Class XI Mathematics Textbook (NCERT) Vocabulary Flashcards

Vocabulary flashcards defining key mathematical terms from the Class XI NCERT textbook chapters, including Sets, Relations, Trigonometry, Algebra, Coordinate Geometry, calculus, Statistics, and Probability.

Set

A well-defined collection of objects.

Empty Set

A set which does not contain any element; also called the null set or the void set, denoted by the symbol $\phi$ or $\{ \}$.

Finite Set

A set which is empty or consists of a definite number of elements.

Equal Sets

Two sets A and B that have exactly the same elements, written as $A = B$.

Subset

A set A is said to be a subset of a set B if every element of A is also an element of B, expressed as $A \subset B$.

Power Set

The collection of all subsets of a set A, denoted by $P(A)$. If $n(A) = m$, then $n[P(A)] = 2^m$.

Universal Set

A basic set relevant to a particular context, usually denoted by $U$, from which all other subsets are considered.

Union of Sets

The set which consists of all the elements of A and all the elements of B, the common elements being taken only once; denoted by $A \cup B$.

Intersection of Sets

The set of all elements which are common to both A and B, denoted by $A \cap B$.

Disjoint Sets

Two sets A and B such that $A \cap B = \phi$.

Complement of a Set

If A is a subset of the universal set $U$, the set of all elements of $U$ which are not elements of A, denoted by $A^{\prime}$.

Cartesian Product

Given two non-empty sets P and Q, the set $P \times Q = \{(p,q) : p \in P, q \in Q\}$ containing all ordered pairs.

Relation

A subset of the cartesian product $A \times B$ derived by describing a relationship between the first element and the second element of the ordered pairs.

Function

A relation f from a set A to a set B such that every element of set A has one and only one image in set B.

Signum Function

The function $f: R \rightarrow R$ defined by $f(x) = 1$ if $x > 0$, $0$ if $x = 0$, and $-1$ if $x < 0$.

Greatest Integer Function

The function $f: R \rightarrow R$ defined by $f(x) = [x]$ which assumes the value of the greatest integer less than or equal to x.

Radian

The measure of an angle subtended at the centre of a unit circle by an arc of length 1 unit.

Complex Number

A number of the form $a + ib$, where a and b are real numbers and $i = \sqrt{-1}$.

Argand Plane

A plane having a complex number assigned to each of its points; the x-axis is the real axis and the y-axis is the imaginary axis.

Permutation

An arrangement in a definite order of a number of objects taken some or all at a time.

Factorial

The product of the first n natural numbers, denoted as $n!$.

Combination

A selection of n different things taken r at a time where the order of selection does not matter.

Arithmetic Progression (A.P.)

A sequence $a_1, a_2, ...$ where each term after the first is obtained by adding a constant $d$ to the preceding term.

Geometric Progression (G.P.)

A sequence where each term is non-zero and the ratio of any term to its preceding term is a constant $r$.

Inclination of a Line

The angle $\theta$ made by a line with the positive direction of the x-axis measured anti-clockwise ($0^{\circ} \le \theta \le 180^{\circ}$).

Slope (Gradient)

If $\theta$ is the inclination of a line, its slope $m$ is defined as $m = \tan(\theta)$, provided $\theta \neq 90^{\circ}$.

Parabola

The set of all points in a plane that are equidistant from a fixed line (directrix) and a fixed point (focus) not on the line.

Ellipse

The set of all points in a plane, the sum of whose distances from two fixed points (foci) is a constant.

Hyperbola

The set of all points in a plane, the difference of whose distances from two fixed points (foci) is a constant.

Latus Rectum

A line segment perpendicular to the transverse axis (or major axis) through any of the foci and whose end points lie on the conic section.

Octants

The eight parts into which the three coordinate planes divide three-dimensional space.

Mathematically Acceptable Statement

A sentence that is either true or false but not both.

Compound Statement

A statement made up of two or more component statements.

Variance

The mean of the squares of the deviations from the mean, denoted by $\sigma^2$.

Standard Deviation

The positive square root of the variance, denoted by $\sigma$.

Random Experiment

An experiment that has more than one possible outcome and where it is not possible to predict the outcome in advance.

Sample Space

The set of all possible outcomes of a random experiment, denoted by $S$.

Event

Any subset of a sample space $S$.

Mutually Exclusive Events

Events A and B such that the occurrence of one excludes the occurrence of the other; they are disjoint sets ($A \cap B = \phi$).

Exhaustive Events

Events $E_1, E_2, ..., E_n$ such that their union equals the entire sample space $S$.