Multiplication and Division of Algebraic Expressions
Various Algebraic Relations to be used in this chapter
1. \[{{(A+B)}^{2}}={{A}^{2}}+{{B}^{2}}+2AB\]
2. \[{{(A-B)}^{2}}={{A}^{2}}+{{B}^{2}}-2AB\]
3. \[{{A}^{2}}-{{B}^{2}}=(A-B)(A+B)\]
4. \[{{(A+B+C)}^{2}}={{A}^{2}}+{{B}^{2}}+{{C}^{2}}+2AB+2BC+2CA\]
5. \[{{A}^{3}}+{{B}^{3}}+{{C}^{3}}-3ABC=(A+B+C)({{A}^{2}}+{{B}^{2}}+{{C}^{2}}\]\[-AB-BC-CA)\]
6. \[{{(A+B)}^{3}}={{A}^{3}}+{{B}^{3}}+3{{A}^{2}}B+3A{{B}^{2}}\]
7. \[{{(A-B)}^{3}}={{A}^{3}}-{{B}^{3}}-3{{A}^{2}}B+3A{{B}^{2}}\]
8. \[{{(A+B)}^{4}}={{A}^{4}}+4{{A}^{3}}B+6{{A}^{2}}{{B}^{2}}+4A{{B}^{3}}+{{B}^{4}}\]
9. \[{{(A-B)}^{4}}={{A}^{4}}-4{{A}^{3}}B+6{{A}^{2}}{{B}^{2}}-4A{{B}^{3}}+{{B}^{4}}\]
10. \[{{A}^{3}}-{{B}^{3}}=(A+B)({{A}^{2}}+{{B}^{2}}-AB)\]
11. \[{{A}^{3}}-{{B}^{3}}=(A-B)({{A}^{2}}+{{B}^{2}}+AB)\]
Find the product of \[(2{{x}^{2}}-5x+4)\] and \[({{x}^{2}}+7x-8)\]
(a) \[(2{{x}^{4}}-9{{x}^{3}}-47{{x}^{2}}+68x+32)\]
(b) \[(2{{x}^{4}}+9{{x}^{3}}-47{{x}^{2}}+68x-32)\]
(c) \[(2{{x}^{4}}-9{{x}^{3}}-47{{x}^{2}}+68x+32)\]
(d) \[(2{{x}^{4}}-9{{x}^{3}}-47{{x}^{2}}-68x-32)\]
(e) None of these
Answer: (b)
The product of \[(3x+5y)\] and \[(5x-7y)\] is.
(a) \[15{{x}^{2}}+4xy-35{{y}^{2}}\]
(b) \[5{{x}^{2}}-4xy+35{{y}^{2}}\]
(c) \[5{{x}^{5}}+4xy+35{{y}^{2}}\]
(d) \[{{x}^{2}}-4xy-35y\]
(e) None of these
Answer: (a)
Explanation:
\[=(3x+5y)(5x-7y)\]
\[=3x(5x-7y)+5y(5x-7y)\]
\[=15{{x}^{2}}-21xy+25xy-35{{y}^{2}}\]
\[=15{{x}^{2}}+4xy-35{{y}^{2}}\]
The product of \[(-3{{x}^{2}}y)(4{{x}^{2}}y-3x{{y}^{2}}+4x-5y)\] is .........
