RRB Group D cheat sheet

Speed = Distance ÷ Time; to convert km/h to m/s multiply by 5/18, and m/s to km/h multiply by 18/5.

Simple Interest = (P × R × T) ÷ 100; Compound Interest amount A = P(1 + r/100)^n, so CI = A − P.

HCF × LCM = product of the two numbers (valid for exactly two numbers).

Sum of first n natural numbers = n(n+1)/2; sum of their squares = n(n+1)(2n+1)/6; sum of cubes = [n(n+1)/2]^2.

Circle: area = πr², circumference = 2πr; triangle area = ½ × base × height; Pythagorean triples include 3-4-5, 5-12-13, 8-15-17.

Average = sum of all observations ÷ number of observations; new average after adding a value = (old sum + value) ÷ (count + 1).

Profit% = (SP − CP)/CP × 100; Loss% = (CP − SP)/CP × 100; discount is always calculated on the marked price.

Divisibility tests: by 3 or 9 use digit sum; by 4 use last two digits; by 8 use last three digits; by 11 check whether the difference of alternate digit sums is 0 or a multiple of 11.

Percentage change in area of a rectangle when both sides change by x% and y% is x + y + xy/100.

Alphabet positions: A = 1 up to Z = 26; the EJOTY anchor set gives E = 5, J = 10, O = 15, T = 20, Y = 25, from which neighbouring letters can be counted quickly.

Mirror image reverses left and right while keeping top and bottom unchanged; water image reverses top and bottom while keeping left and right unchanged.

In a standard die, opposite faces always sum to 7, so faces 1-6, 2-5 and 3-4 can never be adjacent.

Calendar odd days: an ordinary year has 1 odd day, a leap year 2; 100 years give 5 odd days, 200 give 3, 300 give 1 and 400 give 0.

Number series are usually built on constant differences, squares, cubes, primes, or alternating two-series patterns; check differences before assuming a rule.

Direction sense: draw the path on paper and use Pythagoras (displacement = √(x² + y²)) when the question asks for shortest distance.

Blood relations: sketch a family tree with separate male/female symbols and vertical lines for generations before answering relationship questions.

Syllogism: 'All A are B' places the A circle inside B, so 'Some B are A' always follows, while 'All B are A' does not.

Coding-decoding with letters is normally a constant forward or backward shift, a reversal, or a position-based substitution (letter to its alphabet number).

Newton's second law: force = mass × acceleration (F = ma); SI unit of force is the newton (kg·m/s²).

Ohm's law: V = IR, so current is directly proportional to voltage and inversely proportional to resistance at constant temperature.

pH scale runs 0 to 14: below 7 is acidic, exactly 7 is neutral, above 7 is basic; pH is the negative logarithm of hydrogen ion concentration.

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

Human body facts: an adult has 206 bones, 32 teeth, 4 heart chambers, 12 pairs of cranial nerves and 1 pair of kidneys.

Speed of light in vacuum is about 3 × 10⁸ m/s; speed of sound in air at room temperature is about 343 m/s.

Mercury is the only metal that is liquid at room temperature; graphite is a non-metal that conducts electricity.

Deficiency diseases: vitamin A causes night blindness, vitamin C scurvy, vitamin D rickets, iron anaemia, iodine goitre.

SI units: work and energy in joule, power in watt, pressure in pascal, frequency in hertz, electric charge in coulomb.

The Constitution of India was adopted on 26 November 1949 and came into force on 26 January 1950.

Fundamental Rights are in Part III (Articles 12-35); Fundamental Duties are in Article 51A, added by the 42nd Amendment in 1976.

Article 356 allows President's rule in a state when constitutional machinery fails; Article 370 dealt with the special status of Jammu and Kashmir.

The Reserve Bank of India was established on 1 April 1935 and nationalised in 1949; it issues currency notes of ₹2 and above, while coins are minted by the Government.

The Supreme Court is constituted under Article 124; the President appoints the Chief Justice of India.

Chandrayaan-3's Vikram lander touched down near the Moon's south pole on 23 August 2023, making India the fourth country to soft-land on the Moon.

ISRO is headquartered at Bengaluru; its launch centres are Sriharikota (Satish Dhawan Space Centre) and Thumba.

The first President of India was Dr Rajendra Prasad; the President is elected by an electoral college under Article 54.

National symbols: the national bird is the peacock, national animal the Bengal tiger, national flower the lotus and national fruit the mango.