ADRE Grade 3 cheat sheet

The Constitution of India was adopted on 26 November 1949 and came into force on 26 January 1950; Dr B. R. Ambedkar chaired the Drafting Committee.

Fundamental Rights occupy Part III (Articles 12-35); the Right to Constitutional Remedies (Article 32) is called the 'heart and soul of the Constitution' by Ambedkar.

The Governor of a state is appointed by the President, not elected; the Chief Minister is appointed by the Governor as leader of the majority in the Legislative Assembly.

Assam's state animal is the one-horned rhinoceros, state bird the white-winged wood duck, and state flower the foxtail orchid (Kopou Phul).

The UN was founded in 1945 with headquarters in New York; its current Secretary-General is Antonio Guterres, and India is a founding member.

Nobel Prizes are awarded in Physics, Chemistry, Medicine, Literature, Peace and Economics; the Economics prize was added in 1968 by Sveriges Riksbank.

For current affairs, anchor dates to institutions: ISRO's Chandrayaan-3 soft-landed near the lunar south pole on 23 August 2023.

The Rajya Sabha has a maximum strength of 250 members; 12 are nominated by the President for expertise in literature, science, art and social service.

Subject-verb agreement: singular subjects take singular verbs; 'each, every, either, neither, everyone' are grammatically singular ('Each of the boys is ready').

Articles: 'a' before consonant sounds, 'an' before vowel sounds judged by pronunciation ('an hour', 'a university', 'an MLA').

Passive voice forms with 'be' + past participle and keeps the tense: 'She writes a letter' becomes 'A letter is written by her'.

Direct to indirect speech shifts tense back one step and changes pronouns and time words (now to then, today to that day, tomorrow to the next day).

Prepositions of time: 'in' for months, years and long periods; 'on' for days and dates; 'at' for clock times and night.

Conditional type 2 uses past simple in the if-clause and 'would + base verb' in the main clause ('If I were rich, I would travel').

Common error: 'one of the' takes a plural noun but a singular verb ('One of the students is absent').

Synonyms and antonyms are best solved by substituting the word into the sentence and checking whether meaning is preserved or reversed.

Area formulas: rectangle l x b; triangle (1/2) x base x height; circle pi r squared; trapezium (1/2)(a+b)h.

Simple interest = P x R x T / 100; compound interest = P(1 + R/100)^T - P for annual compounding.

Percentage change = (new - old)/old x 100; successive discounts of a% and b% equal a + b - ab/100 percent.

Profit percent = (SP - CP)/CP x 100; if an article is sold at a loss of x%, SP = CP(1 - x/100).

Average of n numbers = sum/n; if every value is increased by k, the average also increases by k.

Speed = distance/time; to convert km/h to m/s multiply by 5/18, and m/s to km/h multiply by 18/5.

LCM x HCF = product of the two numbers (valid for exactly two positive integers).

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

Number series: check differences first, then ratios, then alternating or square/cube patterns before assuming a rule.

Coding-decoding with letter shifts: A=1 to Z=26; a shift of +3 turns CAT into FDW.

Blood relations: draw a family tree with gender markers; 'maternal uncle' means mother's brother, 'paternal aunt' means father's sister.

Direction sense: net displacement uses Pythagoras when movements are perpendicular; a right turn after facing north means facing east.

Ratio and proportion: if a:b = 2:3 and b:c = 4:5, make b common to get a:b:c = 8:12:15.

Time and work: if A finishes in x days and B in y days, together they take xy/(x+y) days.

Permutation vs combination: arrangements where order matters use nPr; selections where order does not matter use nCr = n!/(r!(n-r)!).

Syllogism: a conclusion follows only if it is true in every possible Venn diagram of the premises; 'some A are B' does not imply 'some B are not A'.

The Ahom kingdom was founded in 1228 by Sukaphaa, who entered Assam through the Patkai hills and established rule in the Brahmaputra valley.

The Battle of Saraighat (1671) was won by Ahom general Lachit Borphukan against the Mughal forces led by Ram Singh.

The Treaty of Yandabo (1826) ended the First Anglo-Burmese War and brought Assam under British control.

Bihu is Assam's chief festival, celebrated in three forms: Bohag Bihu (April, Rongali), Kati Bihu (October, Kongali) and Magh Bihu (January, Bhogali).

