NCERT Solutions For Class 12 Mathematics Chapter 1 Relation and Functions

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NCERT Solutions for Class 12 Mathematics Chapter 1 Relation and Functions is included in this article. Relations and functions are two separate concepts in algebra on which binary operations can be performed. The NCERT Solutions include the concepts of types of relations, types of functions, and binary operations.

The chapter Relations and Functions has a weightage of 8 marks in the CBSE Class 12 examination. Around 2-3 descriptive questions from topics like reflexive relations, symmetric relations, transitive and equivalence relations are asked frequently in the examination.

Download PDF: NCERT Solutions for Relations and Functions

NCERT Solutions for Class 12 Mathematics Chapter 1 Relations and Functions

Important Topics in Class 12 Mathematics Chapter 1 Relations and Functions

Relations and Functions is an important topic in the board examination as per CBSE Class 12 exam pattern. In NCERT Class 12 Mathematics Chapter 1, different types of relations and equivalence relations, the composition of functions, invertible functions and binary operations are discussed. The important topics of the chapter include:

Relations and Functions

Functions are defined as rules that relate every element in one set, called domain, to exactly one element in another set, called range.

Functions are classified as Many to one function, One to one function, Signum function, Onto function, One and onto function, Quadratic function, Constant function, Identity function, Modulus function, Rational function, and Greatest integer function.

Example: y = x + 3 and y = x² – 1 are functions because every x-value produces a y-value.

Relation refers to the connection between elements of two or multiple sets. These sets have to be non-empty.

There are 9 types of relations – Empty Relation, Full Relation, Reflexive Relation, Irreflexive Relation, Symmetric Relation, Anti-symmetric Relation, Transitive Relation, Equivalence Relation, and Asymmetric Relation.

Binary Operations

A binary operation is an association of any pair of elements a, b from X to another element of X. Binary Operations include binary addition, Multiplication, Subtraction and Division, as 'binary' means two. .

A binary operation is a function f(x, y) that applies to two elements of the same set S, such that the result is also an element of the set S

NCERT Solutions For Class 12 Maths Chapter 1 Exercises:

The detailed solutions for all the NCERT Solutions for Relations and Functions under different exercises are as follows:

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CBSE CLASS XII Related Questions

1.
Let $f'(x) = 3(x^2 + 2x) - \frac{4}{x^3} + 5$, $f(1) = 0$. Then, $f(x)$ is:

$x^3 + 3x^2 + \frac{2}{x^2} + 5x + 11$
$x^3 + 3x^2 + \frac{2}{x^2} + 5x - 11$
$x^3 + 3x^2 - \frac{2}{x^2} + 5x - 11$
$x^3 - 3x^2 - \frac{2}{x^2} + 5x - 11$

View Solution

2.
Solve the following linear programming problem graphically: Maximise $ Z = x + 2y $ Subject to the constraints: \[ x - y \geq 0 \] \[ x - 2y \geq -2 \] \[ x \geq 0, \, y \geq 0 \]

View Solution

3.
The integrating factor of the differential equation $ \frac{dy}{dx} + y = \frac{1 + y}{x} $ is:

View Solution

4.
Let the polished side of the mirror be along the line \[ \frac{x}{1} = \frac{1 - y}{2} = \frac{2z - 4}{6}. \] A point $ P(1, 6, 3) $, some distance away from the mirror, has its image formed behind the mirror. Find the coordinates of the image point and the distance between the point $ P $ and its image.

View Solution

5.
Evaluate : \[ I = \int_0^{\frac{\pi}{4}} \frac{dx}{\cos^3 x \sqrt{2 \sin 2x}} \]

View Solution

6.
A furniture workshop produces three types of furniture: chairs, tables, and beds each day. On a particular day, the total number of furniture pieces produced is 45. It was also found that the production of beds exceeds that of chairs by 8, while the total production of beds and chairs together is twice the production of tables. Determine the units produced of each type of furniture, using the matrix method.

View Solution

NCERT Solutions For Class 12 Mathematics Chapter 1 Relation and Functions

NCERT Solutions for Class 12 Mathematics Chapter 1 Relations and Functions

Important Topics in Class 12 Mathematics Chapter 1 Relations and Functions

Relations and Functions

Binary Operations

CBSE CLASS XII Related Questions

1.
Let $f'(x) = 3(x^2 + 2x) - \frac{4}{x^3} + 5$, $f(1) = 0$. Then, $f(x)$ is:

2.
Solve the following linear programming problem graphically: Maximise \( Z = x + 2y \) Subject to the constraints: \[ x - y \geq 0 \] \[ x - 2y \geq -2 \] \[ x \geq 0, \, y \geq 0 \]

3.
The integrating factor of the differential equation \( \frac{dy}{dx} + y = \frac{1 + y}{x} \) is:

5.
Evaluate : \[ I = \int_0^{\frac{\pi}{4}} \frac{dx}{\cos^3 x \sqrt{2 \sin 2x}} \]

Similar Mathematics Concepts

Comments

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NCERT Solutions For Class 12 Mathematics Chapter 1 Relation and Functions

NCERT Solutions for Class 12 Mathematics Chapter 1 Relations and Functions

Important Topics in Class 12 Mathematics Chapter 1 Relations and Functions

Relations and Functions

Binary Operations

CBSE CLASS XII Related Questions

1.Let $f'(x) = 3(x^2 + 2x) - \frac{4}{x^3} + 5$, $f(1) = 0$. Then, $f(x)$ is:

2.Solve the following linear programming problem graphically: Maximise \( Z = x + 2y \) Subject to the constraints: \[ x - y \geq 0 \] \[ x - 2y \geq -2 \] \[ x \geq 0, \, y \geq 0 \]

3.The integrating factor of the differential equation \( \frac{dy}{dx} + y = \frac{1 + y}{x} \) is:

5. Evaluate : \[ I = \int_0^{\frac{\pi}{4}} \frac{dx}{\cos^3 x \sqrt{2 \sin 2x}} \]

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Let $f'(x) = 3(x^2 + 2x) - \frac{4}{x^3} + 5$, $f(1) = 0$. Then, $f(x)$ is:

2.
Solve the following linear programming problem graphically: Maximise \( Z = x + 2y \) Subject to the constraints: \[ x - y \geq 0 \] \[ x - 2y \geq -2 \] \[ x \geq 0, \, y \geq 0 \]

3.
The integrating factor of the differential equation \( \frac{dy}{dx} + y = \frac{1 + y}{x} \) is:

5.
Evaluate : \[ I = \int_0^{\frac{\pi}{4}} \frac{dx}{\cos^3 x \sqrt{2 \sin 2x}} \]