NIMCET key terms

An arrangement of a set of objects in a definite order, where changing the order produces a different arrangement. The number of permutations of n distinct objects taken r at a time is n!/(n-r)!.

A selection of objects from a group where order does not matter, so choosing A then B counts the same as B then A. The count is n!/(r!(n-r)!), written nCr.

The product of all positive integers from 1 up to a given whole number n, written n!. By convention 0! equals 1, and n! counts the orderings of n distinct items.

The number nCr appearing in the expansion of (a+b)^n, equal to n!/(r!(n-r)!). It counts ways to choose r items from n and forms the entries of Pascal's triangle.

A formula expanding (a+b)^n as a sum of terms nCr·a^(n-r)·b^r for r from 0 to n. It converts a power of a sum into an explicit polynomial with predictable coefficients.

A formula giving any single term of a sequence or expansion by its position index, such as the (r+1)th term of a binomial expansion or the nth term of an arithmetic progression.

A sequence in which each term after the first is obtained by adding 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 where each term after the first is obtained by multiplying by a fixed nonzero constant called the common ratio. Its nth term is ar^(n-1), and it converges only when the ratio lies between -1 and 1.

The limiting value of an infinite geometric series, equal to a/(1-r) when the absolute value of the common ratio r is less than 1. Otherwise the series diverges and no finite sum exists.

A single number computed from a square matrix that indicates whether the matrix is invertible. A zero determinant means the matrix has no inverse and its rows are linearly dependent.

The matrix B such that AB equals BA equals the identity, existing only when the determinant of A is nonzero. For a 2x2 matrix it is the adjugate divided by the determinant.

A square matrix with ones on the main diagonal and zeros everywhere else. Multiplying any conformable matrix by it leaves that matrix unchanged, so it acts like the number 1.

A method solving a system of linear equations by expressing each unknown as a ratio of two determinants. It applies only when the coefficient matrix has a nonzero determinant.

The value a function or sequence approaches as its input approaches some point, regardless of whether the function is defined there. Limits underpin continuity, derivatives and convergence.

A property of a function at a point where the limit exists, the function is defined there, and the two values agree. Graphically the curve has no break, jump or hole at that point.

The instantaneous rate at which a function changes with respect to its variable, defined as the limit of a difference quotient. Geometrically it gives the slope of the tangent line.

The property that a function has a well-defined derivative at a point. Differentiability at a point implies continuity there, but continuity does not guarantee differentiability, as with the absolute value function at zero.

The reverse process of differentiation, also interpreted as the area under a curve. The definite integral over an interval is evaluated using antiderivatives via the fundamental theorem of calculus.

The signed area between a curve and the x-axis over a stated interval, computed as the difference of an antiderivative evaluated at the interval's endpoints. Sign depends on whether the curve lies above or below the axis.

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

The probability that an event occurs given that another event has already occurred, written P(A|B) and equal to P(A and B) divided by P(B), provided P(B) is nonzero.

A rule that reverses a conditional probability, updating P(A|B) from P(B|A) and the prior probabilities of A and B. It is central to problems involving two-stage or diagnostic testing situations.

Two events whose occurrence does not affect each other's likelihood, so their joint probability equals the product of their individual probabilities. Contrast with mutually exclusive events, which cannot occur together.

A deductive argument with two premises and a conclusion, judged valid when the conclusion must follow if the premises are true. Validity concerns form, not the actual truth of the premises.

A property of an argument where the conclusion necessarily follows from the premises, whatever their content. A valid argument with true premises is sound; validity alone does not guarantee true conclusions.

A conclusion drawn from given statements or evidence rather than stated directly. In reasoning questions you must pick the inference that follows necessarily, not merely one that seems plausible.

An unstated premise that must be true for an argument's conclusion to follow from its stated evidence. Identifying hidden assumptions is the key step in strengthening or weakening arguments.

The main claim an argument tries to establish, usually signalled by words like therefore, hence or thus. Distinguishing it from supporting statements is the first step in analysing any passage.

A diagram using overlapping circles to represent sets and show relationships such as inclusion, exclusion and intersection. It is the standard tool for testing whether categorical syllogisms are valid.

