NPSC Police Constable Exam cheat sheet

Subject-verb agreement: a singular subject takes a singular verb; phrases between subject and verb (with, along with, as well as) do not change the verb number.

Articles: 'a' before consonant sounds (a university, a one-rupee coin), 'an' before vowel sounds (an hour, an MLA).

Tenses: present perfect (has/have + past participle) for past actions with present relevance; simple past for finished past actions with a stated time.

Prepositions of time: 'in' for months/years, 'on' for days/dates, 'at' for clock times and night/noon.

Active to passive: object becomes subject, verb becomes be + past participle, agent introduced by 'by' (e.g., 'She wrote the letter' becomes 'The letter was written by her').

Direct to indirect speech: shift present to past, change pronouns to third person, and change time words (now becomes then, today becomes that day).

Common confusables: affect (verb) vs effect (noun); principal (head/main) vs principle (rule); stationary (not moving) vs stationery (writing material).

Synonyms/antonyms and one-word substitutions are tested as single-sentence items; idioms are tested in context, so read the whole sentence before choosing.

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); Fundamental Duties were added by the 42nd Amendment (1976) on the Swaran Singh Committee recommendation.

The President is the constitutional head of state; the Prime Minister heads the Council of Ministers; the Chief Justice of India heads the judiciary.

Geography: the Tropic of Cancer passes through eight Indian states, including Gujarat, Rajasthan, Madhya Pradesh, and Mizoram.

Indian economy: the Reserve Bank of India was established in 1935 and nationalised in 1949; it controls monetary policy and issues currency.

Science basics: the SI unit of force is the newton, of power the watt, and of electric current the ampere; photosynthesis occurs in chloroplasts.

Current affairs: track national awards (Bharat Ratna, Padma awards), sports championships, space missions (ISRO launches), and UN/global summit themes for the year of the exam.

Static-plus-current link: for any current event, note the person, place, and date, because questions often ask the associated state or country.

Percentage: x% of N = (x/100) x N; successive changes of a% then b% give a net change of a + b + ab/100 percent.

Profit and loss: profit% = (SP - CP)/CP x 100; discount% is always calculated on the marked price, not the cost price.

Simple interest SI = P x R x T/100; compound interest CI = P(1 + R/100)^T - P.

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

Average = sum of observations / number of observations; if every value is increased by k, the average increases by k.

Ratio and proportion: if a:b = c:d then ad = bc; for partnership, profit shares are proportional to capital x time.

Time and work: if A finishes in x days and B in y days, together they finish in xy/(x + y) days; use LCM of days as total work units.

Mensuration: area of circle = pi r^2, circumference = 2 pi r; volume of cylinder = pi r^2 h; area of triangle = (1/2) x base x height.

Number system: HCF x LCM = product of the two numbers; divisibility by 3 or 9 holds when the digit sum is divisible by 3 or 9 respectively.

Number series: check differences first, then ratios, then squares/cubes or alternating patterns; odd-one-out items usually break one consistent rule.

Alphabet positions: A=1 to Z=26; opposite-letter pairs sum to 27 (A-Z, B-Y, C-X), useful for coding-decoding.

Coding-decoding: identify whether letters shift forward/backward by a fixed number, or whether the word is reversed, before applying the rule to the target word.

Blood relations: draw a family tree with gender symbols; 'brother of my father' is uncle, 'son of my mother's brother' is cousin.

Direction sense: draw the path on paper; net displacement uses Pythagoras when the path turns at right angles (result = square root of a^2 + b^2).

Syllogism: 'All A are B' does not imply 'All B are A'; only conclusions that hold in every possible diagram are valid.

Seating arrangement: fix the person with the most constraints first, then place others relative to that anchor; circular arrangements treat left/right as facing-dependent.

Clock and calendar: the minute hand gains 5.5 degrees per minute on the hour hand; a non-leap year shifts the day of the week by one, a leap year by two.

Nagaland attained statehood on 1 December 1963, carved out of Assam; Kohima is the capital and Dimapur is the largest commercial town.

Nagaland shares borders with Assam to the west and north, Arunachal Pradesh to the north-east, Manipur to the south, and Myanmar to the east.

The state has 17 recognised major tribes, including Angami, Ao, Konyak, Lotha, Sumi, Chakhesang, Rengma, Phom, and Zeliang, each with distinct dialects and festivals.

Hornbill Festival is held every year from 1 to 10 December at Kisama Heritage Village near Kohima, showcasing tribal dance, music, and crafts.

The Angami festival Sekrenyi, the Ao festival Moatsu, and the Sumi festival Tuluni are among the major tribal festivals tied to agricultural cycles.

Kohima War Cemetery commemorates soldiers of the 1944 Battle of Kohima; the state is also known for the Naga shawl, log drum, and bamboo craft traditions.

English is the official language and the medium of instruction; Naga languages belong largely to the Tibeto-Burman family and are written in the Roman script.

Mount Saramati on the Nagaland-Myanmar border is the highest peak in the state; the Doyang and Dhansiri are among its main rivers.

Height, chest, and weight are measured barefoot with standard instruments; height is recorded to the nearest 0.5 cm and chest to the nearest 0.5 cm.

Chest measurement is taken in two states: unexpanded (normal) and expanded; the minimum expansion required is typically 5 cm.

Height and chest minimums differ by category (general, scheduled tribe, and other reserved categories) and by gender, so candidates must check the official notification for their category.

Weight must be proportionate to height and age; a candidate who fails the height or chest standard is not permitted to proceed to the Physical Efficiency Test.

Vision and general health are checked alongside physical measurements; knock knees, flat feet, and deformities may lead to rejection at the medical stage.

Measurements are recorded on the official PET/PST form and signed by the measuring officer; candidates should carry the admit card and identity proof.

Standards may be relaxed for candidates from hilly or tribal areas as specified in the notification; relaxations are never automatic and must be claimed with documents.

PET events for constable recruitment typically include a race (often 1600 m or 800 m), long jump, and shot put; qualifying marks are set separately for each event.

Running is time-qualified: finish within the prescribed time; pacing and even breathing matter more than a fast start over a short distance.

Long jump is measured from the take-off line to the nearest landing mark; a foot crossing the take-off board is a foul and the attempt does not count.

Shot put is thrown from within a circle; the put must land within the sector, and the athlete must exit from the rear half of the circle after the implement lands.

Candidates usually get a fixed number of attempts per field event (commonly three), and the best valid attempt is recorded.

Warm-up before the run and cool-down after reduce cramp risk; footwear should be broken in before the test day, not new.

Scores are recorded on the official PET sheet and countersigned; candidates should verify their recorded times and distances before signing.

Negative marking, where applied, makes blind guessing costly; guess only when at least one option can be eliminated with confidence.

Attempt order: clear easy one-line English and general knowledge items first, then reasoning, then arithmetic, to bank marks early.

Time per item: with roughly one minute per question, a question unsolved in 90 seconds should be marked and revisited later.

For arithmetic, substitute answer options into the question when solving algebraically would take longer than checking.

Read the last line of a question first to know exactly what is asked (value, ratio, or 'which is NOT true').

For current affairs, anchor each fact to a person, place, and year; distractors usually swap one of these three.

OMR discipline: fill bubbles fully with a black ballpoint, and reserve the last five minutes for transferring answers and checking roll number fields.

Nagaland has 16 administrative districts; Kohima and Dimapur are the most populous, and Mon lies in the north-east bordering Myanmar.

The state lies in a seismic zone IV-V belt and receives heavy monsoon rainfall, supporting terraced wet rice cultivation in valleys.

Dzukou Valley, on the Southern Angami area border with Manipur, is known for its seasonal lily and biodiversity.

The Naga Hills run north-east to south-west; Saramati (about 3,840 m) is the highest point, near the Myanmar border.

The state legislature is unicameral (Nagaland Legislative Assembly), and the state sends one member to the Lok Sabha and one to the Rajya Sabha.

The Hornbill is the state bird and the rhododendron (Rhododendron arboreum) the state flower; the Mithun is the state animal.

The Naga insurgency and the 1997 ceasefire, followed by peace talks, are key to understanding the state's modern political history.

'One of the + plural noun' takes a singular verb: 'One of the boys is absent.'

'Each', 'every', 'either', 'neither', and 'everyone' are singular and take singular verbs and pronouns.

Collective nouns (team, jury, committee) take a singular verb when acting as a unit and a plural verb when members act individually.

Comparatives: use 'than' after a comparative and 'to' after superior, inferior, senior, junior, and preferable.

'Hardly', 'scarcely', and 'no sooner' are followed by 'when' or 'than' with inverted word order: 'Hardly had he arrived when it rained.'

Avoid double negatives ('didn't do nothing') and redundant comparatives ('more better'); use 'much' or 'far' to intensify a comparative.

Spelling traps in Indian exams: occurrence, committee, separate, government, millennium, and maintenance.

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

If price increases by R%, consumption must fall by 100R/(100 + R) percent to keep expenditure unchanged.

Mixture and alligation: the ratio of two components is the inverse ratio of their deviations from the mean value.

