Relations And Functions Class 11th Notes - Free NCERT Class 11 Maths Chapter 2 notes - Download PDF

Relations And Functions Class 11th Notes - Free NCERT Class 11 Maths Chapter 2 notes - Download PDF

Edited By Ramraj Saini | Updated on Mar 22, 2022 04:40 PM IST

Class 11 Math chapter 2 notes are regarding Relations and Functions. In chapter 2 we will be going through the functions and their relations concepts in Relations and Functions Class 11 notes. This Class 11 Maths chapter 2 notes contains the following topics: Cartesian product, relations, functions, different types of functions, Algebra of a real function, multiplication of two real functions, quotient function.

NCERT Class 11 Math chapter 2 notes also contain important formulas. NCERT Class 11 Math chapter 2 contains systematic explanations of topics using examples and exercises. NCERT Notes for Class 11 Math chapter 2 include FAQ’s or frequently asked questions about the chapter. In CBSE Class 11 Maths chapter 2 notes topics are explained step by step. These concepts can also be downloaded from Class 11 Maths chapter 2 notes pdf download, Class 11 notes Relations and functions, Class 11 Relations and functions notes pdf download.

Also, students can refer,

NCERT Class 11 Math Chapter 2 Notes

Ordered Pair: two elements in an order separated by common.

Representation: (a,b)

NOTE: 2 ordered pairs (a,b) and (c,d) are said to be equal if (a=c) and (b=d)

Cartesian Product: If sets A, B have an ordered pair of (a,b) where a A and b B, is called cartesian product.

Denoted by: AXB

Set builder form: AXB ={(a,b) : a ∈A and b∈ B}

NOTE:

  1. If A=∅ , B= ∅then cartesian product AXB=∅.

  2. It doesn’t satisfy commutative law: (A, B)≠(B, A)

  3. If anyone among the two sets is an infinite set then the whole product becomes infinite.

A=infinite, B=finite then AXB and BXA are also infinite.

  1. If n(A)=m (m=number of elements in A), n(B)=n then the number of elements in the cartesian product is mn.

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Eg: n(A) = 3 and n(B)=2 then n(AXB) = 6.

Relations:

A group of ordered pairs containing one element from each set is called the relation between two sets. Suppose A, B are both non-empty sets, then the relation is a subset of cartesian products of (AXB).

A subset is a relation between the first and second elements of ordered pairs in A × B.

The set of first elements in relations is called the domain and the next element is called images or of range R.

Set builder form: R={(a,b): (a,b)∈R}

Representation Of Relation:2

Note:

  • The range can be represented in set-builder, roaster form, and also using arrow marks with brackets.
  • If n(A)=m (m=number of elements in A), n(B)=n, and cartesian product=mn then a number of relations can be found by using 2^{mn}

Inverse Relation:

Sets A, B are both non-empty sets with R being the relation and the inverse of the relation is called inverse relation R^{-1}from B to A.

Set\ builder\ form:\ R^{-1}=\left \{ (b,a):(a,b)\ \epsilon\ R \right \}

\\ \text{The domain of the relation R will be the range of inverse relation } R^{-1} \\ \text{The range of the relation R will be the domain of inverse relation } R^{-1} \\

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Function:

A relation F from A to B is called to be a function if every element in set A of a function has only one image in set B of a function.

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Real-Valued Functions:

Function denoted as f: A→B is said to be a real-valued function if B is a subset of R . If A, B are subsets of R, in such conditions we can call f is called a real function.

Type Of Functions:

Identity function:

A function is said to be an identity function if a function f: R→R when f(x)=x for each x belongs to R satisfies.

Consider the graph of an identity function f(x)=x:

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Domain= R

Range = C

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Constant Function :

A function is said to be a constant function, if a function f: R R when f(x)=C for each C belonging to R satisfies.

Consider the graph of a constant function:

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Domain= R

Range = C

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Polynomial Function:

A function is said to be a Polynomial function, if a function f: RR when f(x) = a_0 + a_1x + a_2x^2+.....+ a_nx^n for each x belonging to R satisfies.

Rational Functions:

The functions that belong to Real functions, and are represented as f(x)/g(x) where f(x) and g(x) ≠0 are polynomial functions that are represented using x and they belong to R.

