IPMAT Rohtak cheat sheet

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

Profit and loss: profit% is always computed on cost price unless stated otherwise; SP = CP(1 ± p/100). Successive discounts d1, d2 give net factor (1−d1/100)(1−d2/100).

Speed conversion: 1 km/h = 5/18 m/s. For a train of length L crossing a platform of length P at speed v, time = (L+P)/v; crossing a pole gives time = L/v.

Boats: downstream speed = b + s, upstream = b − s, where b is boat speed in still water and s is stream speed. b = (D + U)/2, s = (D − U)/2.

Time and work: if A alone takes a days and B alone takes b days, together they take ab/(a+b) days. Use LCM of days as total work units to avoid fractions.

Averages: new average after adding a value x to n items = (n·A + x)/(n+1). In an arithmetic progression, average = (first + last)/2 = middle term.

Permutations and combinations: nPr = n!/(n−r)!; nCr = n!/[r!(n−r)!]. Arrangements of a word with repeated letters = n!/(p!q!…).

Probability: P(A∪B) = P(A) + P(B) − P(A∩B); for independent events P(A∩B) = P(A)·P(B). Odds in favour a:b correspond to probability a/(a+b).

Mensuration: volume of cylinder = πr²h, cone = (1/3)πr²h, sphere = (4/3)πr³; curved surface of cone = πrl with l = √(r²+h²).

Syllogism: two particular premises never yield a universal conclusion; two negative premises yield no valid conclusion. 'Some A are B' does not imply 'Some B are A' fails - it does convert.

Blood relations: draw a family tree with gender markers (+ male, − female) and generation levels; solve the question from the diagram, not from memory of the passage.

Direction sense: track net displacement using vector components; final distance = √(x² + y²). Turning right from North gives East, left from North gives West.

Seating arrangement: for a circle, fix one person to break rotational symmetry, then place others; for facing-centre arrangements, 'left' is clockwise and 'right' is anticlockwise.

Number series: check first differences, then second differences, then ratios; alternating and prime-based series are common when differences look irregular.

Coding-decoding: compare letter positions (A=1 … Z=26); common patterns are shift by a constant, reversal, or sum/difference of positions of adjacent letters.

Data sufficiency: a statement is sufficient only if it yields a unique answer; if two values satisfy the condition, mark insufficient even if one is 'obvious'.

Clocks: angle between hands = |30H − 5.5M| degrees; hands coincide every 65 5/11 minutes, so a clock gains or loses when this interval differs.

Subject-verb agreement: 'each, every, either, neither, everyone' take singular verbs; 'none' takes singular or plural depending on the noun it refers to.

Parallelism: items joined by and/or/but must share grammatical form - all infinitives, all gerunds, or all noun phrases.

Misplaced modifier rule: a participial phrase at the start of a sentence must describe the subject of the main clause; otherwise it is a dangling modifier.

Reading comprehension: the correct answer must be supported by the passage text, not by outside knowledge or by an extreme restatement of it.

Para jumbles: locate the opening sentence (usually general, no pronouns or connectors), then chain using pronouns, conjunctions and chronology.

Idioms with fixed prepositions: 'comply with', 'differ from', 'superior to', 'capable of', 'insist on', 'prefer to' - these are tested as correctness, not style.

Vocabulary in context: choose the option that preserves the sentence's tone; a synonym with the wrong connotation is a distractor.

Error spotting: check articles, prepositions, tense consistency and countable/uncountable quantifiers ('much' vs 'many', 'less' vs 'fewer').

Indian polity: the Constitution was adopted on 26 November 1949 and came into force on 26 January 1950; Dr B. R. Ambedkar chaired the Drafting Committee.

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

Indian economy: the Reserve Bank of India was established in 1935 and nationalised in 1949; monetary policy is set by the Monetary Policy Committee, which has six members.

Indian geography: the Tropic of Cancer passes through eight states, and the Western Ghats are a biodiversity hotspot running parallel to the west coast.

Awards and institutions: the Bharat Ratna is India's highest civilian award, instituted in 1954; the Nobel Prizes are announced in October each year.

International organisations: the UN was founded in 1945 with headquarters in New York; the WTO, established in 1995, replaced GATT and is based in Geneva.

Science basics: the SI unit of force is the newton, of pressure the pascal, and of power the watt; DNA carries hereditary information in the double-helix structure.

Static current affairs anchors: India's Chandrayaan-3 landed near the lunar south pole in 2023, and the G20 summit of 2023 was hosted by India in New Delhi.