(a) \[12{{x}^{3}}{{y}^{2}}+9{{x}^{2}}{{y}^{2}}-12{{x}^{4}}y+15{{x}^{3}}{{y}^{3}}\]
(b) \[-12{{x}^{4}}{{y}^{2}}+9{{x}^{3}}{{y}^{3}}-12{{x}^{3}}y+15{{x}^{2}}{{y}^{2}}\]
(c) \[-12x{{y}^{2}}+9{{x}^{3}}{{y}^{2}}-12{{x}^{3}}y+15xy\]
(d) \[-12x{{y}^{3}}+9xy-12x{{y}^{2}}+15{{x}^{2}}y\]
(e) None of these
Answer: (b)
Explanation:
\[(-3{{x}^{2}}y)(4{{x}^{2}}y-3x{{y}^{2}}+4x-5y)=\]\[-12{{x}^{4}}{{y}^{2}}+9{{x}^{3}}{{y}^{3}}-12{{x}^{4}}{{y}^{2}}+9{{x}^{3}}{{y}^{3}}-12{{x}^{3}}y+15{{x}^{2}}{{y}^{2}}\]
Therefore, option (b) is correct and rest of options is incorrect.
The product of \[(3{{x}^{2}}+{{y}^{2}})\] and \[(2{{x}^{2}}+3{{y}^{2}})\] is ------.
(a) \[{{x}^{3}}+10{{x}^{2}}{{y}^{3}}+3{{y}^{4}}\]
(b) \[3{{x}^{2}}+5{{x}^{5}}{{y}^{2}}+3{{y}^{4}}\]
(c) \[6{{x}^{5}}+10{{x}^{2}}{{y}^{3}}+3{{y}^{4}}\]
(d)\[6{{x}^{4}}+11{{x}^{2}}{{y}^{2}}+30{{y}^{4}}\]
(e) None of these
Answer: (d)
Explanation:
\[(3{{x}^{2}}+{{y}^{2}})(2{{x}^{2}}+3{{y}^{2}})\]
\[=6{{x}^{4}}+9{{x}^{2}}{{y}^{2}}+2{{x}^{2}}{{y}^{2}}+30{{y}^{4}}\]
\[=6{{x}^{4}}+11{{x}^{2}}{{y}^{2}}+30{{y}^{4}}\]
Problems Based on Identities
Multiply: \[(3x+2y)(3x+2y)\]
(a) \[9{{x}^{2}}+4{{y}^{2}}+12xy\]
(b) \[18{{x}^{3}}+2{{y}^{2}}+10xy\]
(c) \[9{{x}^{2}}+4{{y}^{2}}+8xy\]
(d) \[9{{x}^{2}}+6{{y}^{3}}+12xy\]
(e) None of these
Answer: (a)
Explanation:
\[(3x+2y)+(3x+2y)=3x(3x+2y)+2y(3xx+2y)\]
\[9{{x}^{2}}+6xy+6xy+4{{y}^{2}}=9{{x}^{2}}+12xy+4{{y}^{2}}\]
Solve: \[(4{{x}^{2}}+5)(4{{x}^{2}}+5)\]
(a) \[16{{x}^{4}}+25+40{{x}^{2}}\]
(b) \[16{{x}^{4}}+28+30{{x}^{2}}\]
(c) \[16{{x}^{4}}+30+20{{x}^{2}}\]
(d) \[16{{x}^{4}}+8+25{{x}^{2}}\]
(e) None of these
Answer: (a)
Explanation:
\[(4{{x}^{2}}+5)(4{{x}^{2}}+5)={{(4{{x}^{2}}+5)}^{2}}\]
\[{{(4{{x}^{2}})}^{2}}={{5}^{2}}+2(4{{x}^{2}})\times 5\] [Using\[~{{(\text{a}+\text{b})}^{\text{2}}}={{\text{a}}^{\text{2}}}+{{\text{b}}^{\text{2}}}+\text{2ab}\]]
\[=16{{x}^{4}}+25+40{{x}^{2}}\]
Multiplication of both the expressions is as same as option (a).
