Aptitude trick

 Important Formulas of Number System

Formulas of Number Series
1. 1 + 2 + 3 + 4 + 5 + … + n = n(n + 1)/2
2. (12 + 22 + 32 + ….. + n2) = n ( n + 1 ) (2n + 1) / 6
3. (13 + 23 + 33 + ….. + n3) = (n(n + 1)/ 2)2
4. Sum of first n odd numbers = n2
5. Sum of first n even numbers = n (n + 1)

Mathematical Formulas

1. (a + b)(a – b) = (a2 – b2)
2. (a + b)2 = (a2 + b2 + 2ab)
3. (a – b)2 = (a2 + b2 – 2ab)
4. (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
5. (a3 + b3) = (a + b)(a2 – ab + b2)
6. (a3 – b3) = (a – b)(a2 + ab + b2)
7. (a3 + b3 + c3 – 3abc) = (a + b + c)(a2 + b2 + c2 – ab – bc – ac)
8. When a + b + c = 0, then a3+ b3 + c3 = 3abc
9. (a + b)n = an + (nC1)an-1b + (nC2)an-2b2 + … + (nCn-1)abn-1 + bn

Shortcuts for number divisibility check

1. A number is divisible by 2, if its unit’s digit is any of 0, 2, 4, 6, 8.
2. A number is divisible by 3, if the sum of its digits is divisible by 3.
3. A number is divisible by 4, if the number formed by the last two digits is divisible by 4.
4. A number is divisible by 5, if its unit’s digit is either 0 or 5.
5. A number is divisible by 6, if it is divisible by both 2 and 3.
6. A number is divisible by 8, if the number formed by the last three digits of the given number is divisible by 8.
7. A number is divisible by 9, if the sum of its digits is divisible by 9.
8. A number is divisible by 10, if it ends with 0.
9. A number is divisible by 11, if the difference of the sum of its digits at odd places and the sum of its digits at even places, is either 0 or a number divisible by 11.
10. A number is divisible by 12, if it is divisible by both 4 and 3.
11. A number is divisible by 14, if it is divisible by 2 as well as 7.
12. Two numbers are said to be co-primes if their H.C.F. is 1. To find if a number, say y is divisible by x, find m and n such that m * n = x and m and n are co-prime numbers. If y is divisible by both m and n then it is divisible by x.

Shortcuts for ‘recurring decimal to fraction’ conversion

1. For recurring decimals of format ‘0.abababab…’ (ab repeats), equivalent fraction will be “repeating group (here ab)”/”as many 9’s as the number of digits in repeating group”
2. For recurring decimals of format ‘0.abbbbb…’ (b repeats), equivalent fraction will be (entire decimal group – non-repeating decimal group)/(as many 9’s as the number of repeating digits in the decimal part with as many 0’s as the number of non-repeating digits in the decimal part)
Frequently Asked Questions on Number System
• Given a number x, you will be asked to find the largest n digit number divisible by x.
• You will be given with a set of numbers (n1, n2, n3…) and asked to find how many of those numbers are divisible by a specified number x.
• Given a number series, find the sum of n terms, find nth term etc.
• Find product of two numbers when their sum/difference and sum of their squares is given.
• Find the number when divisibility of its digits with certain numbers is given.
• Find the smallest n digit number divisible by x.
• Which of the given numbers are prime numbers.
• Number x when divided by y gives remainder r, what will be the remainder when x2 is divided by y.
• Given relationship between the digits of number, find the number.

. BASIC FORMULAE:
1. Distance =Average speed × time taken
2. Average speed = Distance travelled/time taken
3. Time taken = Distance travelled/Average Speed
4. X km/hour = x*5/18 meter per second
5. Y meter/second = y×18/5 kilometer per hour.

