Agniveer Army cheat sheet

Area formulas: rectangle = l × b; triangle = ½ × base × height; circle = πr²; trapezium = ½(a + b)h.

Pythagoras theorem: in a right triangle a² + b² = c², where c is the hypotenuse; common triples are 3-4-5, 5-12-13, 8-15-17.

Percentage: x% of N = xN/100; percentage change = (change ÷ original value) × 100.

Simple interest = PRT/100; compound amount = P(1 + R/100)^n, and compound interest = amount − principal.

For two positive integers, HCF × LCM = product of the two numbers.

Speed = distance ÷ time; multiply km/h by 5/18 to get m/s, and multiply m/s by 18/5 to get km/h.

Volumes: cube = a³; cuboid = lbh; cylinder = πr²h; sphere = (4/3)πr³.

Average = sum of observations ÷ number of observations; sum of first n natural numbers = n(n + 1)/2.

Newton's first law: a body stays at rest or in uniform straight-line motion unless a net external force acts; second law: F = ma; third law: every action has an equal and opposite reaction.

SI units: force in newton (N), work and energy in joule (J), power in watt (W), pressure in pascal (Pa), frequency in hertz (Hz).

Ohm's law: V = IR at constant temperature; electrical power P = VI = I²R = V²/R.

Photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂, occurring in chloroplasts using sunlight and chlorophyll.

pH scale runs 0–14: below 7 acidic, 7 neutral, above 7 basic; each unit represents a tenfold change in hydrogen ion concentration.

Blood groups: O negative is the universal donor and AB positive is the universal recipient.

Light travels in vacuum at about 3 × 10⁸ m/s; sound travels in air at roughly 343 m/s at room temperature.

Chemical symbols: Na sodium, K potassium, Fe iron, Au gold, Ag silver, Pb lead, Ca calcium, Mg magnesium.

The Constitution of India was adopted on 26 November 1949 and came into force on 26 January 1950; Dr B. R. Ambedkar chaired the Drafting Committee.

The Constitution now lists six Fundamental Rights; the Right to Property was removed as a fundamental right by the 44th Amendment in 1978.

The Reserve Bank of India was established on 1 April 1935, was nationalised in 1949, and is headquartered in Mumbai.

ISRO was formed in 1969 with headquarters at Bengaluru; Chandrayaan-3 landed near the Moon's south pole on 23 August 2023.

National symbols of India: tiger (animal), peacock (bird), lotus (flower), mango (fruit), banyan (tree).

Rakesh Sharma was the first Indian in space (1984); Indira Gandhi was India's first woman Prime Minister (1966).

The United Nations was founded on 24 October 1945, has 193 member states, and is headquartered in New York City.

The 2023 G20 summit was hosted by India in New Delhi; the 2024 Summer Olympics were held in Paris, France.

Letter positions: A = 1 through Z = 26; the opposite letter of the letter at position n has position 27 − n.

Number series are usually built from differences, ratios, squares, cubes, or two alternating patterns.

Coding-decoding commonly uses fixed letter shifts, reverse alphabets, or letter-position sums.

Blood relations: draw a family tree, marking males and females and using vertical links for parents and horizontal links for spouses or siblings.

Direction sense: each right turn is 90° clockwise and each left turn is 90° anticlockwise; from north, a right turn faces east.

Syllogism: 'all A are B' plus 'all B are C' gives 'all A are C'; 'some A are B' does not justify 'all A are B'.

Clock angle between hands = |30H − 5.5M| degrees, where H is the hour and M is the minute.

Odd-one-out items are solved by identifying the property shared by most options, such as being prime, perfect squares, or divisible by a number.