\[(4x-7y)(4x-7y)\] equal to:
(a) \[16{{x}^{2}}+56xy+49{{y}^{2}}\]
(b) \[16{{x}^{2}}-8xy+49{{y}^{2}}\]
(c) \[16{{x}^{2}}-56xy-49{{y}^{2}}\]
(d)\[16{{x}^{2}}-56xy+49{{y}^{2}}\]
(e) None of these
Answer: (d)
Explanation:
\[(4x-7y)(4x-7y)=(4{{x}^{2}})-2.4x.7y+{{(7y)}^{2}}=\]\[16{{x}^{2}}=56xy+49{{y}^{2}}\]
Solve the expression: \[\left( x-\frac{3}{x} \right)\left( x-\frac{3}{x} \right)=\]
(a) \[{{x}^{2}}+\frac{9}{{{x}^{2}}}-18\]
(b) \[{{x}^{3}}+\frac{9}{{{x}^{2}}}-6\]
(c) \[{{x}^{2}}+\frac{9}{{{x}^{2}}}-6\]
(d) \[{{x}^{2}}+\frac{1}{{{x}^{2}}}-6\]
(e) None of these
Answer: (c)
Explanation:
\[\left( x-\frac{3}{x} \right)\left( x-\frac{3}{x} \right)={{x}^{2}}{{\left( \frac{3}{x} \right)}^{2}}-2\times x\times \frac{3}{x}={{x}^{2}}+\frac{9}{{{x}^{2}}}-6\]
Simplify: \[(4x+5y)(4x-5y)\]
(a) \[16{{x}^{2}}-25xy\]
(b) \[16{{x}^{2}}-5{{y}^{2}}\]
(c) \[16{{x}^{2}}-25{{y}^{2}}\]
(d) \[16{{x}^{2}}-{{y}^{2}}\]
(e) None of these
Answer: (c)
Explanation:
\[(4x+5y)(4x-5y)={{(4x)}^{2}}-{{(-5y)}^{2}}=16{{x}^{2}}-25{{y}^{2}}\]
Simplify: \[(2x+3y)(2x-3y)\]
(a) \[{{x}^{2}}-3{{y}^{2}}\]
(b) \[2{{x}^{2}}-3{{y}^{2}}\]
(c) \[4{{x}^{2}}-9{{y}^{2}}\]
(d) \[{{x}^{2}}-9{{y}^{2}}\]
(e) None of these
Answer: (c)
Explanation:
\[(2x+3y)(2x-3y)={{(2x)}^{2}}-{{(3y)}^{2}}=4{{x}^{2}}-9{{y}^{2}}\]
Properties of Division on the Set Q
Closure Property for Division on Q
For any two rational numbers\[\frac{a}{b}\]and\[\frac{c}{d}\],
\[\left[ \left( \frac{a}{b} \right)\div \left( \frac{c}{d} \right) \right]\]is also a rational number. This is called the Closure Property of Division. Look at the following example:
\[-\frac{1}{8}\div -\frac{4}{3}=-\frac{1}{8}\times -\frac{3}{4}=\frac{3}{32}\in Q;\]
It is true for number Q. So, we can say that division of two rational number is also a rational number.
Division is not Commutative
For any two rational numbers\[\frac{a}{b}\] and \[\frac{c}{d}\],
we have \[\frac{a}{b}\div \frac{c}{d}\ne \frac{c}{d}\div \frac{a}{b}\]
Look at the following example:
\[\frac{11}{4}\div -\frac{1}{9}\ne -\frac{1}{9}\div \frac{11}{4}\]
Therefore, we can say that division is not commutative.
Division is not associative
For any three rational numbers \[\frac{a}{b},\frac{c}{d}\] and \[\frac{e}{f}\in Q\],
we have \[\left( \frac{a}{b}\div \frac{c}{d} \right)\div \frac{e}{f}\ne \frac{a}{b}\div \left( \frac{c}{d}\div \frac{e}{f} \right)\]
Look at the following example:
\[\left( \frac{5}{4}\div -\frac{1}{6} \right)\div \frac{1}{3}\ne \frac{5}{4}\div \left( -\frac{1}{6}\div \frac{1}{3} \right)\]
From the above example, we can say that division is not associative.
Decimal Representation of a Rational Number
There are two forms of decimal representation of the rational numbers. They are terminating or no terminating.