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

Pipes and cisterns: a filling pipe's rate is positive and a draining pipe's rate is negative; add rates algebraically.

Simple interest doubles a sum in 100/R years; for compound interest, use the rule of 72 as a quick doubling estimate.

Permutation vs combination: order matters for permutation (nPr = n!/(n-r)!); order does not for combination (nCr = n!/(r!(n-r)!).

Probability of an event = favourable outcomes / total outcomes; P(not A) = 1 - P(A).

Coding-decoding: test a fixed shift first; if that fails, test reversal, position-based values (A=1), or a shift that alternates between letters.

Number series with rapid growth suggests multiplication or squares; slow growth with irregular gaps suggests alternating addition and subtraction.

Analogy: identify the exact relation (part to whole, worker to tool, young to adult) before applying it to the target pair.

Ranking: if a person is nth from the left and mth from the right, total = n + m - 1.

Calendar: the day repeats after 7 days; for a given date, count odd days from a known reference year.

Statement and assumption: an assumption is unstated but necessary; reject options that merely restate the statement.

Puzzle seating: draw the arrangement and mark fixed positions; if two cases remain, test each against all clues and discard the contradiction.

Train specifically for the event distances: interval running for the race, bounding and approach-run drills for long jump, and glide or spin technique for shot put.

Shot put weights differ by gender and age group (commonly 7.26 kg for senior men, 4 kg for senior women); check the notification for the exact implement.

Long jump requires a measured approach run; mark the start point and repeat the same run-up so take-off is consistent.

Hydration and sleep the night before matter; avoid heavy meals within three hours of the test.

Carry the admit card, identity proof, sports kit, and spikes or running shoes as specified; jewellery is usually not permitted.

Report early for document verification and biometric checks, which precede the physical events.

Naga society is traditionally clan-based, with village councils and the village chief or elders playing a central role in dispute resolution.

The Morung, a traditional bachelor's dormitory, was a centre for oral history, music, and social training among many tribes.

The Hornbill feather is a symbol of bravery and status in several Naga tribes and features on the state emblem.

Naga cuisine is known for smoked and fermented foods, bamboo shoot, and axone (fermented soybean) among the Sumi.

The state's churches and missionary history since the 19th century have shaped education and language use, with English widely used.

Traditional festivals are tied to the agricultural calendar: sowing, harvesting, and thanksgiving festivals follow the jhum cycle.

Blood groups: O negative is the universal donor for red cells and AB positive the universal recipient.

Vitamins: A for vision, B-complex for metabolism, C for immunity and scurvy prevention, D for calcium absorption, K for clotting.

Human body: the largest organ is the skin, the longest bone the femur, and the smallest bone the stapes in the ear.

Electricity: power P = VI = I^2R = V^2/R; household wiring is in parallel so each appliance gets full voltage.

Light: reflection follows the angle of incidence equals the angle of reflection; a convex lens converges and a concave lens diverges.

Chemistry: pH below 7 is acidic and above 7 is basic; litmus turns red in acid and blue in base.

Environment: the greenhouse gases include carbon dioxide, methane, and nitrous oxide; the ozone layer absorbs ultraviolet radiation.

The Indian National Congress was founded in 1885; the partition of Bengal in 1905 triggered the Swadeshi movement.

Key dates: Jallianwala Bagh 1919, Non-Cooperation 1920, Dandi March 1930, Quit India 1942, Independence 15 August 1947.

The Constituent Assembly adopted the Constitution on 26 November 1949; the Preamble was amended by the 42nd Amendment to add socialist, secular, and integrity.

The Directive Principles of State Policy (Part IV) are non-justiciable; Fundamental Rights (Part III) are enforceable through writs.

The three lists of the Seventh Schedule are Union, State, and Concurrent; residuary powers rest with the Union.

The Election Commission of India is a constitutional body under Article 324; the Comptroller and Auditor General is under Article 148.

The Governor is appointed by the President and is the constitutional head of the state; the Chief Minister heads the state executive.

Nagaland's districts include Kohima, Dimapur, Mokokchung, Tuensang, Mon, Wokha, Zunheboto, Phek, and Longleng, among others created by later reorganisations.

Dimapur is the gateway to the state, hosts the only airport, and is the commercial hub with the state's main rail link.

Kohima hosted the 1944 battle and is home to the state civil secretariat, the Nagaland University campus, and the war cemetery.

Mokokchung is the cultural centre of the Ao tribe; Tuensang and Mon are in the eastern hills bordering Myanmar.

The state is administered through districts, subdivisions, and blocks; the Deputy Commissioner heads the district administration.

The Nagaland Public Service Commission conducts state civil service recruitment; the state police are headed by the Director General of Police.

The state's economy is predominantly agrarian, with jhum (shifting) cultivation and terrace rice cultivation as major practices.

For a reading passage, read the questions first, then scan for keywords; answers are usually paraphrases, not verbatim lines.

Inference questions ask what the passage implies, not what it states; eliminate options that go beyond the text.

Antonym questions: consider the word's part of speech and its exact sense before choosing the opposite.

Idioms: 'to let the cat out of the bag' means to reveal a secret; 'a bolt from the blue' means a sudden shock.

One-word substitutions: 'altruist' is a person who lives for others, 'misanthrope' one who hates mankind, 'epicure' one who loves fine food.

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

Average speed over equal distances = 2xy/(x + y) when speeds are x and y; it is never the simple average of the two speeds.

Relative speed: same direction = difference of speeds; opposite direction = sum of speeds.

Trains: time to cross a pole = train length / speed; time to cross a platform = (train length + platform length) / speed.

Work: if A is twice as efficient as B, A takes half the time; efficiency is inversely proportional to time.

Work and wages: wages are shared in the ratio of work done, which equals efficiency x time.

Percentage change in time is inversely related to percentage change in speed for a fixed distance.

Compound interest vs simple interest for two years: the difference equals P x (R/100)^2.

Venn diagrams: 'All A are B' shows circle A inside circle B; 'Some A are B' shows overlapping circles.

Syllogism rules: a conclusion is valid only if it is true in every possible Venn diagram satisfying the premises.

Series with letters: convert letters to numbers, find the numeric pattern, and convert back.

Coding by position: if letters are numbered A=1 to Z=26, the sum or product of positions can form the code.

Direction and distance: draw north up; a left turn from north faces west, and a right turn from east faces south.

Blood relations: use a tree with vertical parent-child lines and horizontal spouse or sibling links to avoid confusion.

Statement-conclusion: a conclusion must follow from the statement alone, not from general knowledge.

Height is measured against a vertical scale with heels together, back straight, and head level (Frankfort plane).

Chest is measured at nipple level with a tape held snug; the candidate exhales normally for the unexpanded reading and inhales fully for the expanded reading.

Weight is measured on a calibrated scale with minimal clothing and no shoes; the reading is recorded in kilograms.

Age is verified from the matriculation certificate or an equivalent document accepted by the commission.

Candidates failing any PST standard are marked absent for PET; there is no second chance on the same day.

Any appeal against measurement must be made on the spot to the presiding officer before signing the form.

Track the annual Hornbill Festival dates and theme, and the state's cultural events held at Kisama.

Note the state's chief minister, governor, and director general of police, as these are common current-affairs questions.

Follow state development news: road and rail connectivity projects, the Dimapur airport, and power projects.

Watch for Naga peace process developments and any agreements with the Government of India.

Sports: note Naga athletes representing the state in national games and the North East Olympic Games.

Environment: Nagaland's community forest conservation and biodiversity records are frequently cited in state exams.

Check for missing articles before singular countable nouns (a, an, the).

Check preposition after verbs: 'discuss about' is wrong, 'discuss' is correct; 'married to', 'comprise' takes no 'of'.

Check parallel structure: items joined by 'and' or 'or' must have the same grammatical form.

Check misplaced modifiers: an introductory participle phrase must refer to the subject of the main clause.

Check tense sequence: past tense in the main clause usually takes past tense in the subordinate clause.

Check redundancy: 'return back', 'repeat again', 'free gift', and 'very unique' are incorrect.

Check countable/uncountable: 'much' with uncountable nouns, 'many' with countable; 'fewer' for countables and 'less' for uncountables.

The United Nations was founded in 1945; its headquarters is in New York, and the Security Council has five permanent members.

The Olympic Games are held every four years; the Summer and Winter Games alternate in a four-year cycle.

FIFA World Cup is held every four years; the Cricket World Cup is also held every four years.

Nobel Prizes are awarded in physics, chemistry, medicine, literature, peace, and economics; the peace prize is announced in Oslo.

SAARC has eight member states; ASEAN has ten members; BRICS includes Brazil, Russia, India, China, and South Africa.

India's space programme: ISRO launched Chandrayaan and Mangalyaan missions, and set records with multi-satellite launches.

Common capitals: Canberra (Australia), Ottawa (Canada), Brasilia (Brazil), and Naypyidaw (Myanmar).

BODMAS order: Brackets, Of/Orders, Division, Multiplication, Addition, Subtraction.

Divisibility: by 4 if the last two digits form a multiple of 4; by 8 if the last three digits form a multiple of 8; by 11 if the alternating digit sum difference is a multiple of 11.