Srimanta Sankardeva (1449-1568) founded the Ek Saran Naam Dharma and introduced Sattras and Namghars; Borgeet and Ankiya Naat are associated with him.

The Brahmaputra enters Assam at Sadiya and flows west; major tributaries include the Subansiri, Manas, Dhansiri and Kopili.

Kaziranga National Park, a UNESCO World Heritage Site in Golaghat and Nagaon districts, holds the largest population of the Indian one-horned rhinoceros.

Assam is bounded by Arunachal Pradesh, Nagaland, Manipur, Mizoram, Tripura, Meghalaya and West Bengal, and shares international borders with Bhutan and Bangladesh.

Moidams, the mound-burial system of the Ahom dynasty at Charaideo, were inscribed on the UNESCO World Heritage List in 2024.

The President of India is elected indirectly by an electoral college of elected MPs and elected MLAs; the term is five years.

The Election Commission of India, a constitutional body under Article 324, conducts elections to Parliament, State Legislatures, and the offices of President and Vice-President.

The National Flag was adopted by the Constituent Assembly on 22 July 1947; the Ashoka Chakra has 24 spokes.

The Reserve Bank of India, established in 1935, controls monetary policy; the repo rate is the rate at which it lends to commercial banks.

The G20 2023 summit was hosted by India in New Delhi, where the African Union was admitted as a permanent member.

Article 370, which gave special status to Jammu and Kashmir, was effectively abrogated in August 2019, and the state was reorganised into two union territories.

The Right to Education Act 2009 guarantees free and compulsory education to children aged 6 to 14 under Article 21A.

Tenses: present perfect ('has done') links past action to the present; past perfect ('had done') marks the earlier of two past actions.

'Since' is used with a point of time and perfect tenses; 'for' is used with a duration ('since 2010', 'for five years').

Idioms carry fixed meaning: 'a piece of cake' means very easy; 'once in a blue moon' means very rarely.

Active to passive with modals: 'You must obey the rules' becomes 'The rules must be obeyed by you'.

Collective nouns take a singular verb when acting as one unit ('The team is playing well') and a plural verb when members act individually.

Degrees of comparison: use the comparative for two items and the superlative for three or more; never use 'more' with an -er form.

'Who' refers to the subject and 'whom' to the object; 'which' refers to things, 'that' can refer to both in defining clauses.

Phrasal verbs change meaning with the particle: 'give up' means quit, 'give in' means surrender, 'give away' means donate.

Volume formulas: cube a cubed; cuboid l x b x h; cylinder pi r squared h; sphere (4/3) pi r cubed.

Pythagoras theorem: in a right triangle, hypotenuse squared equals the sum of the squares of the other two sides.

Ratio and mixture: if two solutions mix in ratio m:n with concentrations p% and q%, final concentration = (mp + nq)/(m+n) percent.

Simple interest doubles the principal when R x T = 100; it triples when R x T = 200.

Boats and streams: downstream speed = boat + stream; upstream speed = boat - stream; boat speed = (down + up)/2.

Mean, median and mode: mean is sum/n; median is the middle value of ordered data; mode is the most frequent value.

Compound interest for 2 years equals simple interest plus interest on the first year's interest: CI - SI = P(R/100) squared.

Divisibility: a number is divisible by 3 if its digit sum is divisible by 3, by 9 if the digit sum is divisible by 9, and by 4 if the last two digits form a multiple of 4.

Ages problems: translate statements into equations using a base year and solve simultaneously; check by substituting back.

Calendar: an ordinary year shifts the day of the week by 1, a leap year by 2; 100 years shift by 5 odd days.

Clock: the minute hand gains 5.5 degrees per minute on the hour hand; hands coincide 11 times in 12 hours.

Analogy and classification: identify the relation type (part-whole, cause-effect, worker-tool) before choosing the matching pair.

Seating arrangement: fix the most constrained person first, then place others relative to that anchor.

Partnership: profit shares are proportional to capital multiplied by time invested, not capital alone.

Average speed for equal distances at speeds a and b is the harmonic mean 2ab/(a+b), not the arithmetic mean.

Statement and assumption: an assumption is valid only if the statement cannot stand without it, not merely if it is plausible.

Assam's capital is Dispur, a locality within Guwahati; the state was reorganised in 1972 when Meghalaya, Mizoram and Arunachal Pradesh were separated.