Thus, we can represent every rational number as either terminating or no terminating decimals. The non-terminating decimals may be repeating or non-repeating. For example:
0.25, 0.625, etc. are terminating decimals and 0.3333...... is non-terminating but repeating decimal whereas 0.01001000100001.........is a non-terminating and non-repeating decimal.
Thomas's monthly salary is Rs. 78,000. He spends 20% on fooding and 10% on house rent. From the remaining he spends 30% on his only son's education and donates 10% of the rest to charity. His monthly saving more... 
Properties of Multiplication
Closure Property of Multiplication
For any two rational numbers \[\frac{a}{b}\] and \[\frac{c}{d}\] we have,
\[\frac{a}{b}\times \frac{c}{d}=\frac{ac}{db}\],
which is again a rational number. Hence, multiplication of two rational number is again a rational. Therefore, multiplication is closed w.r.t. multiplication. Look at the following examples:
\[\frac{1}{3}\times \frac{7}{8}=\frac{7}{24}\in Q;\]
\[\frac{-7}{3}\times \frac{2}{9}=-\frac{14}{27}\in Q;\]
Thus we can say that multiplication of two rational numbers is closed w.r.t. multiplication.
Commutative Property of Multiplication
For any two rational numbers \[\frac{a}{b}\] and \[\frac{c}{d}\],
\[\frac{a}{b}\times \frac{c}{d}=\frac{c}{d}\times \frac{a}{b}\]
Thus multiplication of two rational number is commutative. Look at the following example:
\[-\frac{2}{5}\times \frac{1}{4}=\frac{1}{4}\times -\frac{2}{5}=-\frac{1}{10};\]
\[-\frac{11}{9}\times \left( -\frac{5}{6} \right)=-\frac{5}{6}\times \left( -\frac{11}{9} \right)=\frac{55}{54}\]
Associative Property of Multiplication
For any three rational numbers \[\frac{a}{b},\frac{c}{d}\] and \[\frac{e}{f}\in Q\].
\[\Rightarrow \]\[\frac{a}{b}\times \left( \frac{c}{d}\times \frac{e}{f} \right)=\left( \frac{a}{b}\times \frac{c}{d} \right)\times \frac{e}{f}\]
This is called the Associative Property of Multiplication. Look at the following example:
\[\left( \frac{4}{5}\times -\frac{2}{7} \right)\times \frac{3}{2}=\frac{4}{5}\times \left( -\frac{2}{7}\times \frac{3}{2} \right)=-\frac{12}{35}\]
Multiplicative Identity
For every rational number \[\frac{a}{b},\]
\[\Rightarrow \]\[\frac{a}{b}\times 1=1\times \frac{a}{b}=\frac{a}{b}\]
Thus 1 is the Multiplicative Identity because if we multiply any rational number by 1, the result is the same. Look at the following example:
\[-\frac{98}{75}\times 1=1\times -\frac{38}{75}=-\frac{98}{75}\]
Zero Property of Multiplication
If we multiply any rational number with 0 the result is again 0. This property is called as the zero property of the rational number. For any rational number\[\frac{a}{b}\],
\[\Rightarrow \] \[\frac{a}{b}\times 0=0\times \frac{a}{b}=0\]
Look at the following example:
\[-\frac{23}{4}\times 0=0\times \frac{a}{b}=0\]
Remember for any two rational numbers\[\frac{a}{b}\] and \[\frac{c}{d}\], if\[\frac{a}{b}\times \frac{c}{d}=0\] then either a = 0 or \[c=0\,or\,a=c=0\] 
Introduction
In mathematics we frequently come across different types of numbers. The different types of the numbers are natural numbers, whole numbers, rational numbers, integers, irrational numbers, and real numbers.
The natural number starts form 1 and goes to infinity. Thus we can say that all the positive real numbers starting from 1 are called natural numbers. The whole numbers are all positive real numbers starting from zero.
