PERA CET key terms

A comparison of two quantities showing how many times one contains the other, usually written with a colon such as 3:5. Ratios can be scaled up or down without changing the relationship they express.

An equation stating that two ratios are equal, such as 2:3 = 4:6. In direct proportion both quantities grow together; in inverse proportion one rises as the other falls.

A fraction expressed out of one hundred, so 45% means 45 per 100 or 0.45. Percentages make comparisons between different-sized wholes easier and are converted to fractions by dividing by 100.

Interest calculated only on the original principal for the whole period, using the formula P x R x T / 100. It does not compound, so each year adds the same fixed amount.

Interest computed on the principal plus previously earned interest, so the amount grows geometrically. The formula is P(1 + R/100)^T, and interest is always higher than simple interest for the same rate.

The sum of a set of values divided by how many values there are, also called the arithmetic mean. If every item were replaced by this single value, the total would stay unchanged.

A mean in which each value is multiplied by a weight reflecting its importance or frequency before summing, then divided by the total weight. It differs from a plain average when groups are of unequal size.

The relationship distance = speed x time, used to solve problems about travel, relative motion and average speed. Units must match, so convert km/h to m/s by multiplying by 5/18.

The speed of one moving object as observed from another. When two bodies move in opposite directions their speeds add; when moving in the same direction the slower speed is subtracted from the faster.

A classic application of relative speed: downstream speed is boat speed plus current, upstream speed is boat speed minus current. Adding the two gives twice the boat speed in still water.

Problems where workers complete a task at different rates. Convert each worker's contribution to a per-day fraction of the whole job, then add the fractions of workers acting together.

A technique that first finds the value of a single unit and then multiplies to get the required quantity. It is widely used for proportion, work-rate and cost problems.

An arrangement of items in which order matters, so ABC and CBA count as different. The number of arrangements of r items chosen from n is written nPr.

A selection of items in which order does not matter, so choosing A and B is the same as choosing B and A. It is written nCr and equals nPr divided by r factorial.

A number between 0 and 1 expressing how likely an event is, computed as favourable outcomes divided by total equally likely outcomes. Complementary events sum to one.

A sequence in which each term differs from the previous one by a fixed constant called the common difference. Its nth term is a + (n-1)d and its sum is n/2 times first plus last term.

A sequence in which each term is obtained by multiplying the previous term by a fixed ratio. Terms grow or shrink rapidly, and the nth term is a times r to the power n-1.

The branch of geometry dealing with measuring lengths, areas and volumes of plane and solid figures such as circles, triangles, cylinders and spheres. Formula recall and unit consistency are essential.

In a right-angled triangle the square of the hypotenuse equals the sum of the squares of the other two sides. Common triples such as 3-4-5 and 5-12-13 appear frequently in problems.

The study of relationships between angles and side lengths in triangles, built on sine, cosine and tangent ratios. Standard values for 0, 30, 45, 60 and 90 degrees are usually memorised.

A form of deductive reasoning with two premises and a conclusion, often using words like all, some and none. A conclusion is valid only if it must be true whenever the premises are true.

A diagram using overlapping circles to show how sets relate, making inclusion and exclusion visible. It is a reliable tool for checking whether a syllogistic conclusion actually follows.

Reasoning from general statements to a specific conclusion that is guaranteed if the premises hold. It contrasts with induction, which generalises from particular observations to a probable rule.

Reasoning from specific examples or patterns toward a general rule that is likely but not certain. It is common in number-series and pattern questions where the next term must be predicted.

A sequence of numbers following a hidden rule, where the candidate must find the missing or next term. Differences, ratios, squares and alternating patterns are the usual starting points.

A puzzle in which words or letters are converted into a code by a consistent rule, and the candidate must apply or reverse that rule. Look for letter shifts, reversals and position-based substitutions.

Puzzles describing family links through statements or symbols, requiring the candidate to identify how two people are related. Drawing a quick family tree usually prevents errors.

Problems tracking a person's movement through turns and distances to find final position or facing direction. Sketching each step on paper is the safest method under exam pressure.