Squares up to 30 and cubes up to 15 should be memorised for quick simplification.

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

To convert a recurring decimal to a fraction, use 9s in the denominator for the repeating part and 0s for non-repeating places.

Approximation: round each number to the nearest convenient value and check which option is closest.

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

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

Paper folding and cutting: unfold step by step, reflecting the cut across each fold line.

Rotation: a 90-degree clockwise rotation moves a top position to the right; 180 degrees moves top to bottom.

Embedded figures: look for the exact shape, including orientation, hidden within the complex figure.

Counting figures: count smallest units first, then combinations, systematically to avoid double counting.

Series of figures: track one element at a time (position, shading, number of sides) rather than the whole figure.

Nagaland was created as the 16th state of India on 1 December 1963 under the State of Nagaland Act, 1962.

Article 371A gives special protection to Naga customary law, land, and resources, and restricts application of parliamentary laws on these subjects.

The Nagaland Legislative Assembly has 60 elected members; the state has one Lok Sabha and one Rajya Sabha seat.

The Governor of Nagaland is appointed by the President; the Chief Minister is the head of the elected government.

The state has autonomous district councils under the Sixth Schedule in some areas, with legislative and judicial powers over customary matters.

The Nagaland Public Service Commission and the Staff Selection Board handle state recruitment; the police are headed by the DGP.

Panchayati Raj in Nagaland has been contested because of constitutional protection for customary institutions.

Qualifying in one event does not guarantee overall qualification; each event has a separate minimum.

Running: aim for negative splits (second half faster) to avoid early fatigue.

Long jump: a short, fast approach with a consistent check mark improves take-off accuracy.

Shot put: the implement must be pushed from the shoulder, not thrown; a foul throw is not measured.

Injury prevention: warm up for 10-15 minutes, stretch after, and stop immediately if sharp pain occurs.

Weather and altitude affect performance; Nagaland's hilly terrain means candidates should train on similar gradients if possible.

India's major rivers: Ganga, Brahmaputra, Indus, Godavari, Krishna, and Narmada; the Brahmaputra flows through Assam into Bangladesh.

The Himalayas are young fold mountains; the Western Ghats are a biodiversity hotspot.

Monsoon: the south-west monsoon brings most of India's rainfall from June to September.

Soil types: alluvial (most fertile), black (cotton), red (iron-rich), and laterite (leached).

National parks: Kaziranga (Assam) for the one-horned rhinoceros, and Keibul Lamjao (Manipur) as a floating park.

Environmental conventions: the Kyoto Protocol and the Paris Agreement address climate change; the Ramsar Convention protects wetlands.

The Indian Meteorological Department issues cyclone and monsoon forecasts.

Prefixes: 'un-', 'in-', 'dis-' negate; 're-' means again; 'pre-' means before; 'post-' means after.

Suffixes: '-able' means capable of; '-less' means without; '-tion' forms a noun; '-ous' forms an adjective.

Word roots: 'bene' means good, 'mal' means bad, 'cred' means believe, 'dict' means say, and 'scrib' means write.

Synonyms: 'abundant' means plentiful, 'candid' means frank, 'diligent' means hardworking.

Antonyms: 'benevolent' vs 'malevolent', 'transparent' vs 'opaque', 'ancient' vs 'modern'.

Phrasal verbs: 'give up' means quit, 'put off' means postpone, 'look into' means investigate.

Read the title, units, and legend of a table or chart before calculating.

For percentage share, divide the part by the total and multiply by 100; for growth, use (new - old)/old x 100.

Approximate aggressively when options are far apart; exact calculation is only needed when options are close.

In pie charts, the angle of a sector equals (value/total) x 360 degrees.

In bar graphs, compare heights directly for ranking questions rather than computing each value.

For average questions in DI, sum the values and divide by the count; do not average the percentages.

Agriculture employs the majority of the population; rice, maize, millet, and pulses are major crops.

Jhum cultivation involves clearing and burning forest patches, cropping for a few years, and then moving on.

Terrace rice cultivation is practised in valley areas, especially among the Angami and Chakhesang.

The state's industrial base is small; bamboo, handicrafts, and horticulture are promoted sectors.

Tourism, especially the Hornbill Festival and eco-tourism, is a growing source of income.

The state depends substantially on central transfers for its budget.

The Reserve Bank of India regulates banks and monetary policy; it was nationalised in 1949.

Bank nationalisation occurred in 1969 and 1980; the lead bank scheme assigns districts to banks.

Inflation is measured by the Consumer Price Index and the Wholesale Price Index.

GDP is the total value of goods and services produced in a country in a year.

Direct taxes include income tax and corporate tax; indirect taxes include GST, which replaced many central and state taxes in 2017.

Financial inclusion schemes include Jan Dhan Yojana, Mudra loans, and Atal Pension Yojana.

Data sufficiency: decide whether the data is enough, not what the answer is; test each statement alone and then together.

If either statement alone is sufficient, the answer is 'either statement alone'; if only together, the answer is 'both together'.

Decision making: choose the option that follows rules and procedures, not personal preference.

For eligibility puzzles, list the conditions and test each candidate against all of them.

For ranking puzzles, convert every statement into a relative position and draw a line.

For clock problems, the angle between hands = |30H - 5.5M| degrees.

Carry the admit card, photo identity, and category certificate in the prescribed format.

Educational certificates and age proof are verified before the physical tests.

Medical fitness certificate may be required at the time of the physical test.

Candidates must meet the age limit as on the cut-off date specified in the notification.

Any discrepancy in name or date of birth across documents can lead to disqualification.

Dress code: sports attire for PET; jewellery and electronic devices are usually prohibited.

A paragraph should have one main idea, supporting sentences, and a concluding sentence.

Formal letters include sender's address, date, receiver's address, subject, salutation, body, and closing.

Notice writing includes the heading 'NOTICE', date, title, body, and the writer's name and designation.

Report writing uses past tense and third person, with a headline and byline.

Essay structure: introduction, body paragraphs, and conclusion; each paragraph should have a topic sentence.

Punctuation: use a comma for items in a list and after introductory phrases; use a semicolon to join related independent clauses.

Sum of interior angles of a polygon = (n - 2) x 180 degrees.

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

Area of a triangle = square root of s(s-a)(s-b)(s-c), where s is the semi-perimeter.

Trigonometric ratios: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent.

Standard values: sin 30 = 1/2, cos 60 = 1/2, tan 45 = 1.

Circle: angle in a semicircle is 90 degrees; the perpendicular from the centre bisects a chord.

Kisama Heritage Village near Kohima hosts the annual Hornbill Festival.

Kohima War Cemetery commemorates the 1944 battle and is maintained by the Commonwealth War Graves Commission.

Dzukou Valley is famous for its natural beauty and seasonal flowers.

Japfu Peak near Kohima is one of the highest peaks in the state.

Intanki National Park in Peren district is a wildlife sanctuary with elephants and tigers.

The state museum in Kohima displays Naga artefacts and tribal culture.

ISRO's Chandrayaan-3 achieved a soft landing near the lunar south pole in 2023.

India's Aditya-L1 mission studies the Sun from the L1 point.

5G services were launched in India in 2022; the technology offers higher speed and lower latency.

Artificial intelligence applications include natural language processing, computer vision, and robotics.

Renewable energy targets: India aims for 500 GW of non-fossil capacity by 2030.

Vaccines and biotechnology: mRNA technology was used in COVID-19 vaccines.

Odd one out: identify the common property of all but one item (e.g., all are fruits except one vegetable).

Analogy types: cause-effect, part-whole, worker-tool, synonym, antonym, and degree.

Number analogy: apply the same arithmetic operation to the second pair as the first.

Letter analogy: convert letters to positions and find the relation between the two positions.

Classification by category: group items by function, origin, or material.

Check the order of the relation: 'pen is to write as knife is to cut' preserves the tool-function relation.

Reserved category candidates may get height and chest relaxations as specified in the notification.

Female candidates have separate height and chest standards from male candidates.

Candidates from hilly areas may get additional relaxation, subject to documentary proof.

Relaxations are granted only if claimed and supported by valid certificates at the time of the test.

The commission's decision on eligibility is final; candidates should read the notification carefully.

Failure to meet the relaxed standard also results in rejection.

'At the eleventh hour' means at the last moment.

'To burn the midnight oil' means to study or work late into the night.

'A blessing in disguise' means something that seems bad but turns out good.

'To beat around the bush' means to avoid the main topic.

'To smell a rat' means to suspect something wrong.

'Once in a blue moon' means very rarely.

If a:b = c:d, then ad = bc; also a/b = c/d implies (a+b)/b = (c+d)/d.

Compound ratio of a:b and c:d is ac:bd.

Mean proportional between a and b is the square root of ab.

Partnership profit ratio = capital x time for each partner.

If capitals are equal, profit shares are proportional to time; if time is equal, to capital.

Dividing a number in the ratio a:b gives parts a/(a+b) and b/(a+b) of the total.

The Supreme Court is the apex court; High Courts are at the state level, and district courts below them.

The Election Commission conducts elections to Parliament, state legislatures, and the offices of President and Vice-President.

