IPMAT Rohtak key terms

A fraction expressed out of 100, used to compare quantities on a common scale. Converting between fractions, decimals, and percentages is a core arithmetic skill.

A ratio compares two quantities by division; a proportion states that two ratios are equal. Used to split amounts, scale recipes, and solve mixture problems.

The sum of all values divided by the number of values. Often used in problems where a new element changes the mean and you must find the changed value.

A mean in which each value is multiplied by a weight before summing, then divided by the total weight. Needed when groups of different sizes are combined.

Profit is selling price minus cost price; loss is the reverse. Percentages are conventionally calculated on cost price unless the problem states otherwise.

Interest computed only on the original principal: I = P × R × T / 100. It does not compound, so each year adds the same amount.

Interest calculated on principal plus accumulated interest, so the base grows each period. The amount is P(1 + R/100)^T for annual compounding.

Distance equals speed multiplied by time. Problems often involve two moving objects, relative speed, or converting between km/h and m/s (multiply by 5/18).

The rate at which the gap between two moving bodies changes. Add speeds when moving in opposite directions and subtract when moving in the same direction.

Downstream speed is boat speed plus current speed; upstream speed is boat speed minus current speed. Used to find travel times in flowing water.

Problems where workers or pipes complete a task at given rates. The standard trick is to convert each worker's time into a per-day fraction of the job.

A variant of work problems where inlet pipes fill a tank and outlet pipes empty it. Filling rates are added and emptying rates subtracted.

Permutations count ordered arrangements; combinations count unordered selections. The distinction hinges on whether rearranging the same items makes a new outcome.

The number of favourable outcomes divided by total equally likely outcomes. Values run from 0 (impossible) to 1 (certain), and complementary events sum to 1.

A sequence where each term differs from the previous by a fixed constant. The nth term is a + (n−1)d and the sum is n/2 × (first + last).

A sequence where each term is a fixed multiple of the previous one. The nth term is a·r^(n−1), and infinite sums converge only when |r| < 1.

Highest common factor is the largest number dividing two or more numbers; lowest common multiple is the smallest number they all divide. Product of HCF and LCM equals the product of the two numbers.

Rules that test whether one integer divides another without remainder, such as a number being divisible by 3 when its digit sum is divisible by 3.

When a polynomial is divided by (x − a), the remainder equals the polynomial evaluated at a. Also used for finding remainders of large powers.

Measurement of lengths, areas, and volumes of plane and solid figures. Candidates should recall formulas for circles, triangles, cylinders, cones, and spheres.

A deductive argument with two premises and a conclusion. In these questions you accept the premises as true and judge whether the conclusion necessarily follows.

Overlapping circles representing sets and their relationships. Useful for testing whether a syllogistic conclusion holds in every possible arrangement.

Puzzles describing family links through statements or symbols. The reliable method is to draw a family tree and mark gender and generation explicitly.

Problems tracking a person's movement through turns and distances. Sketching the path on paper and using right-angle geometry usually solves them quickly.

Placing people around a line or circle according to clues about who sits where. Circular arrangements need care about facing inward versus outward.

A family of reasoning questions where several attributes (people, floors, colours, days) must be matched using constraints. A grid or table is the standard solving aid.

A word or number is transformed by a rule, and you must identify the rule or apply it to a new item. Look for letter shifts, reversals, and position-based patterns.

Finding the missing or next element in a sequence of numbers, letters, or figures. Check differences, ratios, alternating patterns, and squares or cubes.

A pair of items related in a certain way, where you must find or judge a second pair with the same relationship. Identify the precise relation before comparing options.

Choosing the item that does not share the property common to the rest. The shared property may be numerical, alphabetical, or conceptual.

An unstated premise the argument relies on. A valid assumption is necessary for the conclusion to follow, not merely plausible or helpful.

A conclusion drawn from given information without being explicitly stated. In reasoning tests, an inference must follow necessarily, not just probably.

The main claim an argument tries to establish. Distinguishing it from supporting statements is essential for strengthen, weaken, and assumption questions.

A word with the opposite meaning to a given word. Questions often test less common senses, so check the part of speech before choosing.

A word with a meaning close to that of a given word. The best answer matches the shade of meaning and the grammatical role in context.

Choosing the word that fits a sentence's meaning and grammar. The correct option must agree with tone, collocation, and the surrounding logic.

A fixed expression whose meaning cannot be derived from its individual words, such as 'to let the cat out of the bag' meaning to reveal a secret.

A verb combined with a preposition or adverb that creates a new meaning, such as 'give up' or 'put off'. The particle changes the sense entirely.

A set of sentences that must be reordered into a coherent paragraph. Find the opening sentence, then track pronouns, connectors, and logical flow.

Answering questions about a passage's main idea, tone, details, and inferences. Answers must be grounded in the text rather than in outside knowledge.

The grammatical categories of words: noun, pronoun, verb, adjective, adverb, preposition, conjunction, and interjection. Needed for error-spotting and sentence correction.

The rule that a verb must match its subject in number and person. Tricky cases involve collective nouns, indefinite pronouns, and phrases between subject and verb.

Rhetorical devices such as metaphor, simile, personification, and hyperbole that create non-literal effects. Recognising them helps in tone and style questions.

A sustained rise in the general price level, reducing purchasing power. Central banks often raise interest rates to contain it.

Gross Domestic Product is the total market value of final goods and services produced within a country in a period. It is a standard measure of economic size.

The interest rate at which the central bank lends short-term funds to commercial banks against securities. It is a key tool of monetary policy.

The gap between government expenditure and revenue excluding borrowings. A large deficit usually implies heavier government borrowing.

Basic freedoms guaranteed to citizens by the Constitution, enforceable through courts. In India they are listed in Part III and include equality, speech, and life.

Guidelines in Part IV of the Indian Constitution for state policy aimed at social and economic welfare. They are not directly enforceable in courts.

India's three-tier system of local self-government in rural areas, established by the 73rd Constitutional Amendment. It covers village, block, and district levels.

A seasonal reversal of wind direction bringing heavy rainfall, central to Indian agriculture. The southwest monsoon arrives around June and withdraws by September.

The latitude about 23.5 degrees north of the equator, the northern limit of the sun's apparent overhead passage. It passes through several Indian states.

Annual international awards recognising outstanding contributions in physics, chemistry, medicine, literature, peace, and economics. They were first awarded in 1901.

A region with exceptionally high numbers of endemic species under serious habitat threat. India contains parts of the Himalaya and Western Ghats hotspots.