NCERT Solutions For 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:

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

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1.
Evaluate : \[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{3}}(\sin|x|+\cos|x|)\,dx \]
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2.
Evaluate : \[ \int_{\frac{1}{12}}^{\frac{5}{12}} \frac{dx}{1+\sqrt{\cot x}} \]
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3.
Find the sub–interval of \((0,\pi)\) in which the function \[ f(x)=\tan^{-1}(\sin x-\cos x) \] is increasing and decreasing.
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4.
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(ii) Integrate the function obtained in (i) with respect to \(x\).
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OR
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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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Mother, Father and Son line up at random for a family picture. Let events \(E\): Son on one end and \(F\): Father in the middle. Find \(P(E/F)\).
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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

1.
Evaluate : \[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{3}}(\sin|x|+\cos|x|)\,dx \]

2.
Evaluate : \[ \int_{\frac{1}{12}}^{\frac{5}{12}} \frac{dx}{1+\sqrt{\cot x}} \]

3.
Find the sub–interval of \((0,\pi)\) in which the function \[ f(x)=\tan^{-1}(\sin x-\cos x) \] is increasing and decreasing.

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

6.
Mother, Father and Son line up at random for a family picture. Let events \(E\): Son on one end and \(F\): Father in the middle. Find \(P(E/F)\).

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

1.Evaluate : \[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{3}}(\sin|x|+\cos|x|)\,dx \]

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

3.Find the sub–interval of \((0,\pi)\) in which the function \[ f(x)=\tan^{-1}(\sin x-\cos x) \] is increasing and decreasing.

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

6.Mother, Father and Son line up at random for a family picture. Let events \(E\): Son on one end and \(F\): Father in the middle. Find \(P(E/F)\).

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Evaluate : \[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{3}}(\sin|x|+\cos|x|)\,dx \]

2.
Evaluate : \[ \int_{\frac{1}{12}}^{\frac{5}{12}} \frac{dx}{1+\sqrt{\cot x}} \]

3.
Find the sub–interval of \((0,\pi)\) in which the function \[ f(x)=\tan^{-1}(\sin x-\cos x) \] is increasing and decreasing.

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

6.
Mother, Father and Son line up at random for a family picture. Let events \(E\): Son on one end and \(F\): Father in the middle. Find \(P(E/F)\).