• Find result of operations (additions, subtractions, multiplications, divisions etc) on given integers. These integers can be large and the question may look difficult and time consuming. But mostly the question will map onto one of the known algebraic equa

Database Management System

 MODULE 1

DBMS Architecture 

The architecture of DBMS depends on the computer system on which it runs. For example, in a client-server DBMS architecture, the database systems at server machine can run several requests made by client machine. We will understand this communication with the help of diagrams.

Types of DBMS Architecture

There are three types of DBMS architecture:

1. Single tier architecture

2. Two tier architecture

3. Three tier architecture

1. Single tier architecture

In this type of architecture, the database is readily available on the client machine, any request made by client doesn’t require a network connection to perform the action on the database.

For example, lets say you want to fetch the records of employee from the database and the database is available on your computer system, so the request to fetch employee details will be done by your computer and the records will be fetched from the database by your computer as well. This type of system is generally referred as local database system.

2. Two tier architecture

DBMS Architecture - 2-tier

In two-tier architecture, the Database system is present at the server machine and the DBMS application is present at the client machine, these two machines are connected with each other through a reliable network as shown in the above diagram.

Whenever client machine makes a request to access the database present at server using a query language like sql, the server perform the request on the database and returns the result back to the client. The application connection interface such as JDBC, ODBC are used for the interaction between server and client.

3. Three tier architecture

DBMS Architecture - 3 tier

In three-tier architecture, another layer is present between the client machine and server machine. In this architecture, the client application doesn’t communicate directly with the database systems present at the server machine, rather the client application communicates with server application and the server application internally communicates with the database system present at the server.

DBMS Three Level Architecture Diagram

This architecture has three levels:
1. External level
2. Conceptual level
3. Internal level

1. External level

It is also called view level. The reason this level is called “view” is because several users can view their desired data from this level which is internally fetched from database with the help of conceptual and internal level mapping.

The user doesn’t need to know the database schema details such as data structure, table definition etc. user is only concerned about data which is what returned back to the view level after it has been fetched from database (present at the internal level).

External level is the “top level” of the Three Level DBMS Architecture.

2. Conceptual level

It is also called logical level. The whole design of the database such as relationship among data, schema of data etc. are described in this level.

Database constraints and security are also implemented in this level of architecture. This level is maintained by DBA (database administrator).

3. Internal level

This level is also known as physical level. This level describes how the data is actually stored in the storage devices. This level is also responsible for allocating space to the data. This is the lowest level of the architecture.

Data Abstraction 

Database systems are made-up of complex data structures. To ease the user interaction with database, the developers hide internal irrelevant details from users. This process of hiding irrelevant details from user is called data abstraction.

We have three levels of abstraction:
Physical level: This is the lowest level of data abstraction. It describes how data is actually stored in database. You can get the complex data structure details at this level.

Logical level: This is the middle level of 3-level data abstraction architecture. It describes what data is stored in database.

View level: Highest level of data abstraction. This level describes the user interaction with database system.

Example: Let’s say we are storing customer information in a customer table. At physical level these records can be described as blocks of storage (bytes, gigabytes, terabytes etc.) in memory. These details are often hidden from the programmers.

At the logical level these records can be described as fields and attributes along with their data types, their relationship among each other can be logically implemented. The programmers generally work at this level because they are aware of such things about database systems.

At view level, user just interact with system with the help of GUI and enter the details at the screen, they are not aware of how the data is stored and what data is stored; such details are hidden from them.

DBMS Schema

Definition of schema: Design of a database is called the schema. Schema is of three types: Physical schema, logical schema and view schema.

For example: In the following diagram, we have a schema that shows the relationship between three tables: Course, Student and Section. The diagram only shows the design of the database, it doesn’t show the data present in those tables. Schema is only a structural view(design) of a database as shown in the diagram below.

The design of a database at physical level is called physical schema, how the data stored in blocks of storage is described at this level.

Design of database at logical level is called logical schema, programmers and database administrators work at this level, at this level data can be described as certain types of data records gets stored in data structures, however the internal details such as implementation of data structure is hidden at this level (available at physical level).

