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.