AdUCET cheat sheet

A gerund is a verb form ending in -ing that functions as a noun, as in 'Swimming is good exercise'.

Indefinite pronouns 'each', 'every', 'either', 'neither', 'everyone' and 'nobody' take a singular verb.

Passive voice pattern: object + correct form of 'be' + past participle + optional 'by' + agent.

In reported speech after a past reporting verb, present simple shifts to past simple and present perfect to past perfect.

A clause contains a subject and a finite verb; a phrase lacks a finite verb and cannot stand alone.

'Fewer' modifies countable plural nouns (fewer books); 'less' modifies uncountable nouns (less water).

Antonym pairs to memorise: benevolent/malevolent, frugal/extravagant, candid/evasive, transient/permanent.

Idiom meanings: 'bite the bullet' = endure pain bravely; 'spill the beans' = reveal a secret; 'at the drop of a hat' = instantly.

In comprehension, the main idea is usually carried by the topic sentence in the first or last line of the paragraph; details support it.

Profit % = (SP − CP)/CP × 100; Loss % = (CP − SP)/CP × 100, always computed on cost price unless stated otherwise.

Simple interest = PRT/100; compound amount A = P(1 + r/100)^n, and CI = A − P.

If a price rises by x%, consumption must fall by 100x/(100 + x)% to keep total expenditure unchanged.

If A finishes a job in a days and B in b days, together they take ab/(a + b) days.

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

Sum of first n natural numbers = n(n+1)/2; sum of first n odd numbers = n²; sum of squares = n(n+1)(2n+1)/6.

Area: circle πr², triangle ½ × base × height, trapezium ½(a + b)h; volume of a cylinder = πr²h.

For two positive integers, LCM × HCF = product of the numbers.

Roots of ax² + bx + c = 0 are x = [−b ± √(b² − 4ac)]/2a; the discriminant b² − 4ac decides real, equal or complex roots.

Syllogism: 'All A are B' plus 'All B are C' validly yields 'All A are C'; a conclusion is valid only if true in every possible diagram.

'Some A are B' converts to 'Some B are A', but 'All A are B' does not convert to 'All B are A'.

The contrapositive of 'If P then Q' is 'If not Q then not P'; it is logically equivalent, whereas the converse is not.

Angle between clock hands at H hours M minutes = |30H − 5.5M| degrees, reduced to the smaller angle if above 180°.

Odd days: ordinary year 1, leap year 2, 100 years 5, 200 years 3, 300 years 1, 400 years 0.

Facing North, a right turn gives East, a second right turn gives South; each right turn is 90° clockwise.

Alphabet-shift coding: test a single constant shift first using A = 1 through Z = 26 before assuming a complex pattern.

Blood relations: if A is the son of B's only daughter, then A is B's grandson and B is A's maternal grandparent.

A cube of side n cut into unit cubes and painted outside has 8 corner cubes with three painted faces.

Article 368 of the Indian Constitution lays down the procedure for amending the Constitution, including special majority requirements.

Fundamental Rights sit in Part III, Articles 12 to 35; the right to constitutional remedies is Article 32.

The Reserve Bank of India was established on 1 April 1935 under the RBI Act 1934 and nationalised in 1949.

The United Nations was founded on 24 October 1945; its headquarters is in New York and the General Assembly is its main deliberative organ.

The Tropic of Cancer at roughly 23.5° N passes through eight Indian states, including Rajasthan, Madhya Pradesh, Chhattisgarh and West Bengal.

Nobel Prize categories are Physics, Chemistry, Physiology or Medicine, Literature, Peace, and Economic Sciences (added in 1968).

The Supreme Court of India was inaugurated on 28 January 1950, two days after the Constitution came into force.

Photosynthesis in chloroplasts converts carbon dioxide and water into glucose and oxygen using light energy and chlorophyll.

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

Physics: Newton's second law gives F = ma; the newton is 1 kg·m/s², and weight equals mg.

Chemistry: pH = −log[H⁺]; at 25 °C a pH of 7 is neutral, below 7 acidic and above 7 basic.

Biology: DNA replication is semi-conservative; adenine pairs with thymine and guanine with cytosine via hydrogen bonds.

Commerce: the accounting equation Assets = Liabilities + Capital holds after every transaction because debits equal credits.

Computer applications: each binary digit is a power of two from the right, so 1010 = 8 + 2 = 10 decimal; one byte = 8 bits.

Economics: GDP at market prices equals C + I + G + (X − M), where the last term is net exports.

History: the Mature Harappan phase of the Indus Valley Civilisation is dated to roughly 2600–1900 BCE.

Mathematics: the derivative of sin x is cos x, of cos x is −sin x, and ∫(1/x)dx = ln|x| + C.

Political science: a federal system divides powers between a central government and constituent units, usually with a written constitution.