A puzzle placing people around a circle or in a row using clues about who sits where. Circular arrangements involve facing centre or facing outward, which flips left and right.

A question pairing two items with a specific relationship and asking for a matching pair. The relationship must be identified precisely, since many pairs share only a loose connection.

Also called odd-one-out: four or five items are given and one does not share the common property. The shared rule may involve meaning, spelling, category or numerical pattern.

A reasoning task in which a short statement is followed by unstated assumptions, and the candidate judges which assumption is implicit. An implicit assumption is necessary for the statement to make sense.

A task where conclusions are tested against a given statement, and only those that follow beyond reasonable doubt are accepted. Outside knowledge and extreme wording usually disqualify a conclusion.

A word with a meaning close to another word, tested to check vocabulary range. In exams the correct choice must fit the sentence's tone, not merely share a dictionary sense.

A word expressing the opposite meaning of another, such as scarce for abundant. Careful reading is needed because a prefix like un- or in- does not always create a true opposite.

Choosing the word that fits the meaning and grammar of a particular sentence rather than matching a definition in isolation. Collocations and tone usually decide between close options.

A fixed expression whose meaning cannot be worked out from its individual words, such as to bury the hatchet meaning to end a quarrel. Idioms must be learned as whole units.

A verb combined with a preposition or adverb that creates a new meaning, such as give up or put off. The particle can change meaning completely, so the pair must be memorised together.

The rule that a verb must match its subject in number and person, so a singular subject takes a singular verb. Intervening phrases and collective nouns are frequent traps.

A word showing the relationship of a noun or pronoun to another element, such as in, on, at, of or to. Fixed combinations like depend on and capable of are commonly tested.

A question type where a sentence is divided into parts and one part contains a grammatical error. Typical errors involve tense, agreement, articles, prepositions and parallel structure.

A question giving a sentence with an underlined portion and options to replace it so the sentence becomes grammatically correct and idiomatic. Only the underlined part may be changed.

A passage followed by questions on its main idea, details, inferences and tone. Answers must be supported by the text rather than by personal opinion or general knowledge.

A conclusion drawn from evidence in a passage without being stated directly. A valid inference must be strongly supported by the text, not merely possible in real life.

The supreme law of India, adopted in 1949 and effective from 26 January 1950, laying down fundamental rights, duties and the structure of government. It is the longest written constitution of any sovereign country.

Six categories of rights guaranteed in Part III of the Indian Constitution, including equality, freedom of speech and life, and constitutional remedies. They are enforceable in courts through writ petitions.

Guidelines in Part IV of the Indian Constitution directing the state toward social and economic welfare. They are not enforceable in courts but are fundamental in governance.

India's three-tier system of local self-government at village, block and district levels, given constitutional status by the 73rd Amendment in 1992. It reserves seats for women and marginalised groups.

A seasonal reversal of wind bringing heavy rainfall to the Indian subcontinent, driven by differential heating of land and sea. The southwest monsoon from June to September dominates Indian agriculture.

The latitude about 23.5 degrees north of the equator that passes through India, marking the northern limit of the sun's overhead position. It crosses several Indian states from Gujarat to Mizoram.

The mid-twentieth-century push in India using high-yielding seed varieties, fertilisers and irrigation to raise food grain output, especially wheat in Punjab and Haryana. It reduced dependence on food imports.

A mass movement launched by Mahatma Gandhi in 1920 urging Indians to withdraw cooperation from British institutions. It was suspended in 1922 after the Chauri Chaura incident turned violent.

Gandhi's 1930 campaign of deliberate law-breaking against British rule, begun with the Dandi Salt March. It made breaking the salt law a symbol of national resistance.

The 1942 resolution demanding an end to British rule, launched with Gandhi's call for do-or-die action. It led to mass arrests of Congress leaders and widespread unrest.

The Reserve Bank of India, the central bank established in 1935, which controls monetary policy, issues currency and regulates banks. Its Monetary Policy Committee sets key interest rates.