Design of database at view level is called view schema. This generally describes end user interaction with database systems.

To learn more about these schemas, refer 3 level data abstraction architecture.

DBMS Instance

Definition of instance: The data stored in database at a particular moment of time is called instance of database. Database schema defines the variable declarations in tables that belong to a particular database; the value of these variables at a moment of time is called the instance of that database.

For example, lets say we have a single table student in the database, today the table has 100 records, so today the instance of the database has 100 records. Lets say we are going to add another 100 records in this table by tomorrow so the instance of database tomorrow will have 200 records in table. In short, at a particular moment the data stored in database is called the instance, that changes over time when we add or delete data from the database.

DBMS languages

Database languages are used to read, update and store data in a database. There are several such languages that can be used for this purpose; one of them is SQL (Structured Query Language).

Types of DBMS languages:

Data Definition Language (DDL)

DDL is used for specifying the database schema. It is used for creating tables, schema, indexes, constraints etc. in database. Lets see the operations that we can perform on database using DDL:

• To create the database instance – CREATE
• To alter the structure of database – ALTER
• To drop database instances – DROP
• To delete tables in a database instance – TRUNCATE
• To rename database instances – RENAME
• To drop objects from database such as tables – DROP
• To Comment – Comment

All of these commands either defines or update the database schema that’s why they come under Data Definition language.

Data Manipulation Language (DML)

DML is used for accessing and manipulating data in a database. The following operations on database comes under DML:

• To read records from table(s) – SELECT
• To insert record(s) into the table(s) – INSERT
• Update the data in table(s) – UPDATE
• Delete all the records from the table – DELETE

Data Control language (DCL)

DCL is used for granting and revoking user access on a database –

• To grant access to user – GRANT
• To revoke access from user – REVOKE

In practical data definition language, data manipulation language and data control languages are not separate language, rather they are the parts of a single database language such as SQL.

Transaction Control Language(TCL)

The changes in the database that we made using DML commands are either performed or rollbacked using TCL.

• To persist the changes made by DML commands in database – COMMIT
• To rollback the changes made to the database – ROLLBACK

Data models in DBMS

Data Model is a logical structure of Database. It describes the design of database to reflect entities, attributes, relationship among data, constrains etc.

Types of Data Models

There are several types of data models in DBMS. We will cover them in detail in separate articles(Links to those separate tutorials are already provided below). In this guide, we will just see a basic overview of types of models.

Object based logical Models – Describe data at the conceptual and view levels.

1. E-R Model
2. Object oriented Model

Record based logical Models – Like Object based model, they also describe data at the conceptual and view levels. These models specify logical structure of database with records, fields and attributes.

1. Relational Model
2. Hierarchical Model
3. Network Model – Network Model is same as hierarchical model except that it has graph-like structure rather than a tree-based structure. Unlike hierarchical model, this model allows each record to have more than one parent record.

Physical Data Models – These models describe data at the lowest level of abstraction.

Entity Relationship Diagram – ER Diagram 

An Entity–relationship model (ER model) describes the structure of a database with the help of a diagram, which is known as Entity Relationship Diagram (ER Diagram). An ER model is a design or blueprint of a database that can later be implemented as a database. The main components of E-R model are: entity set and relationship set.

What is an Entity Relationship Diagram (ER Diagram)?

An ER diagram shows the relationship among entity sets. An entity set is a group of similar entities and these entities can have attributes. In terms of DBMS, an entity is a table or attribute of a table in database, so by showing relationship among tables and their attributes, ER diagram shows the complete logical structure of a database. Lets have a look at a simple ER diagram to understand this concept.

A simple ER Diagram:

In the following diagram we have two entities Student and College and their relationship. The relationship between Student and College is many to one as a college can have many students however a student cannot study in multiple colleges at the same time. Student entity has attributes such as Stu_Id, Stu_Name & Stu_Addr and College entity has attributes such as Col_ID & Col_Name.

