DRDO CEPTAM STA-B cheat sheet

Sum of the first n natural numbers = n(n+1)/2; sum of the first n odd numbers = n²; sum of the first n even numbers = n(n+1).

Number series test order: check successive differences first (constant = arithmetic), then ratios (constant = geometric), then second differences (constant = quadratic).

Coding-decoding: use A=1 to Z=26 and the reverse value 27 − position; letter-shift ciphers usually move each letter by a fixed constant or progressively by +1, +2, +3.

Blood relations: draw a family tree, mark males with '+' and females with '−', and resolve phrases like 'brother of my father' to 'uncle' before answering.

Direction sense: take North = +y, South = −y, East = +x, West = −x; a right turn rotates the facing 90° clockwise, a left turn 90° anticlockwise.

Ranking: if a person is nth from the left and mth from the right, total persons = n + m − 1, valid only when the two counts refer to the same row.

Syllogism: 'All A are B' plus 'All B are C' gives 'All A are C'; 'All A are B' plus 'No B is C' gives 'No A is C'; 'Some' statements do not convert to 'All'.

Clock: angle between the hands = |30H − 5.5M| degrees, and the hands coincide every 65 5/11 minutes.

Mirror image reverses left-right and water image reverses top-bottom; the mirror-image reading of a clock time t is 11:60 − t.

DRDO was formed in 1958 by merging the Defence Science Organisation with the Technical Development Establishment; its motto is 'Balasya Mulam Vigyanam' (science is the root of strength) and its headquarters is in New Delhi.

DRDO laboratories include LRDE (radar), DRDL and RCI (missiles), DMRL (metallurgy) and CAIR (artificial intelligence).

The Integrated Guided Missile Development Programme, launched in 1983, produced Prithvi, Agni, Trishul, Akash and Nag; BrahMos is a separate India–Russia joint venture.

Param Vir Chakra is the highest wartime gallantry award, Ashoka Chakra the highest peacetime gallantry award, and Bharat Ratna the highest civilian award.

ISRO was formed on 15 August 1969, succeeding INCOSPAR, with Vikram Sarabhai as its guiding founder; its headquarters is in Bengaluru.

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 Reserve Bank of India began operations in 1935 and was nationalised in 1949; it issues all currency notes except the one-rupee note, which is issued by the Government of India.

Fundamental Rights occupy Part III (Articles 12–35); Article 32, the Right to Constitutional Remedies, was called the 'heart and soul' of the Constitution by Dr Ambedkar.

Percentage change = (new − old)/old × 100; a rise of x% followed by a fall of x% always gives a net decrease of x²/100 percent.

Profit% = (SP − CP)/CP × 100 when cost price is the base; when selling price is the base the denominator becomes SP instead of CP.

SI = PRT/100; CI = P(1 + R/100)^T − P; for two years the difference CI − SI = P(R/100)².

1 km/h = 5/18 m/s; distance = speed × time; a train crossing a platform covers train length + platform length.

Work: if A alone takes a days and B alone b days, together they take ab/(a + b) days, because efficiency is inversely proportional to time.

Boats: downstream = b + s and upstream = b − s, so still-water speed = (down + up)/2 and stream speed = (down − up)/2.

Average = sum/count; for an arithmetic progression the average = (first + last)/2, and the average of the first n natural numbers is (n + 1)/2.

Mensuration: circle area = πr² and circumference = 2πr; cylinder volume = πr²h; sphere surface area = 4πr²; cone volume = ⅓πr²h.

HCF × LCM = product of the two numbers; divisibility by 3 or 9 is decided by the sum of the digits.

SI base units: metre (length), kilogram (mass), second (time), ampere (current), kelvin (temperature), mole (amount of substance), candela (luminous intensity).

Newton's laws: a body remains at rest or in uniform motion unless a net force acts; F = ma; every action has an equal and opposite reaction.

Ohm's law gives V = IR, and power P = VI = I²R = V²/R; resistors add in series and follow 1/R = 1/R₁ + 1/R₂ in parallel.

Standard values: speed of light in vacuum ≈ 3 × 10⁸ m/s, g ≈ 9.8 m/s², and 1 atmosphere ≈ 1.013 × 10⁵ pascal.

pH below 7 is acidic, exactly 7 is neutral and above 7 is basic; each unit step is a tenfold change in hydrogen-ion concentration.

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

Human body: an adult has 206 bones and 32 teeth; skin is the largest organ, liver the largest gland, and normal blood pH is about 7.4.

Common formulas: water H₂O, common salt NaCl, baking soda NaHCO₃, washing soda Na₂CO₃·10H₂O, quicklime CaO, urea CO(NH₂)₂.

Blood groups: O-negative is the universal red-cell donor and AB-positive the universal recipient; the Rh factor is a separate antigen from the ABO system.

Subject-verb agreement: each, every, either, neither, everyone and nobody are singular and take a singular verb; two subjects joined by 'and' take a plural verb unless they express one idea.

Articles depend on sound, not spelling: 'a' before a consonant sound and 'an' before a vowel sound, hence 'an hour' but 'a university'.

Active to passive: the object becomes the subject, the verb becomes be + past participle, and the doer follows 'by', with the tense of 'be' matching the original tense.

Reported speech: present tenses usually shift to past; 'tomorrow' becomes 'the next day', 'here' becomes 'there' and 'now' becomes 'then'.

Prepositions: 'since' takes a point of time and 'for' a duration; 'between' is used for two items and 'among' for more than two.

Confusables: affect (verb, to influence) vs effect (noun, result); principal (main/head) vs principle (rule); stationary (not moving) vs stationery (paper goods).

Idioms: 'bite the bullet' = endure bravely; 'let the cat out of the bag' = reveal a secret; 'a bolt from the blue' = a complete surprise.

Parallelism: items joined by and, or, but must share the same grammatical form, so 'reading, writing and swimming' is correct where 'to swim' would break the pattern.

Vocabulary pairs: abundant ↔ scarce, benevolent ↔ malevolent, candid = frank, obsolete = outdated.