The rational numbers are the numbers which can be written in the form of \[\frac{p}{q}\], where \[q\ne 0\].
Properties of Rational Numbers
Closure Property
When we add two rational numbers the result is also a rational number.
\[\frac{5}{6}+\frac{8}{9}=\frac{31}{18}\]
The difference between two rational numbers is also a rational number.
\[\frac{5}{6}-\frac{8}{9}=\frac{-1}{18}\]
Multiplication and division of two rational numbers are not necessarily a rational number.
\[\frac{16}{5}\times \frac{25}{4}=20,\frac{12}{5}\times \frac{4}{25}=\frac{48}{125}\]
\[\left( \frac{2}{3} \right)+\left( \frac{1}{6} \right)=\left( \frac{5}{6} \right)\in Q;\]
\[\left( \frac{-1}{8} \right)+\left( \frac{-1}{7} \right)=-\left( \frac{1}{5}+\frac{1}{7} \right)=\frac{-15}{56}\in Q;\]
\[\left( \frac{1}{2} \right)+\left( \frac{-1}{8} \right)=\left( \frac{1}{2}-\frac{1}{8} \right)=\frac{3}{8}\in Q;\]
For any two numbers \[\left( \frac{a}{b} and\,\frac{c}{d} \right)\in Q\],
\[\Rightarrow \] \[\left( \frac{a}{b}+\frac{c}{d} \right)\in Q\] is also a rational number.
This is called the closure property of addition on the set Q.
Commutative Property
The two rational numbers can be added in any order, the result in both cases will be same. Hence we can say that addition of two rational numbers is commutative.
\[\frac{2}{3}+\frac{5}{6}=\frac{5}{6}+\frac{2}{3}=\frac{9}{6},\frac{9}{3}\times \frac{6}{3}=\frac{6}{3}\times \frac{9}{3}=6\]
For any two rational numbers \[\frac{a}{b}\] and \[\frac{c}{d}\in Q\],
\[\Rightarrow \]\[\frac{a}{b}+\frac{c}{d}=\frac{c}{d}+\frac{a}{b}\in Q\]
This is called the commutative property of addition on the set Q.
\[\left( \frac{7}{12} \right)+\left( \frac{-1}{9} \right)=\left( \frac{-1}{9} \right)+\left( \frac{7}{12} \right)\]
\[\left( \frac{-1}{136} \right)+\left( \frac{5}{96} \right)=\left( \frac{5}{96} \right)+\left( \frac{-1}{136} \right)\]
Associative Property
The addition of rational numbers is associative.
\[\left[ \frac{2}{3}+\frac{5}{6} \right]+\frac{3}{5}=\frac{2}{3}+\left[ \frac{5}{6}+\frac{3}{5} \right]=\frac{21}{10},\]\[\left[ \frac{2}{3}\times \frac{5}{6} \right]\times \frac{3}{5}=\frac{2}{3}\times \left[ \frac{5}{6}\times \frac{3}{5} \right]=\frac{1}{3}\]
For any three rational numbers \[\frac{a}{b},\frac{c}{d}\] and \[\frac{e}{f}\in Q\],
\[\Rightarrow \]\[\frac{a}{b}+\left( \frac{c}{d}+\frac{e}{f} \right)=\left( \frac{a}{b}+\frac{c}{d} \right)+\frac{e}{f}\in Q\]
This is called the associative property of addition.
Distributive of Multiplication over Addition
According to this property for any three rational numbers x, y, and z we can say that,
\[x(y+z)=xy+xz;xz(x+y)z=xz+yz\in Q\]
\[\frac{17}{18}\left( \frac{5}{6}+\frac{2}{9} \right)=\left( \frac{17}{18}\times \frac{5}{6} \right)+\left( \frac{17}{18}\times \frac{2}{9} \right),\left( \frac{17}{18}\times \frac{5}{6} \right)\frac{2}{9}=\]\[\left( \frac{17}{18}\times \frac{2}{9} \right)+\left( \frac{5}{6}\times \frac{2}{9} \right)\]
Additive Identity
The additive identity is that number which when added to any rational number gives more... 