Here are the geometric shapes and their meaning in an E-R Diagram. We will discuss these terms in detail in the next section(Components of a ER Diagram) of this guide so don’t worry too much about these terms now, just go through them once.

Rectangle: Represents Entity sets.
Ellipses: Attributes
Diamonds: Relationship Set
Lines: They link attributes to Entity Sets and Entity sets to Relationship Set
Double Ellipses: Multivalued Attributes
Dashed Ellipses: Derived Attributes
Double Rectangles: Weak Entity Sets
Double Lines: Total participation of an entity in a relationship set

Components of a ER Diagram

As shown in the above diagram, an ER diagram has three main components:
1. Entity
2. Attribute
3. Relationship

1. Entity

An entity is an object or component of data. An entity is represented as rectangle in an ER diagram.
For example: In the following ER diagram we have two entities Student and College and these two entities have many to one relationship as many students study in a single college. We will read more about relationships later, for now focus on entities.

Weak Entity:
An entity that cannot be uniquely identified by its own attributes and relies on the relationship with other entity is called weak entity. The weak entity is represented by a double rectangle. For example – a bank account cannot be uniquely identified without knowing the bank to which the account belongs, so bank account is a weak entity.

2. Attribute

An attribute describes the property of an entity. An attribute is represented as Oval in an ER diagram. There are four types of attributes:

1. Key attribute
2. Composite attribute
3. Multivalued attribute
4. Derived attribute

1. Key attribute:

A key attribute can uniquely identify an entity from an entity set. For example, student roll number can uniquely identify a student from a set of students. Key attribute is represented by oval same as other attributes however the text of key attribute is underlined.

2. Composite attribute:

An attribute that is a combination of other attributes is known as composite attribute. For example, In student entity, the student address is a composite attribute as an address is composed of other attributes such as pin code, state, country.

3. Multivalued attribute:

An attribute that can hold multiple values is known as multivalued attribute. It is represented with double ovals in an ER Diagram. For example – A person can have more than one phone numbers so the phone number attribute is multivalued.

4. Derived attribute:

A derived attribute is one whose value is dynamic and derived from another attribute. It is represented by dashed oval in an ER Diagram. For example – Person age is a derived attribute as it changes over time and can be derived from another attribute (Date of birth).

E-R diagram with multivalued and derived attributes:

3. Relationship

A relationship is represented by diamond shape in ER diagram, it shows the relationship among entities. There are four types of relationships:
1. One to One
2. One to Many
3. Many to One
4. Many to Many

1. One to One Relationship

When a single instance of an entity is associated with a single instance of another entity then it is called one to one relationship. For example, a person has only one passport and a passport is given to one person.

2. One to Many Relationship

When a single instance of an entity is associated with more than one instances of another entity then it is called one to many relationship. For example – a customer can place many orders but a order cannot be placed by many customers.

3. Many to One Relationship

When more than one instances of an entity is associated with a single instance of another entity then it is called many to one relationship. For example – many students can study in a single college but a student cannot study in many colleges at the same time.

4. Many to Many Relationship

When more than one instances of an entity is associated with more than one instances of another entity then it is called many to many relationship. For example, a can be assigned to many projects and a project can be assigned to many students.

Total Participation of an Entity set

A Total participation of an entity set represents that each entity in entity set must have at least one relationship in a relationship set. For example: In the below diagram each college must have at-least one associated Student.

FLAT

 Context-Free Grammar (CFG) 

CFG stands for context-free grammar. It is is a formal grammar which is used to generate all possible patterns of strings in a given formal language. Context-free grammar G can be defined by four tuples as: 

1. G = (V, T, P, S) 

Where, 

G is the grammar, which consists of a set of the production rule. It is used to generate the string of a language. 

T is the final set of a terminal symbol. It is denoted by lower case letters. 

V is the final set of a non-terminal symbol. It is denoted by capital letters. 