Assamese is the official language of Assam and is recognised in the Eighth Schedule; Bengali is an official language in the Barak Valley districts.

The Assamese script descends from the Brahmi-derived Kamarupi script; the Assamese alphabet has 11 vowels and 41 consonants.

Kamakhya Temple on Nilachal Hill in Guwahati is a major Shakti Peetha; Ambubachi Mela is its principal festival.

The Assam Accord was signed on 15 August 1985, setting 25 March 1971 as the cut-off date for identifying foreign nationals.

Majuli, in the Brahmaputra, is among the world's largest river islands and is a centre of Vaishnavite Sattras such as Kamalabari and Auniati.

Tea was first commercially cultivated in Assam in the 1830s; the Assam Tea Company was formed in 1839, and the state produces a large share of India's tea.

The Barak Valley, with Silchar as its main city, is drained by the Barak River and is distinct from the Brahmaputra valley in language and terrain.

The Supreme Court of India, established on 28 January 1950, is the highest court; its judges retire at 65, High Court judges at 62.

The Comptroller and Auditor General audits government accounts and is called the guardian of the public purse; the office is independent of the executive.

The Indian Space Research Organisation is headquartered in Bengaluru; Vikram Sarabhai is regarded as the father of the Indian space programme.

The Non-Aligned Movement was founded in Belgrade in 1961 with India, Yugoslavia, Egypt, Ghana and Indonesia as leading members.

The National Human Rights Commission is a statutory body created by the Protection of Human Rights Act 1993, not a constitutional body.

The Constitution's Preamble was amended by the 42nd Amendment (1976), which added 'socialist', 'secular' and 'integrity'.

The Indian currency symbol rupee was designed by D. Udaya Kumar and adopted by the government in 2010.

'Little' means hardly any (negative), 'a little' means some (positive); the same contrast holds for 'few' and 'a few'.

Question tags use the opposite polarity of the statement and repeat the auxiliary ('She is coming, isn't she?').

Gerunds act as nouns ('Swimming is good exercise'); infinitives follow certain verbs such as 'want', 'decide' and 'hope'.

Reported questions drop the question mark and use statement order: 'Where do you live?' becomes 'He asked where I lived'.

'Although' introduces a subordinate clause and takes no 'but'; 'despite' is followed by a noun or gerund.

Homophones: 'their' is possessive, 'there' is place, 'they're' is a contraction; 'its' is possessive, 'it's' means 'it is'.

One-word substitutions: 'altruist' is a person who lives for others, 'misanthrope' hates mankind, 'ephemeral' lasts a very short time.

Sentence correction: check subject-verb agreement, tense consistency, pronoun reference and preposition choice in that order.

Quadratic equation ax squared + bx + c = 0 has roots with sum -b/a and product c/a.

Percentage to fraction shortcuts: 25% = 1/4, 20% = 1/5, 12.5% = 1/8, 16.67% = 1/6.

Simple interest on a sum is the same each year; compound interest grows because interest is added to the principal.

If a pipe fills a tank in x hours and a drain empties it in y hours, the net filling time is xy/(y - x) when y is greater than x.

Area of a rhombus = (1/2) x product of diagonals; area of an equilateral triangle = (sqrt3/4) x side squared.

Simple and compound interest are equal for the first year at the same rate; they diverge from the second year onward.

To find a number when a percentage of it is given, divide the given value by the percentage and multiply by 100.

Speed problems with two trains crossing: relative speed is the sum when moving in opposite directions and the difference when moving in the same direction.

Series with squares and cubes: check n squared, n cubed, and n squared plus or minus a constant before other rules.

Ranking problems: total = (position from left + position from right) - 1 when counting the same person once.

Data interpretation: read units and axes first; percentage share is computed against the stated total, not the largest value.

Venn diagram problems: for two sets, n(A or B) = n(A) + n(B) - n(A and B).

Odd one out in numbers: check divisibility, prime status, digit sum, and square or cube status in that order.

Alphabet series: write the alphabet with positions 1 to 26; reverse positions sum to 27 (A pairs with Z).

Mixture and alligation: the ratio of two ingredients equals the difference of their values from the mean, taken crosswise.

Coding by pattern shift: if letters are reversed within words, decode by reversing each coded word back before reading the sentence.

The Kachari kingdom had its capital at Dimapur and later at Maibong and Khaspur; the Dimasa are its principal descendants.

