PERA CET cheat sheet

Simple interest: SI = PRT/100; compound interest: A = P(1 + R/100)^T, so CI = A − P. For 2 years, CI − SI = P(R/100)^2.

Profit and loss: profit% = (SP − CP)/CP × 100. Successive discounts of a% and b% equal a single discount of a + b − ab/100 percent.

Time-speed-distance: distance = speed × time. Convert km/h to m/s by multiplying by 5/18; m/s to km/h by 18/5. Trains: time to cross a pole = length/speed.

Boats: downstream speed = boat + stream, upstream = boat − stream; boat speed = (down + up)/2, stream speed = (down − up)/2.

Work: if A finishes in x days and B in y days, together they take xy/(x + y) days. Work rate is additive; use LCM of days as total work units.

Averages: new average after adding value v to n items = (n·old average + v)/(n + 1). Average of first n natural numbers = (n + 1)/2.

Permutations and combinations: nPr = n!/(n − r)!; nCr = n!/[r!(n − r)!]. Probability = favourable outcomes / total equally likely outcomes.

Mensuration: circle area πr², circumference 2πr; sphere volume (4/3)πr³, surface 4πr²; cylinder volume πr²h; cone volume (1/3)πr²h.

Ratio and mixture: alligation gives ratio of quantities = (mean − cheaper) : (dearer − mean). If a:b = c:d then ad = bc (product of extremes equals product of means).

Syllogism: two particular premises give no universal conclusion; two negative premises give no conclusion. 'Some A are B' converts to 'Some B are A', but 'All A are B' does not convert to 'All B are A'.

Blood relations: draw a family tree with gender symbols and vertical parent-child links; a cousin's parent is a sibling of your parent, not your parent.

Direction sense: net displacement uses Pythagoras when turns are 90°. Facing north, a right turn is east; facing south, a right turn is west.

Seating arrangement: for a circle, clockwise order reverses when viewed from the opposite side. Fix one person to break rotational symmetry, then place others relative to fixed anchors.

Series completion: check differences, then second differences, then ratios; alternating series often mix two independent patterns (e.g., +3, ×2, +3, ×2).

Coding-decoding: compare letter positions (A = 1 … Z = 26). Common shifts are +1, −1, reversal (A↔Z), or position-based substitution; test one rule against all given pairs.

Clocks: angle between hands = |30H − 5.5M| degrees. Hands coincide every 65 5/11 minutes; they are opposite every 32 8/11 minutes after 6:00 style anchors.

Calendars: a normal year shifts the weekday by 1, a leap year by 2. 100 years shift by 5 odd days, 400 years by 0; use odd days to fix a reference date.

Subject-verb agreement: singular subjects take singular verbs; 'each, every, either, neither, everyone' are singular. 'Neither…nor' follows the nearer subject.

Articles: 'a' before consonant sounds, 'an' before vowel sounds (an hour, a university). 'The' is used for unique nouns, superlatives, and rivers/ranges.

Tenses: present perfect (has/have + past participle) for past actions with present relevance; past perfect (had + participle) for the earlier of two past actions.

Prepositions: 'since' with a point in time, 'for' with a duration; 'between' for two, 'among' for more than two; 'discuss' and 'married to' take no extra preposition.

Common error pairs: 'lie/lay', 'affect/effect', 'its/it's', 'principal/principle', 'complement/compliment'. Affect is usually a verb, effect usually a noun.

Idioms: 'at the drop of a hat' = immediately; 'to bite the bullet' = endure something painful; 'a wild goose chase' = futile search.

Synonyms/antonyms: use context and word roots. Prefixes like 'bene-' (good), 'mal-' (bad), 'ante-' (before), 'post-' (after) often reveal meaning.

Reading comprehension: locate the topic sentence, distinguish stated fact from inference, and eliminate options that overstate, contradict, or add outside information.

Indian Constitution: adopted 26 November 1949, came into force 26 January 1950. Dr B. R. Ambedkar chaired the Drafting Committee; the Preamble was amended by the 42nd Amendment (1976).

Fundamental Rights appear in Part III (Articles 12–35); Directive Principles in Part IV (Articles 36–51). The Right to Education (Article 21A) was added by the 86th Amendment (2002).

Indian polity offices: the President is elected by an electoral college; the Prime Minister leads the Lok Sabha majority; the Rajya Sabha has a maximum strength of 250 members.

Geography: the Tropic of Cancer passes through eight Indian states; the Deccan Plateau lies between the Western and Eastern Ghats; the Sundarbans is the world's largest mangrove forest.

Science basics: the SI unit of force is the newton, of power the watt, of pressure the pascal. Water's boiling point at sea level is 100 °C; light travels about 3 × 10^8 m/s in vacuum.

Awards and institutions: the Bharat Ratna is India's highest civilian award; the Nobel Prizes were established by Alfred Nobel's 1895 will; the RBI was established in 1935 and nationalised in 1949.

Economics terms: GDP measures output within a country's borders; inflation is a sustained rise in the general price level; repo rate is the rate at which the RBI lends to commercial banks.

International organisations: the UN was founded in 1945 with headquarters in New York; the WHO is based in Geneva; SAARC's secretariat is in Kathmandu.

Static GK: the national bird of India is the peacock, the national aquatic animal is the Ganges river dolphin, and the national calendar is the Saka calendar.