The Finance Commission recommends distribution of taxes between the Union and states.

The Union Public Service Commission conducts central recruitment; state PSCs handle state services.

The National Human Rights Commission protects human rights and can inquire into violations.

The Attorney General advises the Government of India on legal matters.

English is the official language and the medium of instruction in schools and government offices.

Naga languages are mostly Tibeto-Burman and are written in the Roman script.

Nagaland University is a central university with campuses in Kohima and Lumami.

Literacy rates have risen steadily, with Kohima and Mokokchung among the more literate districts.

Missionary activity in the 19th century led to the spread of education and Christianity.

The state promotes tribal dialects through cultural organisations and church-run schools.

A false start in a race leads to disqualification under current athletics rules.

In long jump, the take-off foot must be behind the take-off line; measurement is from the line to the nearest mark.

In shot put, the implement must be put from the shoulder and must land within the sector lines.

Field event attempts are measured perpendicular to the take-off line or arc.

Athletes must not receive assistance during the event; pacing by other athletes may be restricted.

The best valid attempt counts; fouls are recorded but not measured.

Skim the passage for the main idea before reading the questions.

Scan for specific names, dates, and numbers when a question asks for detail.

For 'author's tone' questions, look at adjectives and adverbs the author uses.

For 'meaning in context', substitute each option into the sentence and check coherence.

Eliminate options that are too broad, too narrow, or contradicted by the passage.

Do not bring outside knowledge into comprehension answers unless the passage supports it.

If cost price is C and profit is P%, selling price = C(1 + P/100).

If selling price and profit% are known, cost price = SP x 100/(100 + P).

Marked price after discount: SP = MP(1 - d/100).

Successive discounts of a% and b% equal a + b - ab/100 percent.

If an article is sold at a loss of L%, SP = C(1 - L/100).

To find the profit percentage when CP and SP are known: ((SP - CP)/CP) x 100.

Linear arrangement: fix the extremes first, then place people relative to fixed positions.

Circular arrangement: for people facing the centre, left is clockwise and right is anticlockwise.

Floor puzzles: draw a vertical stack with the top floor at the top of the diagram.

Scheduling puzzles: draw a table of days or times and fill fixed entries first.

Use elimination: when a clue contradicts a placement, discard that case.

Double-check the final arrangement against every clue before answering.

The Mahatma Gandhi National Rural Employment Guarantee Act guarantees 100 days of wage employment per rural household per year.

The Public Distribution System provides subsidised food grains to eligible households.

Ayushman Bharat provides health insurance coverage for eligible families.

The Pradhan Mantri Kisan Samman Nidhi gives direct income support to farmers.

The state implements central schemes through district administrations and village councils.

Scholarship schemes support students from scheduled tribes and other reserved categories.

The Bharat Ratna is India's highest civilian award.

The Padma Vibhushan, Padma Bhushan, and Padma Shri are civilian awards in descending order of precedence.

The Param Vir Chakra is the highest wartime military decoration.

The Ashoka Chakra is the highest peacetime military decoration.

The Jnanpith Award is given for literary achievement in Indian languages.

The Arjuna Award recognises outstanding sporting achievement.

Simple present: 'writes' becomes 'is written'.

Simple past: 'wrote' becomes 'was written'.

Present continuous: 'is writing' becomes 'is being written'.

Present perfect: 'has written' becomes 'has been written'.

Future: 'will write' becomes 'will be written'.

Modal: 'can write' becomes 'can be written'.

The object of the active sentence becomes the subject of the passive sentence.

Average of first n natural numbers = (n + 1)/2.

If a person's average increases by x after scoring y in the next test, the number of tests is y - old average divided by x.

Alligation: ratio of quantities = (mean - cheaper)/(dearer - mean).

When a quantity is replaced repeatedly, the remaining pure quantity = original x (1 - replaced/total)^n.

Weighted average = sum of (value x weight) / sum of weights.

If the average of n numbers is A and one number is removed, the new average is (nA - removed)/(n - 1).

A course of action must be practical, relevant, and address the problem in the statement.

Reject actions that are extreme, punitive without cause, or unrelated to the problem.

If the statement describes a problem, a valid action should reduce or solve it.

If the statement describes a fact, actions that follow logically from it may be valid.

Check whether the action can be implemented by the authority mentioned.

Prefer actions that address the root cause over those that only treat symptoms.

BMI = weight in kg / (height in metres)^2; a normal range is roughly 18.5 to 24.9.

Aerobic exercise improves endurance; strength training improves power for shot put and jumping.

Rest days are part of training; overtraining increases injury risk.

Hydration before, during, and after exercise prevents cramps and heat exhaustion.

A balanced diet includes carbohydrates for energy, protein for repair, and fats for essential functions.

Sleep of 7-9 hours supports recovery and performance.

The Naga Hills came under British administration in the 19th century after several expeditions.

The Battle of Kohima in 1944 was a turning point in the Burma campaign of World War II.

Naga leaders submitted a memorandum to the Simon Commission in 1929 seeking protection of Naga identity.

The Naga National Council was formed in 1946, and the demand for autonomy emerged in the late 1940s.

The 1960 agreement led to the creation of Nagaland as a state in 1963.

The 1997 ceasefire between the Government of India and the NSCN (IM) began a peace process that continues.

The largest continent is Asia; the smallest is Australia (Oceania).

The longest river is the Nile; the largest ocean is the Pacific.

The Sahara is the largest hot desert; the Amazon is the largest rainforest.

Mount Everest is the highest peak above sea level.

The Equator passes through South America, Africa, and Asia.

Time zones: the Earth rotates 360 degrees in 24 hours, so each 15 degrees of longitude equals one hour.

'In' for enclosed spaces or months and years; 'on' for surfaces and days; 'at' for points and clock times.

Verbs followed by 'to': listen to, belong to, reply to, prefer to.

Verbs followed by 'of': consist of, beware of, accused of, aware of.

Verbs followed by 'for': wait for, look for, care for, apologise for.

'Between' is used for two, 'among' for more than two.

'Since' is used with a point in time, 'for' with a duration.

Linear equation: ax + b = 0 gives x = -b/a.

Quadratic equation: ax^2 + bx + c = 0, roots = (-b +/- square root of (b^2 - 4ac)) / 2a.

Sum of roots = -b/a; product of roots = c/a.

Identity: (a + b)^2 = a^2 + 2ab + b^2; (a - b)^2 = a^2 - 2ab + b^2.

Difference of squares: a^2 - b^2 = (a + b)(a - b).

If x + 1/x = k, then x^2 + 1/x^2 = k^2 - 2.

Letter-to-number coding: A=1, B=2, and so on; reverse coding uses A=26, B=25.

Sum-of-letters coding: the code is the sum of the letter positions in the word.

Symbol substitution: replace each symbol with the given operation and apply BODMAS.

If '+' means 'x' and 'x' means '+', rewrite the expression before solving.

Matrix coding: identify the row and column rule before decoding.

Check the code direction: sometimes the word is coded from right to left.

The state bird is the Hornbill and the state animal is the Mithun.

The state flower is the rhododendron, and the state tree is the alder.

Intanki National Park and the Fakim Wildlife Sanctuary protect elephants, tigers, and the Blyth's tragopan.

The Blyth's tragopan is a threatened pheasant found in Nagaland's forests.

Community forests are protected by village councils under customary law.

The state's forests support bamboo, orchids, and medicinal plants.

Classical dances include Bharatanatyam, Kathak, Kathakali, Odissi, Manipuri, Kuchipudi, and Mohiniyattam.

The Ajanta and Ellora caves are in Maharashtra; Khajuraho temples are in Madhya Pradesh.

The Taj Mahal is a UNESCO World Heritage Site in Agra.

Hindustani and Carnatic music are the two major classical music traditions.

The Sangeet Natak Akademi promotes performing arts in India.

Folk dances vary by state, such as Bihu in Assam and Garba in Gujarat.

A clock gains 5.5 degrees per minute on the hour hand relative to the minute hand.

Hands coincide every 65 5/11 minutes.

A leap year has 366 days, and February has 29 days.

Odd days: a normal year has 1 odd day; a leap year has 2 odd days.

The day of the week repeats every 7 days.

Century years are leap years only if divisible by 400.

'All A are B' and 'All B are C' implies 'All A are C'.

'Some A are B' implies 'Some B are A'.

'No A is B' implies 'No B is A'.

A conclusion with 'some' cannot be drawn from two 'all' premises unless existence is assumed.

Draw all possible Venn diagrams for the premises and check the conclusion in each.

Reject conclusions that introduce terms not present in the premises.

For the 1600 m race, train with interval runs of 400 m repeats and one weekly long run.

For long jump, practise the approach run, take-off, and landing separately before combining them.

For shot put, drill the glide or spin technique with a lighter implement first.

Strength training for the legs and core improves jumping and throwing performance.

Flexibility exercises reduce injury risk and improve range of motion.

Taper training in the week before the test to arrive fresh.

Naga folk music is often accompanied by drums and bamboo instruments.

The log drum is a large wooden drum used in festivals and community events.