The Koch kingdom under Naranarayan and Chilarai expanded in the 16th century; Chilarai is remembered as a celebrated general.

Assam's highest peak is in the Patkai range region; the state's terrain includes the Brahmaputra valley, the Barak valley, the Karbi Anglong and North Cachar hills.

Kaziranga, Manas, Nameri, Orang and Dibru-Saikhowa are Assam's national parks; Manas is also a UNESCO World Heritage Site and a tiger reserve.

Bihu dance and the Husori and Bihu Geet traditions accompany Bohag Bihu; the dhol, pepa and gagana are associated instruments.

The Assamese 'Buranji' are chronicles of the Ahom kingdom, written in the Assamese language and important historical sources.

Assam shares its longest interstate boundary with Arunachal Pradesh and its main international boundary with Bangladesh.

Sankardeva's Vaishnavite movement used the Namghar as a community prayer hall and the Sattra as a monastic institution, with the Kirtan Ghosha as a core text.

The Governor-General of India who introduced the Doctrine of Lapse was Lord Dalhousie; it annexed Satara, Jhansi and Nagpur.

The Indian National Congress was founded in 1885 in Bombay, with W. C. Bonnerjee as its first president.

The Quit India Movement was launched in August 1942 at Gowalia Tank, Bombay, following the Cripps Mission's failure.

The Constitution of India has 448 articles across 25 parts and 12 schedules as amended; there have been over 100 amendments.

The Union Budget is presented by the Finance Minister; the fiscal deficit is the gap between total expenditure and total receipts excluding borrowings.

The World Health Organization is a UN specialised agency headquartered in Geneva, established on 7 April 1948.

India's 2011 Census recorded a literacy rate of about 74 percent, with Kerala highest among states.

'Each other' is used for two people and 'one another' for more than two.

'Between' takes two items and 'among' takes three or more; 'between' is followed by object pronouns ('between you and me').

Modal verbs: 'should' expresses advice, 'must' strong obligation, 'may' permission or possibility, 'can' ability.

'Used to' plus base verb expresses a past habit ('He used to play'); 'be used to' plus gerund means accustomed to.

Prefixes reverse meaning: 'un-', 'dis-', 'in-', 'im-', 'il-', 'ir-'; the choice matches the following consonant sound.

Antonym pairs often share a root with a negative prefix: 'possible' and 'impossible', 'legal' and 'illegal'.

Cloze tests: read the whole passage first, then choose the option that fits both grammar and the surrounding meaning.

'A number of' takes a plural verb, while 'the number of' takes a singular verb.

Logarithm rules: log(ab) = log a + log b; log(a/b) = log a - log b; log(a to the power n) = n log a.

Simple interest formula rearranged: rate = 100 x SI/(P x T); time = 100 x SI/(P x R).

Successive percentage increase of a% then b% equals a + b + ab/100 percent.

If the price of an item rises by x%, consumption must fall by 100x/(100 + x) percent to keep expenditure unchanged.

HCF of fractions = HCF of numerators / LCM of denominators; LCM of fractions = LCM of numerators / HCF of denominators.

Sum of interior angles of an n-sided polygon = (n - 2) x 180 degrees; each exterior angle of a regular polygon = 360/n degrees.

Arithmetic progression: nth term = a + (n - 1)d; sum of n terms = n/2 [2a + (n - 1)d].

Geometric progression: nth term = a x r to the power (n - 1); sum of n terms = a(r to the power n - 1)/(r - 1) when r is not 1.

Cubes and dice: opposite faces of a standard die sum to 7; in a painted cube of side n, cubes with exactly two painted faces = 12(n - 2).

Mirror image: left and right are interchanged while top and bottom stay the same; water image reverses top and bottom.

Paper folding and cutting: unfold in reverse order, mirroring the cut across each fold line.

Data sufficiency: a statement is sufficient only if it gives a unique answer, not merely a possible one.

Ratio comparison: to compare a/b and c/d, cross-multiply; ad greater than bc means a/b is larger.

Profit and loss with two articles sold at the same price, one at gain x% and one at loss x%, always yields a net loss of x squared/100 percent.

Time, speed and distance with a train crossing a platform: total distance = train length + platform length.

Logical deduction: 'all A are B' plus 'all B are C' yields 'all A are C'; 'no A is B' plus 'all C are A' yields 'no C is B'.

