MAH MCA CET key terms

An ordered arrangement of a set of items, where changing the order creates a different arrangement. The count of arrangements of r items chosen from n distinct items is n! divided by (n minus r) factorial.

A selection of items from a group where order does not matter, so picking A then B counts the same as B then A. Calculated as n! divided by r!(n minus r)!.

The product of all positive integers from 1 up to a given whole number, written with an exclamation mark. For example, 4! equals 4 times 3 times 2 times 1, which is 24; by convention 0! equals 1.

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 plus (n minus 1)d, and the sum of n terms is n/2 times twice the first term plus (n minus 1)d.

A sequence where each term after the first is found by multiplying the previous term by a fixed non-zero ratio. The nth term is a times r to the power (n minus 1), and the sum of n terms is a(r^n minus 1)/(r minus 1) when r is not 1.

The exponent to which a fixed base must be raised to produce a given number. For instance, log base 10 of 1000 is 3, because 10 cubed equals 1000; logarithms turn multiplication into addition of exponents.

A single number computed from a square matrix that indicates whether the matrix has an inverse; it is zero exactly when the matrix is singular. For a 2x2 matrix with rows (a, b) and (c, d), it equals ad minus bc.

A rectangular array of numbers arranged in rows and columns, used to represent systems of equations or transformations. Addition is entry-wise, and multiplication is possible only when the column count of the first equals the row count of the second.

A method for solving a system of linear equations using determinants. Each unknown equals the determinant of the coefficient matrix with its column replaced by the constant column, divided by the determinant of the coefficient matrix.

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

The accumulation of a quantity over an interval, computed as a limit of sums of small pieces. The definite integral gives signed area under a curve, and it reverses differentiation through the fundamental theorem of calculus.

The value a function's output approaches as its input approaches some point, regardless of what happens exactly at that point. Limits underpin both derivatives and integrals and can exist even where the function is undefined.

A number between 0 and 1 expressing how likely an event is, computed for equally likely outcomes as favourable outcomes divided by total outcomes. The probabilities of all mutually exclusive outcomes of an experiment sum to 1.

A type of average found by dividing the number of values by the sum of their reciprocals. It suits rates such as average speed over equal distances and is always less than or equal to the arithmetic mean.

A form of deductive argument with two premises and a conclusion, where the conclusion must follow if the premises are true. A classic pattern: all A are B, all B are C, therefore all A are C.

A diagram using overlapping circles to show sets and their relationships, such as intersection, union, and exclusion. It is commonly used to test whether a proposed conclusion follows from given statements.

The logically equivalent form of a conditional statement obtained by swapping and negating both parts. If the original is 'if P then Q', the contrapositive is 'if not Q then not P', which is always equally true.

The statement formed by swapping the hypothesis and conclusion of a conditional. The converse of 'if P then Q' is 'if Q then P', and it is not automatically true just because the original is true.

A reasoning problem that describes family links through statements or coded symbols and asks how two people are related. Candidates draw a quick family tree, tracking gender and generation to avoid confusing in-laws with blood relatives.

A puzzle requiring placement of people around a circle or in a row using clues about who sits beside, opposite, or to the left of whom. Working from the most restrictive clue and fixing one position simplifies solving.

A reasoning task tracking a person's movement through turns and distances to find final position or facing direction. Sketching each leg on paper and applying the Pythagorean theorem for net displacement prevents errors.

A sequence of numbers with a hidden rule, where the candidate must find the next term or the odd one out. Common patterns involve constant differences, multiplying factors, alternating operations, or squares and cubes.

A reasoning question where words or letters are transformed by a rule and the candidate must apply or reverse that rule. Letter-shift, reversal, and position-based substitutions are the most frequent patterns.

A question presenting a pair of related items and asking for another pair with the same relationship. The key is to name the exact link, such as worker to tool or cause to effect, before choosing an option.

The rule that a verb must match its subject in number and person, so a singular subject takes a singular verb. Intervening phrases, collective nouns, and either/or constructions are frequent traps in error-spotting questions.

A word such as in, on, at, or between that links a noun or pronoun to another part of the sentence, often showing place, time, or direction. Examiners test fixed pairings like 'comply with' and 'averse to'.

A fixed expression whose meaning cannot be worked out from its individual words, such as 'a bolt from the blue'. Idiom questions test recognition of the accepted phrasing and its correct meaning in context.

A word that has the same or nearly the same meaning as another word in a given context. Vocabulary questions ask candidates to pick the closest match, so subtle differences in tone and usage matter.

A word with a meaning opposite to another word, such as 'scarce' for 'abundant'. Answering correctly requires attention to the part of speech and to the exact sense in which the given word is used.

Two ways of presenting the same action: active voice makes the doer the subject, while passive voice makes the receiver the subject and uses a form of 'be' with the past participle. Transformation questions test tense and agreement preservation.

Reporting someone's words either exactly, inside quotation marks, or paraphrased in a subordinate clause. Conversion requires consistent changes in pronouns, tense, and time or place words such as 'now' becoming 'then'.

Answering questions about a passage by locating stated information and drawing supported inferences. Correct options restate the passage's meaning, whereas wrong options exaggerate, reverse, or import outside knowledge.

A base-2 system using only the digits 0 and 1, where each position represents a power of 2. Computers use it because two states, such as on and off, map naturally to its digits.

The smallest unit of digital information, holding a single binary value of 0 or 1. Bits are grouped to represent larger values, characters, 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 usually quoted in bytes, with kilobyte, megabyte, and gigabyte as larger multiples.

Random Access Memory is the computer's volatile working memory, holding programs and data currently in use. Its contents vanish when power is switched off, and more RAM generally allows more programs to run at once.

Read Only Memory is non-volatile storage whose contents are retained without power and normally cannot be changed by ordinary programs. It typically holds firmware such as the startup instructions a computer runs first.

System software that manages hardware, files, memory, and processes, and provides services on which application programs run. Common examples include Windows, Linux, macOS, and Android.

A program that translates an entire source program written in a high-level language into machine code before execution. It reports syntax errors for the whole program and produces an executable file.

A program that translates and executes source code one statement at a time rather than producing a separate executable. It stops at the first error it meets and is often used in languages such as Python.