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.

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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.
An NGO organises a charity event in which they decide to distribute woollen caps to protect children from winter. The caps to be distributed are in three separate boxes, Box I has 30 red caps, Box II has 20 red and 10 green caps, and Box III has 30 green caps. The probability that a Box i is selected and a cap picked out is i/6, where i = 1, 2, 3.
Based on the above information, answer the following questions :

2.
Find the vector and cartesian equations of the line passing through the point of intersection of the lines \( \vec{r} = (\hat{i} + \hat{j} - \hat{k}) + \lambda(3\hat{i} - \hat{j}) \) and \( \vec{r} = (4\hat{i} - \hat{k}) + \mu(2\hat{i} + 3\hat{k}) \) and parallel to the line \( \frac{x - 1}{-2} = \frac{7 - y}{-3} = z \).

View Solution

3.
If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).

View Solution

4.
Find:

The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:

\(-\frac{\pi}{2}\)
\(-\frac{\pi}{4}\)
\(\frac{\pi}{4}\)
\(\frac{\pi}{2}\)

View Solution

5.
A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length.

6.
Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]

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

3.
If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).

4.
Find:

The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:

5.
A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length.

6.
Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]

Similar Mathematics Concepts

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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

3.If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).

4. Find: The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:

5.A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length.

6.Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

3.
If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).

4.
Find:

The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:

5.
A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length.

6.
Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]