The Ahom capital was shifted to Rangpur (Sibsagar) by Rudra Singha and later to Jorhat by Gaurinath Singha; Charaideo was the original royal burial site.

The Moamoria rebellion in the late 18th century weakened the Ahom kingdom and contributed to the Burmese invasions.

Assam's principal rivers include the Brahmaputra, Barak, Subansiri, Manas, Dhansiri, Kopili and Jia Bharali; the Brahmaputra is called Tsangpo in Tibet and Dihang on entry.

Guwahati is the largest city and gateway to the northeast; it lies on the south bank of the Brahmaputra and is home to the Kamakhya and Umananda temples.

The Assam Regiment is a regiment of the Indian Army raised in 1941 at Shillong; its regimental centre is at Happy Valley, Shillong.

The Assam Sahitya Sabha, founded in 1917, promotes Assamese language and literature and holds annual sessions.

Bodos, Mishings, Karbis, Dimasas, Rabhas, Tiwas and Sonowal Kacharis are among Assam's recognised plains tribes.

The Assam Chah Bagicha Dhan Puraskar scheme and the Assam Accord relate to tea garden worker welfare and foreigner detection respectively.

The President can declare a National Emergency under Article 352 on grounds of war, external aggression or armed rebellion.

Financial emergency is declared under Article 360; it has never been invoked in India.

The Attorney General of India is appointed by the President under Article 76 and advises the government on legal matters.

The Goods and Services Tax came into effect on 1 July 2017 as a destination-based indirect tax replacing multiple taxes.

The National Green Tribunal, established in 2010, hears environmental disputes and applies the polluter-pays and precautionary principles.

The Nobel Peace Prize is awarded in Oslo by a Norwegian committee, while the other Nobel Prizes are awarded in Stockholm.

The Asian Development Bank is headquartered in Manila; the World Bank and IMF are headquartered in Washington, DC.

'Since' and 'for' with present perfect continuous: 'He has been working here since 2015 for eight years'.

'Hardly' and 'scarcely' are followed by 'when', and 'no sooner' by 'than', in past perfect constructions.

'Neither...nor' and 'either...or' take a verb agreeing with the nearer subject.

'If I had known' introduces a third conditional with 'would have + past participle' in the main clause.

Adjectives ending in '-ly' are not adverbs: 'friendly', 'lovely' and 'likely' are adjectives.

'Comprise' takes no 'of': 'The team comprises five members', not 'comprises of'.

'The' is used with superlatives, unique objects and rivers and mountain ranges, but not with most proper names of countries.

Direct speech punctuation: the reporting clause is separated by a comma and the exact words are enclosed in quotation marks.

Percentage of a number: x% of N = (x/100) x N; to increase N by x%, multiply by (1 + x/100).

Discount and marked price: SP = MP(1 - discount/100); profit is computed on cost price unless stated otherwise.

Simple interest on a sum becomes 2P when the rate and time product equals 100, so R x T = 100.

Work and wages: wages are shared in the ratio of work done, which equals the ratio of efficiencies multiplied by time.

Probability of an event = favourable outcomes / total equally likely outcomes; the sum of all probabilities is 1.

Area of a sector = (theta/360) x pi r squared; length of an arc = (theta/360) x 2 pi r.

Total surface area of a cylinder = 2 pi r(r + h); curved surface area = 2 pi r h.

To find the original value after a percentage decrease, divide the final value by (1 - decrease/100).

Simple interest and compound interest on the same sum at the same rate: CI exceeds SI from the second year onward.

Ratio of ages: if the present ratio is a:b, write ages as ax and bx and use the future or past condition to find x.

Pipes and cisterns: if a pipe fills in x hours, its one-hour work is 1/x; add rates for pipes working together.

Direction with turns: track facing direction after each turn; a left turn from east gives north.

Coding by letter position: if the code for 'CAT' is 'DBU', the shift is +1; verify with all letters before applying.

Counting figures: number of straight lines in a grid of m by n points is m x n(n - 1)/2 plus n x m(m - 1)/2.

Average of consecutive numbers is the middle term; for an even count, it is the mean of the two middle terms.

Statement and conclusion: reject conclusions that merely restate a possibility or bring in information not given in the statement.

Assam's climate is humid subtropical with heavy monsoon rainfall; the Brahmaputra valley records high humidity and the state is prone to floods and erosion.

