NCERT Solutions Class 11 Maths Chapter 2 Relations and Functions

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NCERT Solutions for class 11 mathematics Chapter 2 Relations and Functions are provided in the article below. Relations and functions define a mapping between two sets (Inputs and Outputs) such that they have ordered pairs of the form (Input, Output). Class 11 Mathematics Chapter covers important concepts including Addition of Two Real Functions, Real Valued Functions, and Ordered Pairs.

Download: NCERT Solutions for Class 11 Mathematics Chapter 2 pdf

Class 11 Maths NCERT Solutions Chapter 2 Relations and Functions

Class 11 Maths NCERT Solutions Chapter 2 Relations and Functions are as provided below:

Also check: Relations and Functions

Important Topics for Class 11 Maths NCERT Solutions Chapter 2 Relations and Functions

Important Topics for Class 11 Maths NCERT Solutions Chapter 2 Relations and Functions are as follows:

Cartesian Product of Sets

Cartesian product is the product of any two sets. This product’s resultant set contains all possible and ordered pairs so that the first element of the pair belongs to the first set and the second element belongs to the second set.

Example. Given two sets C = {1,2,6} and D = {8,3}. Find the cartesian product C × D.

Solution: The first element 1 is taken from the set C {1,2,6} and the second element 8 is taken from the second set D {8, 3} to form the first ordered pair (1,8).

Same step is repeated until all possible combinations are chosen. After multiplying two sets C and D, 6 ordered pairs are obtained: {(1,8),(1,3),(2,8),(2,3),(6,8),(6,3)}.

This is the cartesian product of the two sets C and D.

Relations

Relations are used to describe a connection between elements of two sets. They help to map elements of one set (domain) to elements of another set (range). The resulting ordered pairs are of the form (input, output). It can also be said that a function is a subset of a relation.

Example: Find the inverse relation of R = {(4, 8), (-3, -6), (7.1, 2.3)}

Solution: Inverse relation is defined as R-1 = {(y, x) : (x, y) ∈ R}

Therefore, R-1 = {(8, 4), (-6, -3), (2.3, 7.1)}

Therefore, the inverse relation R-1 = {(8, 4), (-6, -3), (2.3, 7.1)}

Functions

Function is the relation between a set of inputs and a set of permissible outputs. Each input is related to exactly one output.

Example: In the function f(x)=x² f (x) = x² any input for x will give one output only.

NCERT Solutions For Class 11 Maths Chapter 2 Exercises:

The detailed solutions for all the NCERT Solutions for Chapter 2 Relations and Functions under different exercises are as follows:

Also check:

Chapter Related Topics
Polynomial Function	Greatest Integer Function	Function notation formula
Product to sum formula	Analytic Function	Ordered Pairs

Also check:

Math Study Guides
Maths Important Formulas	Maths MCQs	Comparison Articles in Maths
Difference Between Topics in Maths	Math Study Material	Arithmetic

CBSE CLASS XII Related Questions

1.
A line passing through the points \(A(1,2,3)\) and \(B(6,8,11)\) intersects the line \[ \vec r = 4\hat i + \hat j + \lambda(6\hat i + 2\hat j + \hat k) \] Find the coordinates of the point of intersection. Hence write the equation of a line passing through the point of intersection and perpendicular to both the lines.

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2.
If \[ P = \begin{bmatrix} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{bmatrix} \quad \text{and} \quad Q = \begin{bmatrix} 2 & 2 & -4 \\ -4 & 2 & -4 \\ 1 & -1 & 5 \end{bmatrix} \] find \( QP \) and hence solve the following system of equations using matrix method:
\[ x - y = 3,\quad 2x + 3y + 4z = 13,\quad y + 2z = 7 \]

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3.
Evaluate : \[ \int_{\frac{1}{12}}^{\frac{5}{12}} \frac{dx}{1+\sqrt{\cot x}} \]

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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.
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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Smoking increases the risk of lung problems. A study revealed that 170 in 1000 males who smoke develop lung complications, while 120 out of 1000 females who smoke develop lung related problems. In a colony, 50 people were found to be smokers of which 30 are males. A person is selected at random from these 50 people and tested for lung related problems. Based on the given information answer the following questions:

(i) What is the probability that selected person is a female?
(ii) If a male person is selected, what is the probability that he will not be suffering from lung problems?
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NCERT Solutions For Class 11 Maths Chapter 2: Relations and Functions

Class 11 Maths NCERT Solutions Chapter 2 Relations and Functions

Important Topics for Class 11 Maths NCERT Solutions Chapter 2 Relations and Functions

NCERT Solutions For Class 11 Maths Chapter 2 Exercises:

CBSE CLASS XII Related Questions

3.
Evaluate : \[ \int_{\frac{1}{12}}^{\frac{5}{12}} \frac{dx}{1+\sqrt{\cot x}} \]

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.

5.
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 \[ x^{-1} + y^{-1} + z^{-1} = -1 \]

Similar Mathematics Concepts

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NCERT Solutions For Class 11 Maths Chapter 2: Relations and Functions

Class 11 Maths NCERT Solutions Chapter 2 Relations and Functions

Important Topics for Class 11 Maths NCERT Solutions Chapter 2 Relations and Functions

NCERT Solutions For Class 11 Maths Chapter 2 Exercises:

CBSE CLASS XII Related Questions

3.Evaluate : \[ \int_{\frac{1}{12}}^{\frac{5}{12}} \frac{dx}{1+\sqrt{\cot x}} \]

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.

5.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 \[ x^{-1} + y^{-1} + z^{-1} = -1 \]

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

3.
Evaluate : \[ \int_{\frac{1}{12}}^{\frac{5}{12}} \frac{dx}{1+\sqrt{\cot x}} \]

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.

5.
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 \[ x^{-1} + y^{-1} + z^{-1} = -1 \]