Naga shawls carry tribal patterns that indicate status and identity.

Bamboo and cane craft are important traditional industries.

The Hornbill Festival features tribal dance performances by different tribes.

Pottery and weaving are practised in several villages.

The Indian Army, Navy, and Air Force are the three armed forces.

The President is the supreme commander of the armed forces.

The National Security Guard handles counter-terrorism operations.

The Central Reserve Police Force is a central armed police force.

The Border Security Force guards India's land borders with Pakistan and Bangladesh.

The Indo-Tibetan Border Police guards the border with China.

Replace 'discuss about' with 'discuss'.

Replace 'return back' with 'return'.

Replace 'more better' with 'better'.

Replace 'one of my friend' with 'one of my friends'.

Replace 'each of the boys are' with 'each of the boys is'.

Replace 'hardly had I reached than' with 'hardly had I reached when'.

Mean = sum of values / number of values.

Median is the middle value when data is arranged in order.

Mode is the most frequently occurring value.

Range = highest value - lowest value.

For grouped data, the modal class is the class with the highest frequency.

Probability values range from 0 to 1.

Track the number of sides, lines, or dots in each figure.

Check rotation direction and angle between successive figures.

Check whether shading alternates or moves.

In figure analogy, apply the same transformation to the second figure.

In figure classification, identify the property shared by all but one figure.

In mirror images, reverse left and right only.

Nagaland has a monsoon climate with heavy rainfall from May to September.

Jhum cultivation is practised on hill slopes and involves clearing and burning vegetation.

Terrace rice cultivation is practised in valley areas with irrigation.

Major crops include rice, maize, millet, potato, and pulses.

Horticulture crops include oranges, pineapples, and passion fruit.

The state promotes organic farming and bamboo-based industries.

The 42nd Amendment (1976) added 'socialist', 'secular', and 'integrity' to the Preamble.

The 44th Amendment (1978) removed the right to property from Fundamental Rights.

The 73rd and 74th Amendments (1992) gave constitutional status to panchayats and municipalities.

The 86th Amendment (2002) made elementary education a Fundamental Right under Article 21A.

The 101st Amendment (2016) introduced the Goods and Services Tax.

The 103rd Amendment (2019) provided reservation for economically weaker sections.

Simple present for habitual actions and universal truths.

Present continuous for actions happening now or planned future events.

Present perfect for past actions with present relevance; use 'since' and 'for'.

Simple past for completed actions with a definite past time.

Past continuous for actions in progress in the past, often interrupted by a simple past action.

Future perfect for actions completed before a future time.

Distance = speed x time; speed = distance / time.

Average speed = total distance / total time, not the average of speeds.

For a round trip at speeds x and y, average speed = 2xy/(x + y).

Trains crossing each other in opposite directions: relative speed = sum of speeds.

Trains crossing in the same direction: relative speed = difference of speeds.

To convert km/h to m/s, multiply by 5/18.

Draw the path on paper with north up.

A right turn from north faces east; a left turn from north faces west.

Net displacement uses Pythagoras for right-angled turns.

Shadow direction: in the morning the shadow falls west; in the evening it falls east.

If a person faces north, his left is west and his right is east.

Track the final direction separately from the final distance.

Hornbill Festival: 1-10 December at Kisama.

Sekrenyi: celebrated by the Angami in February.

Moatsu: celebrated by the Ao in May after sowing.

Tuluni: celebrated by the Sumi in July.

Aoleang: celebrated by the Konyak in April.

Festivals are tied to agricultural cycles and include community feasts and dances.

26 January: Republic Day.

15 August: Independence Day.

2 October: Gandhi Jayanti.

5 September: Teachers' Day.

1 December: Nagaland Statehood Day.

10 December: Human Rights Day.

Synonym of 'abundant': plentiful.

Antonym of 'ancient': modern.

Synonym of 'candid': frank.

Antonym of 'benevolent': malevolent.

Synonym of 'diligent': hardworking.

Antonym of 'transparent': opaque.

Rectangle: area = length x breadth; perimeter = 2(length + breadth).

Triangle: area = 1/2 x base x height.

Circle: area = pi r^2; circumference = 2 pi r.

Cylinder: volume = pi r^2 h; curved surface = 2 pi r h.

Sphere: volume = 4/3 pi r^3; surface area = 4 pi r^2.

Cone: volume = 1/3 pi r^2 h.

Father's brother: uncle; father's sister: aunt.

Mother's brother: maternal uncle; mother's sister: maternal aunt.

Brother's son: nephew; sister's daughter: niece.

Grandfather's son: father or uncle.

Draw a tree with vertical lines for parent-child and horizontal lines for spouse or sibling.

Use gender symbols to avoid confusion.

Height is measured with a stadiometer or vertical scale.

Chest is measured with a flexible tape at nipple level.

Weight is measured on a calibrated weighing scale.

Measurements are recorded in centimetres and kilograms.

The candidate must stand straight and breathe normally for the unexpanded chest reading.

The expanded chest reading is taken after a full inhalation.

The Governor is the constitutional head of the state, appointed by the President.

The Chief Minister is the head of the elected government.

The Nagaland Legislative Assembly has 60 members.

The state sends one member to the Lok Sabha and one to the Rajya Sabha.

The Director General of Police heads the state police.

The Chief Secretary heads the state administration.

The Ganga originates in the Gangotri glacier and flows into the Bay of Bengal.

The Brahmaputra flows through Assam and into Bangladesh.

The Narmada and Tapi flow westward into the Arabian Sea.

The Bhakra Nangal Dam is on the Sutlej.

The Hirakud Dam is on the Mahanadi.

The Sardar Sarovar Dam is on the Narmada.

Use 'a' before consonant sounds and 'an' before vowel sounds.

Use 'the' for specific or previously mentioned nouns.

Do not use articles before proper nouns, except for rivers, oceans, and mountain ranges.

Use 'some' in affirmative sentences and 'any' in negative and interrogative sentences.

Use 'much' with uncountable nouns and 'many' with countable nouns.

Use 'fewer' with countable nouns and 'less' with uncountable nouns.

Simple interest = P x R x T / 100.

Amount under simple interest = P + SI.

Compound interest = P(1 + R/100)^T - P.

For two years, the difference between CI and SI = P(R/100)^2.

If interest is compounded half-yearly, use R/2 and 2T.

If interest is compounded quarterly, use R/4 and 4T.

Alphabet positions: A=1 to Z=26.

Opposite letters sum to 27: A-Z, B-Y, C-X.

Number series: check differences, then ratios, then squares and cubes.

Alternating series: separate odd and even positions.

Letter series: convert to numbers and check the pattern.

Odd one out: identify the rule that all but one item follow.

Village councils govern local affairs under customary law.

The village chief or elders play a key role in dispute resolution.

The Morung was a traditional dormitory for young men.

Clan exogamy is practised in many Naga tribes.

Customary law is protected under Article 371A.

The Dobashi system was used by the British for administration in the Naga Hills.

ISRO is headquartered in Bengaluru.

Chandrayaan-3 landed near the lunar south pole in 2023.

Mangalyaan was India's first Mars orbiter mission.

The Brahmos missile is a supersonic cruise missile developed with Russia.

The DRDO is India's defence research organisation.

The Tejas is an indigenous light combat aircraft.

'Myself' should not be used as a subject; use 'I'.

'Revert back' should be 'revert' or 'reply'.

'Prepone' is informal; use 'advance'.

'Cousin brother' should be 'cousin'.

'Order for' should be 'order'.

'Discuss about' should be 'discuss'.

Probability = favourable outcomes / total outcomes.

P(not A) = 1 - P(A).

nPr = n! / (n - r)!

nCr = n! / (r!(n - r)!).

nC0 = 1 and nCn = 1.

For independent events, P(A and B) = P(A) x P(B).

The minute hand moves 6 degrees per minute; the hour hand moves 0.5 degrees per minute.

The angle between the hands = |30H - 5.5M| degrees.

Hands coincide every 65 5/11 minutes.

A normal year has 1 odd day; a leap year has 2 odd days.

The day of the week repeats every 7 days.

Century years are leap years only if divisible by 400.

Nagaland hosts the North East Olympic Games and participates in national events.

Football is a popular sport in the state.

The state has produced athletes in athletics and boxing.

The Nagaland Olympic Association promotes sports in the state.

The Hornbill Festival includes traditional sports events.

Sports infrastructure is being developed in districts.

Primary sector: agriculture, mining, and fishing.

Secondary sector: manufacturing and construction.

Tertiary sector: services such as banking, trade, and transport.

India's economy is dominated by the services sector in terms of GDP share.

MSMEs play a significant role in employment generation.

Make in India and Start-up India promote manufacturing and entrepreneurship.

'Mitigate' means to reduce or lessen.

'Augment' means to increase.

'Obsolete' means out of date.

'Pragmatic' means practical.

'Ambiguous' means unclear or having more than one meaning.

'Meticulous' means very careful and precise.

If a:b = 2:3 and b:c = 4:5, then a:b:c = 8:12:15.

Percentage increase = (increase/original) x 100.

Percentage decrease = (decrease/original) x 100.