Majuli has lost significant area to Brahmaputra erosion; the island is home to the Satras of Kamalabari, Auniati, Garamur and Bengenaati.

The Assam roofed turtle, hoolock gibbon and pygmy hog are among Assam's endangered species; the pygmy hog is found in Manas.

The Assam Medical College at Dibrugarh, established in 1947, is among the oldest medical colleges in northeast India.

Gopinath Bordoloi, Assam's first Chief Minister after independence, received the Bharat Ratna in 1999 for his role in keeping Assam in India.

Jyoti Prasad Agarwala, Bishnu Prasad Rabha and Bhupen Hazarika are cultural icons; Agarwala is called Rupkonwar and Hazarika received the Dadasaheb Phalke Award.

The Assam Legislative Assembly has 126 seats; the state sends 14 members to the Lok Sabha and 7 to the Rajya Sabha.

The Karbi Anglong and Dima Hasao districts are hill districts administered under the Sixth Schedule of the Constitution.

The Indian Army's highest peacetime gallantry award is the Ashoka Chakra; the Param Vir Chakra is the highest wartime gallantry award.

The National Sports Awards include the Major Dhyan Chand Khel Ratna, the Arjuna Award and the Dronacharya Award for coaches.

The Ramsar Convention, signed in 1971 in Iran, protects wetlands; Deepor Beel near Guwahati is a Ramsar site.

The Bharatiya Nyaya Sanhita replaced the Indian Penal Code in 2024, alongside the Bharatiya Nagarik Suraksha Sanhita and Bharatiya Sakshya Adhiniyam.

The Finance Commission, constituted every five years under Article 280, recommends devolution of taxes between the Union and states.

The National Population Register and the Census are conducted by the Office of the Registrar General and Census Commissioner under the Ministry of Home Affairs.

The Indian Constitution's Eighth Schedule currently lists 22 languages, including Assamese, Bodo and Dogri.

'Lie' and 'lay': 'lie' is intransitive (recline), 'lay' is transitive (place something); past forms are lay/lain and laid/laid.

'Affect' is usually a verb and 'effect' usually a noun; 'advice' is the noun and 'advise' the verb.

'Too' means excessively and 'very' means to a high degree; 'too' before an adjective often implies a negative result.

'Enough' follows adjectives ('good enough') but precedes nouns ('enough money').

'Such' is used before a noun phrase and 'so' before an adjective or adverb ('such a tall boy', 'so tall').

'In spite of' and 'despite' take a noun or gerund; 'although' and 'though' take a clause.

'Whoever' is a subject pronoun and 'whomever' an object pronoun; choose by its role inside the clause.

'The number of' is followed by a plural noun and a singular verb; 'a number of' is followed by a plural noun and a plural verb.

Simple interest is calculated on the original principal only; compound interest is calculated on the principal plus accumulated interest.

If a sum doubles in T years at simple interest, the rate is 100/T percent per annum.

Percentage error = (error/true value) x 100; it measures accuracy of a measurement.

Ratio of areas of similar figures equals the square of the ratio of corresponding sides; ratio of volumes equals the cube.

Median of an even number of ordered values is the average of the two middle values.

Probability of at least one event = 1 - probability of none occurring.

If the selling price of two articles is the same and one is sold at a gain of x% and the other at a loss of x%, the net result is a loss of x squared/100 percent.

To convert a fraction to a percentage, multiply by 100; to convert a percentage to a decimal, divide by 100.

Syllogism with 'some': 'some A are B' plus 'all B are C' yields 'some A are C' but not 'some C are A' unless stated.

Blood relation with generations: mark each person's generation level; a difference of two levels indicates grandparent or grandchild.

Calendar: the same calendar repeats after 28 years in the Gregorian system for ordinary years, and after 6 or 11 years in some cases.

Clock: hands are at right angles 22 times in 12 hours and opposite 11 times in 12 hours.

Seating in a circle: for n people, the number of arrangements is (n - 1)! when clockwise and anticlockwise are distinct.

Data interpretation: average = total/n; compute totals from the chart before dividing, and keep units consistent.

Number series with alternating operations: check whether two interleaved series are combined before assuming a single rule.

Direction and distance: after moving north then east, the shortest distance to the start is the hypotenuse of the right triangle formed.

