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.
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following:

(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).

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2.
Obtain the value of \[ \Delta = \begin{vmatrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{vmatrix} \] in terms of \(x, y, z\). Further, if \(\Delta = 0\) and \(x, y, z\) are non–zero real numbers, prove that \[ x^{-1} + y^{-1} + z^{-1} = -1 \]

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3.
Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]

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4.
A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.

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5.
The probability of hitting the target by a trained sniper is three times the probability of not hitting the target on a stormy day due to high wind speed. The sniper fired two shots on the target on a stormy day when wind speed was very high. Find the probability that
(i) target is hit.
(ii) at least one shot misses the target.

View Solution

6.
Find the general solution of the differential equation \[ y\log y\,\frac{dx}{dy}+x=\frac{2}{y}. \]

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

2.
Obtain the value of \[ \Delta = \begin{vmatrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{vmatrix} \] in terms of \(x, y, z\). Further, if \(\Delta = 0\) and \(x, y, z\) are non–zero real numbers, prove that \[ x^{-1} + y^{-1} + z^{-1} = -1 \]

3.
Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]

4.
A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.

6.
Find the general solution of the differential equation \[ y\log y\,\frac{dx}{dy}+x=\frac{2}{y}. \]

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

2.Obtain the value of \[ \Delta = \begin{vmatrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{vmatrix} \] in terms of \(x, y, z\). Further, if \(\Delta = 0\) and \(x, y, z\) are non–zero real numbers, prove that \[ x^{-1} + y^{-1} + z^{-1} = -1 \]

3.Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]

4.A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.

6.Find the general solution of the differential equation \[ y\log y\,\frac{dx}{dy}+x=\frac{2}{y}. \]

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

2.
Obtain the value of \[ \Delta = \begin{vmatrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{vmatrix} \] in terms of \(x, y, z\). Further, if \(\Delta = 0\) and \(x, y, z\) are non–zero real numbers, prove that \[ x^{-1} + y^{-1} + z^{-1} = -1 \]

3.
Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]

4.
A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.

6.
Find the general solution of the differential equation \[ y\log y\,\frac{dx}{dy}+x=\frac{2}{y}. \]