Photosynthesis (plants only), Nucleus=Control center (DNA).
Newton's Laws Quick Recall — 1st: Inertia (rest/motion continues). 2nd: F=ma (force=mass×acceleration). 3rd: Action-reaction equal-opposite. Remember sequence: REST→FORCE→REACTION.
Vitamin Deficiency Diseases — A=Night blindness, B1=Beriberi, B12=Anemia, C=Scurvy, D=Rickets, E=Sterility, K=Bleeding. Mnemonic: A Boy Can Dance Even Karaoke for A-B-C-D-E-K.