If A is x% more than B, B is less than A by x/(100 + x) x 100 percent.

To divide a number in the ratio a:b, multiply by a/(a+b) and b/(a+b).

Ratio comparison: cross-multiply to compare fractions.

Arrange items by size, age, or position as specified.

For ranking, use n + m - 1 when a person is nth from one end and mth from the other.

For circular arrangement, fix one person and place others relative to them.

For floor puzzles, draw a vertical stack.

For scheduling, draw a table of days or times.

Check the final arrangement against every clue.

Tourism is a growing sector, with the Hornbill Festival as a major attraction.

Eco-tourism and trekking attract visitors to Dzukou Valley and Japfu Peak.

Handicrafts and handloom products support rural livelihoods.

Bamboo is promoted as an industrial and construction material.

Horticulture, including oranges and passion fruit, supports farmers.

The state depends on central transfers for its budget.

Article 14: equality before the law.

Article 19: freedom of speech and expression.

Article 21: right to life and personal liberty.

Article 32: right to constitutional remedies.

Article 44: uniform civil code (Directive Principle).

Article 356: President's rule in a state.

Read the whole sentence or passage before choosing an option.

Check the grammar of the blank: noun, verb, adjective, or adverb.

Look for clues such as 'because', 'although', and 'therefore' that signal meaning.

Eliminate options that do not fit grammatically.

Choose the option that fits both meaning and grammar.

For cloze passages, read the passage once fully before filling blanks.

HCF x LCM = product of two numbers.

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

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

A number is divisible by 3 if the digit sum is divisible by 3.

A number is divisible by 9 if the digit sum is divisible by 9.

A number is divisible by 11 if the alternating digit sum difference is divisible by 11.

Letter shift coding: each letter is shifted by a fixed number.

Reverse coding: the word is written backwards.

Position coding: letters are replaced by their positions.

Symbol coding: letters are replaced by symbols according to a rule.

Mixed coding: a combination of shifts and reversals.

Check the rule on all letters of the word before applying it.

English is the medium of instruction in most schools.

Nagaland University is a central university with campuses in Kohima and Lumami.

The state has primary health centres and district hospitals.

Missionary schools have played a major role in education.

Literacy rates have improved, with Kohima among the more literate districts.

The state promotes health schemes through district administrations.

1757: Battle of Plassey.

1857: First War of Independence.

1885: Indian National Congress founded.

1919: Jallianwala Bagh massacre.

1930: Dandi March.

1947: Independence and Partition.

'To let the cat out of the bag' means to reveal a secret.

'A bolt from the blue' means a sudden shock.

'To burn the midnight oil' means to work late.

'To beat around the bush' means to avoid the main topic.

'Once in a blue moon' means very rarely.

'To smell a rat' means to suspect something wrong.

If A finishes in x days, A's one-day work = 1/x.

Together, A and B finish in xy/(x + y) days.

If A is twice as efficient as B, A takes half the time.

A filling pipe has positive rate; a draining pipe has negative rate.

If a pipe fills a tank in x hours and another empties it in y hours, together they fill it in xy/(y - x) hours (y > x).

Use LCM of times as total work units for easier calculation.

'All A are B': circle A inside circle B.

'Some A are B': overlapping circles.

'No A is B': separate circles.

The union of two sets includes all elements in either set.

The intersection includes elements in both sets.

Draw all possible diagrams before concluding.

Community forests are protected by village councils under customary law.

Intanki National Park protects elephants and other wildlife.

The Blyth's tragopan is a threatened pheasant found in the state.

Bamboo forests are a major resource.

The state promotes organic farming and conservation.

Dzukou Valley is known for its biodiversity.

Cricket is the most popular sport in India.

The Board of Control for Cricket in India governs cricket.

Hockey is India's national sport in popular understanding.

The Olympic Games are held every four years.

The Asian Games are held every four years.

The Arjuna Award recognises sporting achievement.

To change affirmative to negative, use 'not' with an antonym.

To change simple to complex, use a subordinate clause.

To change direct to indirect speech, change pronouns and tense.

To change active to passive, make the object the subject.

To change degrees of comparison, use 'as...as' or 'more...than'.

Keep the meaning the same when transforming sentences.

Sum of angles in a triangle = 180 degrees.

Pythagoras theorem: hypotenuse squared = sum of squares of the other two sides.

Area of a triangle = 1/2 x base x height.

Hero's formula: area = square root of s(s-a)(s-b)(s-c).

The exterior angle of a triangle equals the sum of the two opposite interior angles.

In an equilateral triangle, all angles are 60 degrees.

Check differences between consecutive terms.

Check ratios between consecutive terms.

Check squares and cubes of natural numbers.

Check alternating patterns in odd and even positions.

Check combinations such as n^2 + 1 or n^3 - 1.

Check letter series by converting to numbers.

The Deputy Commissioner heads the district administration.

The Chief Secretary heads the state administration.

The Nagaland Public Service Commission conducts state recruitment.

The state police are headed by the Director General of Police.

Village councils handle local governance under customary law.

Article 371A protects Naga customary law and land.

The United Nations was founded in 1945; headquarters in New York.

The World Health Organization is headquartered in Geneva.

The International Monetary Fund is headquartered in Washington, D.C.

The World Bank is headquartered in Washington, D.C.

UNESCO is headquartered in Paris.

The International Court of Justice is in The Hague.

Prefix 'un-' negates: happy becomes unhappy.

Prefix 're-' means again: do becomes redo.

Suffix '-able' means capable of: read becomes readable.

Suffix '-less' means without: hope becomes hopeless.

Suffix '-tion' forms a noun: inform becomes information.

Suffix '-ous' forms an adjective: danger becomes dangerous.

x% of N = (x/100) x N.

Successive changes a% and b% give a + b + ab/100 percent.

If price increases by R%, consumption must fall by 100R/(100 + R) percent.

To find a number when x% of it is y, the number is y x 100/x.

Percentage error = (error/actual value) x 100.

Profit percentage = ((SP - CP)/CP) x 100.

Identify the fixed clues first.

Draw a table or diagram for the arrangement.

Test each case against all clues.

Discard cases that contradict any clue.

Check the final arrangement against every clue.

Answer only what is asked, not the whole arrangement.

The Hornbill feather symbolises bravery and status.

The log drum is used in festivals and community events.

Naga shawls carry tribal patterns indicating identity.

The Morung was a traditional dormitory for young men.

Festivals are tied to agricultural cycles.

Bamboo and cane crafts are traditional industries.

The Himalayas are young fold mountains.

The Western Ghats are a biodiversity hotspot.

The Thar Desert is in Rajasthan.

The Sundarbans is a mangrove forest in West Bengal.

The Deccan Plateau lies between the Western and Eastern Ghats.

The Indo-Gangetic Plain is formed by alluvial soil.

The main idea is the central point of the passage.

It is often stated in the first or last sentence.

Supporting details explain or illustrate the main idea.

Eliminate options that are too broad or too narrow.

Do not choose an option that is only a detail.

Check that the option covers the whole passage.

(a + b)^2 = a^2 + 2ab + b^2.

(a - b)^2 = a^2 - 2ab + b^2.

a^2 - b^2 = (a + b)(a - b).

(a + b)^3 = a^3 + b^3 + 3ab(a + b).

(a - b)^3 = a^3 - b^3 - 3ab(a - b).

a^3 + b^3 = (a + b)(a^2 - ab + b^2).

Use circles to represent sets.

Overlap circles for 'some' relations.

Place one circle inside another for 'all' relations.

Keep circles separate for 'no' relations.

Shade the region that satisfies the conclusion.

Check whether the conclusion holds in all possible diagrams.

Dr. Neilhouzhü Kire was the first Chief Minister of Nagaland.

The state's first Governor was Vishnu Sahay.

Naga leaders such as A. Z. Phizo led early political movements.

The Hornbill Festival was started in 2000 to promote tribal culture.

The state has produced notable athletes and civil servants.

Local leaders play a key role in customary institutions.

GDP is the total value of goods and services produced in a year.

Inflation is a sustained rise in the general price level.

The Reserve Bank of India controls monetary policy.

GST was introduced in 2017.

Direct taxes include income tax and corporate tax.

Indirect taxes include GST and customs duty.

'And' joins similar ideas; 'but' joins contrasting ideas.

'Because' shows cause; 'so' shows effect.

'Although' shows contrast; 'therefore' shows result.

'Either...or' presents alternatives; 'neither...nor' negates both.

'Not only...but also' adds emphasis.

Use a comma before 'but' when joining two independent clauses.

Profit = SP - CP; loss = CP - SP.

Profit% = (profit/CP) x 100.

Loss% = (loss/CP) x 100.

Discount is calculated on the marked price.

SP = MP(1 - discount/100).

Successive discounts a% and b% equal a + b - ab/100 percent.

Replace symbols with operations as defined.

Rewrite the expression before solving.

Apply BODMAS after substitution.

Check the direction of each symbol.

Solve step by step to avoid errors.

Verify the answer by substituting back.

Mount Saramati is the highest peak in the state.

The Doyang and Dhansiri are major rivers.

