HEC LAT cheat sheet

Subject-verb agreement: a singular subject takes a singular verb even when a prepositional phrase intervenes - "The box of pens is on the desk." Indefinite pronouns (each, everyone, neither, anybody) are singular; "both," "few," and "several" are plural.

Pronoun case: use the subjective form after "than" or "as" when it is the subject of an implied verb ("She runs faster than I [do]"). Use "who" for subjects and "whom" for objects of verbs or prepositions.

Dangling and misplaced modifiers: an introductory participial phrase must describe the subject of the main clause. "Walking home, the rain soaked him" is wrong because the rain was not walking.

Tense consistency and sequence: keep the tense of a subordinate clause logical to the main clause; use past perfect ("had gone") only for an action completed before another past action.

Parallel structure: items joined by "and," "or," "not only...but also" must share the same grammatical form - all nouns, all infinitives, or all gerunds, never a mix.

Punctuation decision rules: a semicolon joins two independent clauses; a colon must follow a complete clause and introduce a list, explanation, or quotation; a comma cannot join two independent clauses (that creates a comma splice).

Vocabulary in context: infer meaning from surrounding clauses and from contrast or cause signals ("although," "because," "unlike"); a synonym must fit both the sentence's logic and its register.

Reading comprehension: the main idea is broader than any single supporting detail; eliminate options that are true but too narrow, too extreme ("always," "never"), or outside the passage's scope.

Conditional logic: "If P then Q" (P → Q) is equivalent to its contrapositive "If not Q then not P." It does not imply "If Q then P" (converse) or "If not P then not Q" (inverse).

Necessary vs sufficient: "P is sufficient for Q" means P → Q; "P is necessary for Q" means Q → P. Confusing the two is the most common reasoning error.

"Only if" translates as a necessary condition: "P only if Q" becomes P → Q. "Unless" translates as "if not": "P unless Q" becomes not-Q → P.

Syllogism validity: an argument is valid if the conclusion follows necessarily from the premises, regardless of whether the premises are factually true; soundness requires both validity and true premises.

Ordering and seating puzzles: convert each clue into a fixed relation (before/after, adjacent, not adjacent, exactly between), then test the most restrictive clue first and eliminate answer choices.

Number series: check differences first, then ratios, then alternating or two-interleaved sequences; look for squares, cubes, primes, and Fibonacci-type sums before assuming a complex rule.

Percent and ratio reasoning: successive percentage changes multiply rather than add (a 20% rise then a 20% fall gives 0.96 of the original, a net 4% loss); average speed for equal distances is the harmonic mean, not the arithmetic mean.

Assumption and inference questions: an assumption is an unstated premise the argument needs; a valid inference must be supported by the stated facts alone, not by outside knowledge.

Fundamental science constants: speed of light ≈ 3 × 10⁸ m/s; acceleration due to gravity ≈ 9.8 m/s²; water boils at 100 °C at sea level and freezes at 0 °C; the chemical formula of water is H₂O and of carbon dioxide CO₂.

Human biology basics: the heart has four chambers; the largest organ is the skin; red blood cells carry oxygen via hemoglobin; the normal adult resting heart rate is roughly 60–100 beats per minute.

Solar system order from the Sun: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune. The Sun is a star; the Moon is Earth's only natural satellite.

Geography: the largest ocean is the Pacific; the largest continent is Asia; the longest river is the Nile (or the Amazon by volume); the highest peak is Mount Everest at 8,849 m.

Pakistan geography anchors: capital Islamabad; largest city Karachi; highest peak K2 (8,611 m); longest river the Indus; provinces are Punjab, Sindh, Khyber Pakhtunkhwa, Balochistan, plus Gilgit-Baltistan and Azad Kashmir.

International organizations: the UN was founded in 1945 with headquarters in New York; its Security Council has five permanent members (China, France, Russia, UK, US); the WHO, UNESCO, and UNICEF are UN agencies.

Economics and civics terms: GDP measures total output within borders; inflation is a sustained rise in the general price level; a constitution defines state powers and citizens' rights.

Current-affairs strategy: verify dates and officeholders against a recent almanac, because names of heads of state, UN Secretaries-General, and similar facts change and are frequent exam traps.

Timeline of key dates: All-India Muslim League founded 1906 (Dhaka); Lahore Resolution 1940; Pakistan established 14 August 1947; first constitution promulgated 1956; present constitution 1973.

Founders and leaders: Muhammad Ali Jinnah (Quaid-e-Azam) was the first Governor-General; Liaquat Ali Khan was the first Prime Minister; Allama Iqbal's 1930 Allahabad Address proposed a separate Muslim state in the northwest.

Constitutional features of 1973: parliamentary system with a Prime Minister as chief executive; bicameral legislature (National Assembly and Senate); Islam declared the state religion; Objectives Resolution (1949) is its preamble.

