CAPF HC Ministerial cheat sheet

Indian Constitution: adopted 26 November 1949, came into force 26 January 1950; the Preamble was amended once, by the 42nd Amendment Act 1976, which added socialist, secular, and integrity.

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

Directive Principles of State Policy are in Part IV (Articles 36–51) and are non-justiciable; Fundamental Duties were added by the 42nd Amendment on the Swaran Singh Committee's recommendation.

Parliament comprises the President, Rajya Sabha, and Lok Sabha; the Rajya Sabha has a maximum of 250 members and the Lok Sabha a maximum of 552 (530 states, 20 UTs, 2 Anglo-Indians).

Geography: the Tropic of Cancer passes through eight Indian states - Gujarat, Rajasthan, Madhya Pradesh, Chhattisgarh, Jharkhand, West Bengal, Tripura, and Mizoram.

Indian economy: the Reserve Bank of India was established on 1 April 1935 and nationalised in 1949; monetary policy is set by the six-member Monetary Policy Committee, which targets CPI inflation at 4% ± 2%.

Science: SI base units number seven (metre, kilogram, second, ampere, kelvin, mole, candela); the pH scale runs 0–14, with values below 7 acidic and above 7 basic at 25 °C.

Modern history: the Indian National Congress was founded in 1885 (first session Bombay, W. C. Bonnerjee presiding); the Quit India Movement was launched on 8 August 1942 in Bombay.

Static awareness: the Jnanpith Award recognises literary achievement in Indian languages, and the Bharat Ratna is India's highest civilian honour, instituted in 1954.

Percentage change: successive changes of a% and b% give a net change of a + b + ab/100 percent; a 20% rise then 20% fall leaves a net 4% decrease.

Profit and loss: profit% is always calculated on cost price unless stated otherwise; selling price = CP × (100 + profit%)/100, and discount% is calculated on marked price.

Simple interest = PRT/100; compound interest = P(1 + R/100)^T − P, and for two years the CI exceeds SI by P(R/100)².

Time, speed, distance: distance = speed × time; for equal distances at speeds x and y, average speed = 2xy/(x + y), not the arithmetic mean.

Trains and boats: a train crossing a platform covers its own length plus the platform length; downstream speed = boat + stream and upstream = boat − stream, so stream speed = (down − up)/2.

Work and time: if A finishes in x days and B in y days, together they take xy/(x + y) days; efficiency is inversely proportional to time taken.

Ratio and mixtures: in an alligation, the ratio of quantities = (mean − cheaper)/(dearer − mean); repeated replacement leaves final quantity = initial × (1 − replaced/total)^n.

Mensuration: area of circle = πr², circumference = 2πr; volume of cylinder = πr²h, sphere = (4/3)πr³, cone = (1/3)πr²h; total surface area of a cube = 6a².

Averages and numbers: average = sum/count; sum of first n natural numbers = n(n+1)/2, of squares = n(n+1)(2n+1)/6, of cubes = [n(n+1)/2]².

Permutation and combination: arrangements of n distinct objects = n!; selections of r from n = nCr = n!/[r!(n−r)!]; probability = favourable outcomes / total equally likely outcomes.

Subject-verb agreement: a singular subject takes a singular verb; with "either…or" and "neither…nor" the verb agrees with the nearer subject, and collective nouns take a singular verb when acting as a unit.

Tense sequencing: a past-tense main clause takes a past-tense subordinate clause for reported speech ("He said that he was ill"); use present perfect for an action continuing to now.

Articles: "a/an" is indefinite and depends on the initial sound (an hour, a university); "the" is definite and is used with superlatives, unique objects, and rivers or mountain ranges.

Prepositions: use "since" with a point in time and "for" with a duration; "between" takes two items and "among" more than two.

Active to passive: object becomes subject, verb becomes be + past participle, and the agent is introduced by "by"; only transitive verbs can be made passive.

Direct to indirect speech: change pronouns to the third person, shift tense back one step (present to past), and convert "today" to "that day" and "tomorrow" to "the next day".

Common error traps: "one of the" takes a plural noun with a singular verb; "each," "every," and "either" are singular; avoid double comparatives such as "more better".

Vocabulary: a synonym shares meaning, an antonym opposes it, and an idiom's meaning is figurative - "to bite the bullet" means to endure a difficult situation bravely.

Reading comprehension: locate the main idea in the topic sentence, distinguish stated fact from inference, and answer only from the passage rather than outside knowledge.