Dzukou Valley is known for its natural beauty.

Intanki National Park is in Peren district.

The state shares a border with Myanmar to the east.

The Naga Hills run north-east to south-west.

The Election Commission conducts elections.

The Finance Commission recommends tax distribution.

The UPSC conducts central recruitment.

The NHRC protects human rights.

The CAG audits government accounts.

The Attorney General advises the government on legal matters.

'Abundant' means plentiful.

'Candid' means frank.

'Diligent' means hardworking.

'Mitigate' means to reduce.

'Augment' means to increase.

'Obsolete' means out of date.

A's one-day work = 1/x if A finishes in x days.

Together, A and B finish in xy/(x + y) days.

If A is twice as efficient as B, A takes half the time.

Work done = rate x time.

Wages are shared in the ratio of work done.

Use LCM of times as total work units.

Identify the relation between the first pair.

Apply the same relation to the second pair.

For numbers, check addition, multiplication, or squares.

For letters, convert to positions and check the shift.

Check the order of the relation.

Verify the answer by applying the relation in reverse.

State bird: Hornbill.

State animal: Mithun.

State flower: Rhododendron.

State tree: Alder.

State emblem features the Hornbill.

These symbols reflect the state's biodiversity and culture.

The Constitution is the supreme law of the land.

It provides for a parliamentary system of government.

It guarantees Fundamental Rights.

It includes Directive Principles of State Policy.

It provides for an independent judiciary.

It can be amended by Parliament under Article 368.

A simple sentence has one independent clause.

A compound sentence has two or more independent clauses.

A complex sentence has one independent and one or more dependent clauses.

A compound-complex sentence has multiple independent and dependent clauses.

Each sentence must have a subject and a predicate.

Avoid sentence fragments and run-on sentences.

Alligation: ratio of quantities = (mean - cheaper)/(dearer - mean).

When a quantity is replaced repeatedly, remaining pure = original x (1 - replaced/total)^n.

Weighted average = sum of (value x weight) / sum of weights.

To divide a number in ratio a:b, multiply by a/(a+b) and b/(a+b).

Compound ratio of a:b and c:d is ac:bd.

Mean proportional between a and b is the square root of ab.

Draw the path with north up.

A right turn from north faces east.

A left turn from north faces west.

Net displacement uses Pythagoras for right-angled turns.

Shadow in the morning falls west; in the evening it falls east.

Track final direction separately from final distance.

Jhum cultivation involves clearing and burning vegetation.

Terrace rice cultivation is practised in valleys.

Major crops include rice, maize, and millet.

Horticulture crops include oranges and passion fruit.

Organic farming is promoted in the state.

Bamboo is an important resource.

The Indian Army, Navy, and Air Force are the three armed forces.

The President is the supreme commander.

The NSG handles counter-terrorism.

The CRPF is a central armed police force.

The BSF guards borders with Pakistan and Bangladesh.

The ITBP guards the border with China.

Benevolent vs malevolent.

Transparent vs opaque.

Ancient vs modern.

Abundant vs scarce.

Candid vs secretive.

Diligent vs lazy.

Time to cross a pole = train length / speed.

Time to cross a platform = (train length + platform length) / speed.

Trains in opposite directions: relative speed = sum of speeds.

Trains in the same direction: relative speed = difference of speeds.

Convert km/h to m/s by multiplying by 5/18.

Average speed = total distance / total time.

A=1, B=2, ..., Z=26.

Reverse coding: A=26, B=25, ..., Z=1.

Sum-of-letters coding: code is the sum of letter positions.

Product-of-letters coding: code is the product of positions.

Check whether the code uses forward or reverse positions.

Verify the rule on all letters.

Hornbill Festival: 1-10 December at Kisama.

Sekrenyi: Angami festival in February.

Moatsu: Ao festival in May.

Tuluni: Sumi festival in July.

Aoleang: Konyak festival in April.

Festivals include community feasts and dances.

The Ganga originates in the Gangotri glacier.

The Brahmaputra flows through Assam.

The Narmada and Tapi flow westward.

The Bhakra Nangal Dam is on the Sutlej.

The Hirakud Dam is on the Mahanadi.

The Sardar Sarovar Dam is on the Narmada.

'Bene' means good.

'Mal' means bad.

'Cred' means believe.

'Dict' means say.

'Scrib' means write.

'Aud' means hear.

SI = P x R x T / 100.

Amount = P + SI.

To find rate: R = 100 x SI / (P x T).

To find time: T = 100 x SI / (P x R).

SI doubles a sum in 100/R years.

SI is calculated on the principal only.

Father's brother: uncle.

Mother's brother: maternal uncle.

Brother's son: nephew.

Sister's daughter: niece.

Grandfather's son: father or uncle.

Draw a tree to avoid confusion.

Nagaland became a state on 1 December 1963.

The State of Nagaland Act was passed in 1962.

Article 371A protects Naga customary law.

The Naga National Council was formed in 1946.

The 1997 ceasefire began a peace process.

The state has 60 assembly seats.

Bharat Ratna is the highest civilian award.

Padma Vibhushan is the second-highest civilian award.

Param Vir Chakra is the highest wartime military decoration.

Ashoka Chakra is the highest peacetime military decoration.

Jnanpith Award is for literature.

Arjuna Award is for sports.

Check subject-verb agreement.

Check tense consistency.

Check pronoun reference.

Check preposition use.

Check parallel structure.

Check for redundancy.

Area = pi r^2; circumference = 2 pi r.

The angle in a semicircle is 90 degrees.

The perpendicular from the centre bisects a chord.

Equal chords are equidistant from the centre.

The tangent at a point is perpendicular to the radius.

The angle between a tangent and a chord equals the angle in the alternate segment.

Identify the common property of all but one item.

Check category, function, or origin.

For numbers, check divisibility or squares.

For letters, check vowel/consonant or position.

Verify the rule for each option.

Choose the option that does not fit.

Kisama Heritage Village hosts the Hornbill Festival.

Kohima War Cemetery commemorates the 1944 battle.

Dzukou Valley is known for its natural beauty.

Japfu Peak is one of the highest peaks.

Intanki National Park is in Peren district.

The state museum in Kohima displays Naga artefacts.

Canberra is the capital of Australia.

Ottawa is the capital of Canada.

Brasilia is the capital of Brazil.

Naypyidaw is the capital of Myanmar.

Tokyo is the capital of Japan.

Berlin is the capital of Germany.

'At the eleventh hour' means at the last moment.

'To burn the midnight oil' means to work late.

'A blessing in disguise' means something good from something bad.

'To beat around the bush' means to avoid the main topic.

'To smell a rat' means to suspect something wrong.

'Once in a blue moon' means very rarely.

CI = P(1 + R/100)^T - P.

For two years, CI - SI = P(R/100)^2.

Half-yearly compounding: use R/2 and 2T.

Quarterly compounding: use R/4 and 4T.

CI is calculated on principal plus accumulated interest.

The rule of 72 estimates doubling time as 72/R years.

A normal year has 1 odd day; a leap year has 2 odd days.

The day of the week repeats every 7 days.

Century years are leap years only if divisible by 400.

Count odd days from a known reference year.

For a given date, find the day by counting odd days.

February has 29 days in a leap year.

Ayushman Bharat provides health insurance coverage.

District hospitals and primary health centres serve the state.

The state implements central welfare schemes through districts.

Scholarships support students from reserved categories.

MGNREGA guarantees rural wage employment.

The PDS provides subsidised food grains.

ISRO is headquartered in Bengaluru.

Chandrayaan-3 landed near the lunar south pole in 2023.

Mangalyaan was India's first Mars orbiter.

Aditya-L1 studies the Sun from the L1 point.

PSLV and GSLV are Indian launch vehicles.

Aryabhata was India's first satellite.

'Mitigate' means to reduce.

'Augment' means to increase.

'Pragmatic' means practical.

'Ambiguous' means unclear.

'Meticulous' means very careful.

'Obsolete' means out of date.

x% of N = (x/100) x N.

If A is x% more than B, B is less than A by x/(100 + x) x 100 percent.

To divide a number in ratio a:b, multiply by a/(a+b) and b/(a+b).

Percentage increase = (increase/original) x 100.

Ratio comparison: cross-multiply to compare fractions.

Successive changes a% and b% give a + b + ab/100 percent.

'All A are B' and 'All B are C' implies 'All A are C'.

'Some A are B' implies 'Some B are A'.

'No A is B' implies 'No B is A'.

Draw all possible Venn diagrams.

Reject conclusions that introduce new terms.

Check the conclusion in every possible diagram.

Naga society is clan-based.

Village councils govern local affairs.

The Morung was a traditional dormitory.

The Hornbill feather symbolises bravery.

Festivals are tied to agriculture.

Bamboo and cane crafts are traditional industries.

Part III contains Fundamental Rights.

Part IV contains Directive Principles.

Part IVA contains Fundamental Duties.

Part V deals with the Union government.

Part VI deals with state governments.

Part IX deals with panchayats.

Read the whole sentence first.

Check the grammar of the blank.

Look for clue words such as 'because' and 'although'.

Eliminate options that do not fit grammatically.