Geography: the Indus River system supports the world's largest contiguous irrigation network; the Thar Desert lies in the southeast; the Khyber Pass links Pakistan with Afghanistan; the Arabian Sea forms the southern boundary.

Neighbours and borders: India to the east, China to the north, Afghanistan to the northwest, Iran to the southwest; the Durand Line (1893) marks the Pakistan–Afghanistan border.

Economy and resources: agriculture employs a large share of the workforce; major crops include wheat, rice, cotton, and sugarcane; textile exports are a leading foreign-exchange earner.

Symbols and institutions: national language Urdu; national animal markhor; national tree deodar; the Supreme Court is the apex court, seated in Islamabad.

Five Pillars of Islam: Shahadah (declaration of faith), Salah (five daily prayers), Zakat (annual alms, generally 2.5% of qualifying wealth), Sawm (fasting in Ramadan), and Hajj (pilgrimage to Makkah, obligatory once for those able).

Sources of guidance: the Qur'an (revealed to Prophet Muhammad over about 23 years) and the Sunnah (the Prophet's practice recorded in hadith) are the primary sources; Ijma (consensus) and Qiyas (analogy) are recognized secondary sources in Sunni jurisprudence.

Qur'an structure: 114 surahs, arranged roughly from longest to shortest after the opening Al-Fatihah; the longest surah is Al-Baqarah; the shortest is Al-Kawthar.

Prophethood: Muslims believe in a line of prophets ending with Muhammad, who is regarded as the final prophet (Khatam an-Nabiyyin); earlier prophets include Adam, Nuh, Ibrahim, Musa, and Isa.

Pillars of faith (Iman): belief in Allah, His angels, His books, His messengers, the Day of Judgment, and divine decree (qadar).

Calendar and worship: the Islamic calendar is lunar, with 12 months beginning with Muharram; Ramadan is the ninth month; Eid al-Fitr follows Ramadan and Eid al-Adha falls in Dhul-Hijjah during Hajj.

Ethics and practice: the Qur'an emphasizes justice, honesty, charity, and care for orphans and the poor; riba (interest) is prohibited in Islamic finance, which uses profit-and-loss sharing such as mudarabah and musharakah.

Countable vs uncountable: use "fewer" with countable nouns (fewer books) and "less" with uncountable nouns (less water); "amount" pairs with uncountable, "number" with countable.

Misplaced comparison: compare like with like - "The population of Lahore is larger than that of Quetta," not "larger than Quetta."

Active vs passive: prefer active voice unless the doer is unknown or the object deserves emphasis; passive is formed with "be" + past participle.

Idiomatic prepositions: "differ from," "similar to," "capable of," "insist on," "comprise" (no "of"), "superior to" (not "than").

Grouping puzzles: when a rule says "A and B cannot be together," treat them as mutually exclusive and place one in each of two groups if group sizes are fixed.

"If A then B" in a grouping puzzle means any group containing A must contain B; the contrapositive means any group without B cannot contain A.

Counting arrangements: permutations apply when order matters (nPr), combinations when it does not (nCr); with repetition allowed, multiply choices per position.

Venn reasoning: "some A are B" does not imply "some B are not A"; only "all," "no," and "some" statements have fixed logical consequences.

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

Force is measured in newtons, energy in joules, power in watts, pressure in pascals; one newton equals one kilogram-metre per second squared.

The pH scale runs 0–14; below 7 is acidic, above 7 is basic, and 7 is neutral at standard conditions.

Earth facts: roughly 71% of the surface is water; the atmosphere is about 78% nitrogen and 21% oxygen; one rotation takes about 24 hours and one revolution about 365.25 days.

1857 War of Independence; 1885 Indian National Congress founded; 1906 All-India Muslim League founded; 1909 Minto-Morley Reforms introduced separate electorates.

1916 Lucknow Pact; 1919 Rowlatt Act and Jallianwala Bagh; 1930 Iqbal's Allahabad Address; 1933 name "Pakistan" coined by Choudhry Rahmat Ali in the pamphlet "Now or Never."

1940 Lahore Resolution; 1946 Cabinet Mission; 1947 independence and Radcliffe Award; 1948 death of Jinnah; 1951 assassination of Liaquat Ali Khan.

Constitutional sequence: 1956 constitution (first), 1962 constitution (Ayub Khan), 1973 constitution (current, framed under Zulfikar Ali Bhutto).

Hijrah: migration of Prophet Muhammad from Makkah to Madinah in 622 CE, which marks year 1 of the Islamic calendar.

Battle of Badr (2 AH) was the first major battle; the Treaty of Hudaybiyyah (6 AH) preceded the peaceful conquest of Makkah (8 AH).

Khulafa-e-Rashidun (Rightly Guided Caliphs): Abu Bakr, Umar ibn al-Khattab, Uthman ibn Affan, and Ali ibn Abi Talib.

Key terms: wahy (revelation), tawhid (oneness of God), shirk (associating partners with God), taqwa (God-consciousness), and sunnah (prophetic practice).