A well-defined collection of distinct objects, called elements, considered as a single entity. Operations include union, intersection, difference and complement, often visualised with Venn diagrams.

A set whose every element also belongs to another set, written A is contained in B. Every set is a subset of itself, and the empty set is a subset of every set.

A reasoning puzzle describing family links through statements or a diagram, requiring you to deduce how two people are related. Drawing a family tree with clear gender and generation markers prevents errors.

A puzzle tracking a person's movement through turns and distances to find final position or facing direction. Sketching each move on paper, with north fixed upward, is the reliable method.

A puzzle placing people in rows or around a table using clues about relative positions, facing directions and neighbours. Circular arrangements fix one person's position to remove rotational duplicates.

A sequence of numbers following a hidden rule, where you must identify the pattern to find a missing or wrong term. Common rules involve differences, ratios, squares, cubes or alternating operations.

A puzzle where words or letters are transformed by a rule and you must decode a new word or infer the rule. Check letter shifts, reversals, position sums and vowel-consonant substitutions systematically.

A finite, unambiguous sequence of steps that transforms an input into a desired output. Every algorithm must terminate and each step must be precisely defined so it can be executed mechanically.

A diagram that represents an algorithm using standard symbols: ovals for start and end, parallelograms for input and output, rectangles for processing and diamonds for decisions. Arrows show the order of execution.

A structured, English-like description of an algorithm that borrows programming constructs without obeying any language's syntax. It lets you express logic that can later be translated into real code.

Software that translates an entire source program into machine code before execution, reporting all syntax errors together. Compiled programs generally run faster than interpreted ones because translation happens once.

Software that translates and executes a program line by line, stopping at the first error encountered. It needs no separate compilation step but typically executes more slowly than a compiled program.

A base-2 positional system using only the digits 0 and 1, where each place value is a power of two. It underlies all digital storage, and conversion to decimal sums the set bit weights.

A base-16 number system using digits 0 to 9 and letters A to F, widely used as shorthand for binary because one hex digit represents exactly four bits. Conversion is done by grouping bits in fours.

The smallest unit of digital information, holding a single value of either 0 or 1. Groups of bits encode characters, numbers and instructions inside a computer.

A group of eight bits treated as one unit, capable of representing 256 distinct values. Memory and storage sizes are conventionally expressed in bytes and their multiples.

System software that manages hardware resources, files and processes, and provides services to application programs. It acts as the intermediary between the user and the machine's hardware.

A word having the same or nearly the same meaning as another word in a given context, such as begin and commence. Exact interchangeability is rare, since register and connotation often differ.

A word expressing a meaning opposite to another word, such as scarce and abundant. Some antonyms are gradable, like hot and cold, while others are absolute, like alive and dead.

The sense a word carries in a particular sentence, which may differ from its dictionary definition. Choosing the right synonym or filling a blank requires reading the surrounding clues carefully.

A fixed expression whose meaning cannot be worked out from its individual words, such as spill the beans meaning to reveal a secret. Idioms must be learned as whole units.

A verb combined with a preposition or adverb that together carry a new meaning, such as give up or look after. The particle can change the meaning entirely and sometimes makes the verb separable.

The grammatical 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 verb form ending in -ing that functions as a noun, as in swimming is healthy. It can serve as subject, object or complement, and some verbs take only a gerund as object.

A verb form used as an adjective, either present (-ing) or past (-ed or irregular), as in a running tap or a broken vase. Dangling participles occur when the modified noun is unclear.

A sentence construction where the subject performs the action, as in the committee approved the plan. It is usually more direct and concise than the passive alternative.

A construction where the subject receives the action, formed with a form of be plus the past participle, as in the plan was approved. It suits cases where the doer is unknown or unimportant.

Reporting someone's exact words inside quotation marks, as in she said, I will come. Tense and pronouns stay as originally spoken, with reporting verbs often placed before or after the quote.

Reporting what someone said without quoting exact words, as in she said she would come. Pronouns, tense and time expressions usually shift back one step from the original utterance.

The skill of extracting stated facts, implied ideas, tone and the author's purpose from a passage. Correct answers must be supported by the text rather than by outside knowledge.