Modulus Function:

Real function f: R → R is said to be a modulus function if

\\ f(x) = \left | x \right | \text {for all x belongs to R}\\ Domain: R \\ Range: R^+ \cup {0}\ in\ the\ interval\ \left [ 0,\infty \right )\\ f(x)=\begin{Bmatrix} -x \ \ \ \ \ \ if \ x<0 \\ x \ \ \ \ \ \ if \ x\geq 0 \end{Bmatrix}

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Signum Function:

Real function f: R → R is said to be Signum function if f(x) = lxl / x where x≠0 and when x=0 we get

8


Domain= R

Range={-1,0,1}

Greatest Integer Function:

Real function f: R → R is said to be the greatest integer function if f(x)=[x] where x belongs to R and values of x are the greatest integer or less than or equal to x.

Fractional Function:

Real function f : R → R is said to be Fractional Function function if f(x)={x} where x belongs to R.

f(x) = {x} = x – [x]

Domain: R

Range : [0,1)

Algebra Of Real Function:

Addition Of Two Algebraic Functions:

If f : X → R , g : X → R are real functions, then we represent: (f + g) : X → R as (f + g) (x) = f (x) +g(x) where x belongs to X.

Subtraction Of Real Functions:

If f : X → R and g : X → R are real functions, then we represent : (f – g) : X → R as (f – g) (x) = f (x) – g(x) where x belongs to X.

Multiplication Of Scalar:

If f : X → R is real functions, K is any scalar

product of Kf is defined by : (Kf)(x) = Kf(x)

Multiplication Of Two Real Functions:

If f : X → R and g : X → R are real functions,

product of the two functions is defined by: (fg) x = f(x) . g(x)

The Quotient Of Two Real Functions:

if f and g are two real functions, then the

The quotient of f by g is given by fg from XR.

(f/g)(x) = f(x)/g(x) where g(x)≠0

With this topic we conclude NCERT Class 11 chapter 2 notes.

The link for the NCERT textbook pdf is given below:

URL: ncert.nic.in/pdf/publication/exemplarproblem/classXI/mathematics/keep202.pdf

Significance of NCERT Class 11 Maths Chapter 2 Notes:

NCERT Class 11 Maths chapter 2 notes will be very much helpful for students to score maximum marks in their 11 board exams. In Relations and Functions Class 11 chapter 2 notes we have discussed many topics: Cartesian product, relations, functions, different types of functions, Algebra of a real function, multiplication of two real functions, quotient function. NCERT Class 11 Maths chapter 2 covers important topics of Class 11 CBSE Maths Syllabus.

The CBSE Class 11 Maths chapter 2 will help to understand the formulas, statements, rules in detail. This pdf also contains previous year questions and NCERT textbook pdf. The next part contains FAQ’s or frequently asked questions along with topic-wise explanations. These topics can als be downloaded from Class 11 chapter 2 Relations and Functions pdf download.

NCERT Class 11 Notes Chapter Wise.

Subject Wise NCERT Exemplar Solutions

Subject Wise NCERT Solutions

NCERT Books and Syllabus

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A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1)

0.34\; J

Option 2)

0.16\; J

Option 3)

1.00\; J

Option 4)

0.67\; J

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

Option 1)

2.45×10−3 kg

Option 2)

 6.45×10−3 kg

Option 3)

 9.89×10−3 kg

Option 4)

12.89×10−3 kg

 

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1)

2,000 \; J - 5,000\; J

Option 2)

200 \, \, J - 500 \, \, J

Option 3)

2\times 10^{5}J-3\times 10^{5}J

Option 4)

20,000 \, \, J - 50,000 \, \, J

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)

K/2\,

Option 2)

\; K\;

Option 3)

zero\;

Option 4)

K/4

In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

Option 1)

0.02

Option 2)

3.125 × 10-2

Option 3)

1.25 × 10-2

Option 4)

2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

Option 2)

increase two fold

Option 3)

remain unchanged

Option 4)

be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1)

Molality

Option 2)

Weight fraction of solute

Option 3)

Fraction of solute present in water

Option 4)

Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

Option 2)

6.023 × 1022

Option 3)

half that in 8 g He

Option 4)

558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

Option 2)

more than 3 but less than 6

Option 3)

more than 6 but less than 9

Option 4)

more than 9

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