Choose the option that fits meaning and grammar.

For cloze passages, read the passage fully first.

HCF x LCM = product of two numbers.

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

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

A number is divisible by 3 if the digit sum is divisible by 3.

A number is divisible by 9 if the digit sum is divisible by 9.

A number is divisible by 11 if the alternating digit sum difference is divisible by 11.

Letter shift coding: fixed shift per letter.

Reverse coding: word written backwards.

Position coding: letters replaced by positions.

Symbol coding: letters replaced by symbols.

Mixed coding: combination of rules.

Check the rule on all letters before applying.

English is the medium of instruction.

Nagaland University is a central university.

Missionary schools played a major role.

Literacy rates have improved.

The state promotes tribal dialects.

Church-run schools are common.

1757: Battle of Plassey.

1857: First War of Independence.

1885: Indian National Congress founded.

1919: Jallianwala Bagh massacre.

1930: Dandi March.

1947: Independence and Partition.

'To let the cat out of the bag' means to reveal a secret.

'A bolt from the blue' means a sudden shock.

'To burn the midnight oil' means to work late.

'To beat around the bush' means to avoid the main topic.

'Once in a blue moon' means very rarely.

'To smell a rat' means to suspect something wrong.

A's one-day work = 1/x if A finishes in x days.

Together, A and B finish in xy/(x + y) days.

If A is twice as efficient as B, A takes half the time.

Work done = rate x time.

Wages are shared in the ratio of work done.

Use LCM of times as total work units.

'All A are B': circle A inside circle B.

'Some A are B': overlapping circles.

'No A is B': separate circles.

Union includes all elements in either set.

Intersection includes elements in both sets.

Draw all possible diagrams before concluding.

Community forests are protected by village councils.

Intanki National Park protects wildlife.

The Blyth's tragopan is a threatened pheasant.

Bamboo forests are a major resource.

The state promotes organic farming.

Dzukou Valley is known for its biodiversity.

Cricket is the most popular sport in India.

The BCCI governs cricket.

Hockey is India's national sport in popular understanding.

The Olympic Games are held every four years.

The Asian Games are held every four years.

The Arjuna Award recognises sporting achievement.

To change affirmative to negative, use 'not' with an antonym.

To change simple to complex, use a subordinate clause.

To change direct to indirect speech, change pronouns and tense.

To change active to passive, make the object the subject.

To change degrees of comparison, use 'as...as' or 'more...than'.

Keep the meaning the same when transforming.

Sum of angles in a triangle = 180 degrees.

Pythagoras theorem: hypotenuse squared = sum of squares of the other two sides.

Area of a triangle = 1/2 x base x height.

Hero's formula: area = square root of s(s-a)(s-b)(s-c).

The exterior angle equals the sum of the two opposite interior angles.

In an equilateral triangle, all angles are 60 degrees.

Check differences between consecutive terms.

Check ratios between consecutive terms.

Check squares and cubes of natural numbers.

Check alternating patterns in odd and even positions.

Check combinations such as n^2 + 1.

Check letter series by converting to numbers.

The Deputy Commissioner heads the district administration.

The Chief Secretary heads the state administration.

The NPSC conducts state recruitment.

The DGP heads the state police.

Village councils handle local governance.

Article 371A protects customary law.

The UN was founded in 1945; headquarters in New York.

The WHO is headquartered in Geneva.

The IMF is headquartered in Washington, D.C.

The World Bank is headquartered in Washington, D.C.

UNESCO is headquartered in Paris.

The ICJ is in The Hague.

Prefix 'un-' negates: happy becomes unhappy.

Prefix 're-' means again: do becomes redo.

Suffix '-able' means capable of: read becomes readable.

Suffix '-less' means without: hope becomes hopeless.

Suffix '-tion' forms a noun: inform becomes information.

Suffix '-ous' forms an adjective: danger becomes dangerous.

x% of N = (x/100) x N.

Successive changes a% and b% give a + b + ab/100 percent.

If price increases by R%, consumption must fall by 100R/(100 + R) percent.

To find a number when x% of it is y, the number is y x 100/x.

Percentage error = (error/actual value) x 100.

Profit percentage = ((SP - CP)/CP) x 100.

Identify the fixed clues first.

Draw a table or diagram.

Test each case against all clues.

Discard cases that contradict any clue.

Check the final arrangement against every clue.

Answer only what is asked.

The Hornbill feather symbolises bravery.

The log drum is used in festivals.

Naga shawls carry tribal patterns.

The Morung was a traditional dormitory.

Festivals are tied to agriculture.

Bamboo and cane crafts are traditional industries.

The Himalayas are young fold mountains.

The Western Ghats are a biodiversity hotspot.

The Thar Desert is in Rajasthan.

The Sundarbans is a mangrove forest in West Bengal.

The Deccan Plateau lies between the Western and Eastern Ghats.

The Indo-Gangetic Plain is formed by alluvial soil.

The main idea is the central point of the passage.

It is often stated in the first or last sentence.

Supporting details explain the main idea.

Eliminate options that are too broad or too narrow.

Do not choose an option that is only a detail.

Check that the option covers the whole passage.

(a + b)^2 = a^2 + 2ab + b^2.

(a - b)^2 = a^2 - 2ab + b^2.

a^2 - b^2 = (a + b)(a - b).

(a + b)^3 = a^3 + b^3 + 3ab(a + b).

(a - b)^3 = a^3 - b^3 - 3ab(a - b).

a^3 + b^3 = (a + b)(a^2 - ab + b^2).

Use circles to represent sets.

Overlap circles for 'some' relations.

Place one circle inside another for 'all' relations.

Keep circles separate for 'no' relations.

Shade the region that satisfies the conclusion.

Check whether the conclusion holds in all diagrams.

Dr. Neilhouzhü Kire was the first Chief Minister of Nagaland.

The state's first Governor was Vishnu Sahay.

A. Z. Phizo led early political movements.

The Hornbill Festival started in 2000.

The state has produced notable athletes and civil servants.

Local leaders play a key role in customary institutions.

GDP is the total value of goods and services produced in a year.

Inflation is a sustained rise in the price level.

The RBI controls monetary policy.

GST was introduced in 2017.

Direct taxes include income tax and corporate tax.

Indirect taxes include GST and customs duty.

'And' joins similar ideas; 'but' joins contrasting ideas.

'Because' shows cause; 'so' shows effect.

'Although' shows contrast; 'therefore' shows result.

'Either...or' presents alternatives.

'Neither...nor' negates both.

Use a comma before 'but' when joining two independent clauses.

Profit = SP - CP; loss = CP - SP.

Profit% = (profit/CP) x 100.

Loss% = (loss/CP) x 100.

Discount is calculated on the marked price.

SP = MP(1 - discount/100).

Successive discounts a% and b% equal a + b - ab/100 percent.

Replace symbols with operations as defined.

Rewrite the expression before solving.

Apply BODMAS after substitution.

Check the direction of each symbol.

Solve step by step.

Verify the answer by substituting back.

Mount Saramati is the highest peak.

The Doyang and Dhansiri are major rivers.

Dzukou Valley is known for natural beauty.

Intanki National Park is in Peren district.

The state borders Myanmar to the east.

The Naga Hills run north-east to south-west.

The Election Commission conducts elections.

The Finance Commission recommends tax distribution.

The UPSC conducts central recruitment.

The NHRC protects human rights.

The CAG audits government accounts.

The Attorney General advises on legal matters.

'Abundant' means plentiful.

'Candid' means frank.

'Diligent' means hardworking.

'Mitigate' means to reduce.

'Augment' means to increase.

'Obsolete' means out of date.

A's one-day work = 1/x if A finishes in x days.

Together, A and B finish in xy/(x + y) days.

If A is twice as efficient as B, A takes half the time.

Work done = rate x time.

Wages are shared in the ratio of work done.

Use LCM of times as total work units.

Identify the relation between the first pair.

Apply the same relation to the second pair.

For numbers, check addition, multiplication, or squares.

For letters, convert to positions and check the shift.

Check the order of the relation.

Verify by applying the relation in reverse.

State bird: Hornbill.

State animal: Mithun.

State flower: Rhododendron.

State tree: Alder.

The state emblem features the Hornbill.

These symbols reflect biodiversity and culture.

The Constitution is the supreme law.

It provides a parliamentary system.

It guarantees Fundamental Rights.

It includes Directive Principles.

It provides an independent judiciary.

It can be amended under Article 368.

A simple sentence has one independent clause.

A compound sentence has two or more independent clauses.

A complex sentence has one independent and one or more dependent clauses.

A compound-complex sentence has multiple independent and dependent clauses.

Each sentence must have a subject and a predicate.

Avoid fragments and run-on sentences.

Alligation: ratio of quantities = (mean - cheaper)/(dearer - mean).

When a quantity is replaced repeatedly, remaining pure = original x (1 - replaced/total)^n.

Weighted average = sum of (value x weight) / sum of weights.

To divide a number in ratio a:b, multiply by a/(a+b) and b/(a+b).

Compound ratio of a:b and c:d is ac:bd.

Mean proportional between a and b is the square root of ab.