Reading E-mail
E-mail (Electronic mail) is a digital correspondence that provides the facility to send and receive text messages, picture files and any other file to and from anyone with an e-mail address. E-mail is fast, easy and inexpensive. Email is a formal conversation. It should be point to point and well written. In current market there are many service providers who provide free e-mail services on the Internet, such as www.gmail.com, www.yahoo.com, www.hotmail.com and www.msn.com. The first part of the address is a user name. The second part or domain name defines the Internet provider where the mail is sent. The two parts are separated by an @ sign (pronounced as "at the rate"). The domain name is '' followed by an extension that indicates the type of organization to which the network belongs.
To read new e-mail:
To print e-mail:
To save an e-mail to disk:
Network topology refers to the way a computer network is laid out, either physically or logically. Which of the following are the types of Network topology?
(A) Star
(B) Bus
(C) Ring
(D) All of these
(E) None of these
Answer: (d)
Explanation
Correct Option:
(D) Network topology, such as star, bus and ring refers to the way a computer network is laid out. Incorrect Option: Rests of the options are invalid.
In..............topology all nodes are connected together to the parallel cable.
(A) Star
(B) Bus
(C) Ring
(D) All of these
(E) None of these
Answer: (b)
Explanation
Correct Option:
(B) In bus topology all nodes are connected together to the parallel cable by drop lines and taps/T-connectors.
Incorrect Options:
(A) In star topology each node is directly connected with hub.
(C) In ring topology all computers are connected in a ring shape.
Browser allows you to open website. Which of the following browsers allow saving your favorite sites?
(A) Internet Explorer 6
(B) Internet Explorer 7
(C) Mozila Firefox
(D) more... 
Saving your Favorite Sites
All the Browsers, such as Internet Explorer and Mozila Firefox provide the facility to save your favorite website.
To save your favorite sites through Internet Explore you need to perform the following steps:
Network Topologies
Network topology refers to the way a computer network is laid out, either physically or logically. It defines the way in which network devices are organized geometrically.
The following are the types of topologies:
1.Mesh topology
2. Star topology
3. Bus topology
4. Ring topology
Mesh Topology
In mesh topology each node has a dedicated point-to-point link to every other device. The main advantage of a mesh topology is reliability. It provides more security because if any node fails, it does not affect the entire network. The disadvantage of mesh topology is that it is very costly because mesh is related to the amount of cabling and the number of I/O ports required. It is also very complex structure to design. The following figure shows a network that is based on mesh topology:
Star Topology
In this topology each node is directly connected with hub. Thus the devices in the network are not directly linked to each other. The main advantage of star topology is that if any node fails, it does not affect the entire network. It's also less expensive than mesh, and hence easy to configure and maintain. The following figure shows a network that is based on star topology:
Bus Topology
In this topology all nodes are connected together to the parallel cable by drop lines and taps/T-connectors. The cable is arranged in a straight line and each node connects to the cable with a T-connector.
The advantages of bus topology are the following:
Ring Topology
In this topology all computers are connected in a ring shape. In this topology each node has an input and an output connection. It contains wiring that allows information to pass from one device to another in a circle or ring. The main advantages of ring topology, it is easy to install and provides good signal quality. The main disadvantages of ring topology: II one node fails or the ring is broken, then the network is down. ? The following figure shows a network that is based on ring topology:
Intranet
Network connections between two offices and branches are the good example of Intranet. It plays an important role in today's life for those who are sharing data from one of the main branches to its sub branch. It is also used in playing game on LAN in which all the systems are connected to one of the system which is main among them. This feature is basically used in LAN (Local Area Network).