The Ahom administrative system included the Borphukan, Borbarua, Borphukan and Barbaruah offices; Lachit Borphukan commanded the Saraighat defence.

Sukaphaa's followers were called the Tai-Ahom; the Ahom chronicles, the Buranjis, record their history in Assamese.

The Kirtan Ghosha by Sankardeva and the Nam Ghosha by Madhavdeva are foundational Vaishnavite texts in Assamese.

The Assamese Bihu is associated with the agricultural calendar; Bohag Bihu marks the Assamese New Year in mid-April.

Assam's forests include tropical evergreen, semi-evergreen, moist deciduous and grassland types; the Brahmaputra floodplain has extensive grasslands.

The Assam government's Orunodoi scheme provides monthly financial assistance to eligible women; the name comes from the first Assamese newspaper, Orunodoi (1846).

The Battle of Itakhuli in 1682 secured Assam's western boundary against the Mughals and followed Saraighat.

Assam's state song is 'O Mur Apunar Desh', written by Lakshminath Bezbaroa, a leading figure of Assamese literature.

'Whose' shows possession and can refer to people or things; 'who's' is a contraction of 'who is'.

'Farther' refers to physical distance and 'further' to additional or figurative extent.

'Fewer' is used with countable nouns and 'less' with uncountable nouns.

'Between you and me' uses the object pronoun because 'between' is a preposition.

'Older' and 'elder' differ: 'elder' is used only for family members and precedes the noun.

'Each' is followed by a singular noun and verb; 'every' cannot stand alone as a pronoun.

'A lot of' and 'plenty of' take either singular or plural verbs depending on the noun that follows.

'Used to' for past habits is not used in the present tense; 'be used to' describes a current state of familiarity.

If two numbers are in ratio a:b and their sum is S, the numbers are Sa/(a+b) and Sb/(a+b).

If the difference between two numbers in ratio a:b is D, the numbers are Da/(b-a) and Db/(b-a) with b greater than a.

Simple interest on a sum for T years at R% is PTR/100; if the amount is A, then P = 100A/(100 + RT).

Compound interest for 2 years at R% equals P[(1 + R/100) squared - 1], which simplifies to P(2R/100 + R squared/10000).

The sum of the first n even numbers is n(n+1).

Area of a circle is pi r squared and circumference is 2 pi r; use pi = 22/7 for quick calculation when the radius is a multiple of 7.

Diagonal of a square of side a is a times sqrt2; diagonal of a rectangle is sqrt(l squared + b squared).

If the price of an item falls by x%, the new price is the old price multiplied by (1 - x/100).

Analogy with numbers: check the operation linking the first pair (multiply, square, add) and apply it to the second pair before choosing.

Classification of words: group by category (animal, tool, occupation) and find the word that belongs to a different category.

Ordering by rank: if A is taller than B and B is taller than C, then A is taller than C; draw a chain to answer.

Coding with mixed operations: check whether the code uses the previous letter, the next letter, or a positional sum before applying a rule.

Data sufficiency with two statements: test each statement alone first, then together, and mark the option that matches the unique-answer rule.

Venn diagram of three sets: total = sum of individual counts - sum of pairwise overlaps + triple overlap.

Profit and loss: if cost price and selling price are in ratio a:b, profit percent = (b - a)/a x 100.

Time and work with efficiency: if A is twice as efficient as B, A takes half the time B takes for the same work.

The Brahmaputra is one of the world's largest rivers by discharge; it is braided in Assam and forms chars and sandbars used for settlement and cultivation.

Assam's tea-growing districts include Dibrugarh, Tinsukia, Sivasagar, Golaghat, Jorhat and Cachar; the Brahmaputra valley produces most of the state's tea.

The Assam Valley and Barak Valley are separated by the Karbi Anglong and North Cachar Hills, which form a watershed between the two river systems.

Sivasagar, formerly Rangpur, has Ahom monuments including the Rang Ghar, Talatal Ghar and Sivadol, built under Ahom kings.

The Assamese festival of Bihu is secular-agricultural, while Bihugeet and Husori are performed by groups visiting households.

The Assam Police and the state's administrative divisions include 35 districts as of recent reorganisation; Guwahati is the largest urban centre.

The Assam government's 'Nijut Moina' and 'Orunodoi' schemes address education and women's welfare respectively.

Assam's official state tree is the nahor (Mesua ferrea); the state fish is the kurhi (a type of carp).