The set of protocols enables two systems to communicate and transfer data on the network. Which one of the following protocols is used in Novell NetWare networks?
(A) AppleTalk
(B) NW Link
(C) NetBEUI
(D) All of these
(E) None of these
Answer: (b)
Explanation
Correct Option:
(B) NW Link is used in Novell NetWare networks.
Incorrect Option:
(A) Apple Talk is used to communicate with Macintosh computers on the network. Rests of the options are invalid.
The NW Link protocol is faster than TCP/IP but slower than the NetBEUI. Which one of the following protocols is used to communicate with Macintosh computers?
(A) AppleTalk
(B) NW Link
(C) NetBEUI
(D) All of these
(E) None of these
Answer: (a)
Explanation
Correct Option:
(A) Apple Talk is a used to communicate with Macintosh computers on the network. Rests of the options are invalid.
Incorrect Option:
(B) NW Link is used in Novell NetWare networks.
In old days Internet was known as ARPANET. What is the correct full form of ARPANET?
(A) Advanced Research Projects Agency Network
(B) Area Research Projects Agency Network
(C) Advanced Research Projects Area Network
(D) Advanced Research Network Protocol
(E) None of these
Answer: (a)
Explanation
Correct Option:
(A) In old days Internet was known as Advanced Research Projects Agency Network (ARPANET), was started online in 1969.
Incorrect Option:
Rests of the options are invalid. 
Internet
The Internet goes back to early 1960's. J.C.R. Licklider of MIT (Massachusetts Institute of Technology), first proposed a global network of computers in 1962 and moved forward to the DARPA (Defense Advanced Research Projects Agency) in late 1962 to head the work for its development. In old days Internet was known as ARPANET (Advanced Research Projects Agency Network). It was started online in 1969 under a contract led by the renamed ARPA (Advanced Research Projects Agency), which initially connected four major computers at universities in the southwestern US UCLA ( University of California, Los Angeles), Stanford Research Institute, UCSB ( University of California, Santa Barbara) and the University of Utah). Internet is the best example of WAN (Wide Area Network). A WAN is one of the computer networks which was established on a large geographical area. While connecting the Internet with your computer you need modem. Basically modem is one of the most important parts for using Internet services. This works as a key because it receives the packet of data or signals through the service provider and thus after receiving it, it allows user to use the packet of data for surfing. Without modem surfing is unable to proceed.
The following are the advantages of the Internet:
Email
Using Internet you can send any information, greeting and any type of file, such as picture to any location of the world.
Ticket
booking Using Internet you can book your railway ticket, air ticket and cinema ticket. You do not need to go anywhere just connect your computer with the Internet. Chatting Using Internet you can chat with your friend in live environment. There are various chatting tools available in market, such as Google Talk.
Banking
Using Internet you can check the status of your bank account. You can also transfer money from one account to other account.
Searching
Is one of the important features through which we are able to grasp knowledge of any thing through any of the search engine? GOOGLE is one of the common search engines through which we can capture any information regarding any topic, organization and many other things can be learnt through this. 
Network Protocol
In the world of Information Technology, some set of rules are defined and these are known as protocols. Basically the set of protocols enables two systems to communicate and transfer data on the network. Any electronic device which is having a capability of sending and receiving data is a system. Protocols are generally implemented by software, hardware or a combination of the two.
The information which identifies the protocols are the following:
Network Protocol Description
Net BIOS Enhanced User Interface (NetBEUI) is the fastest protocol and does not require any configuration to implement. NetBEUI is simple to use. AppleTalk Is a routable protocol and is mainly used to communicate with Macintosh computers on the network.
Transmission Control Protocol/Internet Protocol (TCP/IP) is also a routable protocol. TCP/IP is supported by most of the OS. It is more reliable than other protocols. NWLink is used in Novell NetWare networks. This protocol is easy to install and also a routable protocol. The NWLink protocol is faster than TCP/IP but slower than the NetBEUI. 
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