P is a set of production rules, which is used for replacing non-terminals symbols(on the left side of the production) in a string with other terminal or non-terminal symbols(on the right side of the production).

 S is the start symbol which is used to derive the string. We can derive the string by repeatedly replacing a non-terminal by the right-hand side of the production until all non-terminal have been replaced by terminal symbols. 

Example 1: Construct the CFG for the language having any number of a's over the set ∑= {a}. Solution: As we know the regular expression for the above language is 1. r.e. = a*

Production rule for the Regular expression is as follows: 

1. S → aS rule 1 

2. S → ε rule 2 

Now if we want to derive a string "aaaaaa", we can start with start symbols. 

1. S 

2. aS 

3. aaS rule 1 

4. aaaS rule 1 

5. aaaaS rule 1 

6. aaaaaS rule 1 

7. aaaaaaS rule 1 

8. aaaaaaε rule 2 

9. aaaaaa 

The r.e. = a* can generate a set of string {ε, a, aa, aaa,.....}. We can have a null string because S is a start symbol and rule 2 gives S → ε

linux command

 

Linux Directory Commands

1. pwd Command

The pwd command is used to display the location of the current working directory.

Syntax:

1. pwd  

2. mkdir Command

The mkdir command is used to create a new directory under any directory.

Syntax:

1. mkdir <directory name> 

3. rmdir Command

The rmdir command is used to delete a directory.

Syntax:

1. rmdir <directory name>  

4. ls Command

The ls command is used to display a list of content of a directory.

Syntax:

1. ls

5. cd Command

The cd command is used to change the current directory.

Syntax:

1. cd <directory name>  

Linux File commands

6. touch Command

The touch command is used to create empty files. We can create multiple empty files by executing it once.

Syntax:

1. touch <file name>  
2. touch <file1>  <file2> ....  

7. cat Command

The cat command is a multi-purpose utility in the Linux system. It can be used to create a file, display content of the file, copy the content of one file to another file, and more.

Syntax:

1. cat [OPTION]... [FILE]..  

To create a file, execute it as follows:

1. cat > <file name>  
2. // Enter file content  

Press "CTRL+ D" keys to save the file. To display the content of the file, execute it as follows:

1. cat <file name>  

8. rm Command

The rm command is used to remove a file.

Syntax:

rm <file name>

9. cp Command

The cp command is used to copy a file or directory.

Syntax:

To copy in the same directory:

1. cp <existing file name> <new file name>  

To copy in a different directory:

Output:

10. mv Command

The mv command is used to move a file or a directory form one location to another location.

Syntax:

1. mv <file name> <directory path>  

11. rename Command

The rename command is used to rename files. It is useful for renaming a large group of files.

Syntax:

1. rename 's/old-name/new-name/' files  

For example, to convert all the text files into pdf files, execute the below command:

1. rename 's/\.txt$/\.pdf/' *.txt  

Linux File Content Commands

12. head Command

The head command is used to display the content of a file. It displays the first 10 lines of a file.

Syntax:

1. head <file name>  

13. tail Command

The tail command is similar to the head command. The difference between both commands is that it displays the last ten lines of the file content. It is useful for reading the error message.

Syntax:

1. tail <file name>  

14. tac Command

The tac command is the reverse of cat command, as its name specified. It displays the file content in reverse order (from the last line).

Syntax:

1. tac <file name>  

15. more command

The more command is quite similar to the cat command, as it is used to display the file content in the same way that the cat command does. The only difference between both commands is that, in case of larger files, the more command displays screenful output at a time.

In more command, the following keys are used to scroll the page:

ENTER key: To scroll down page by line.

Space bar: To move to the next page.

b key: To move to the previous page.

/ key: To search the string.

Syntax:

1. more <file name>  

16. less Command

The less command is similar to the more command. It also includes some extra features such as 'adjustment in width and height of the terminal.' Comparatively, the more command cuts the output in the width of the terminal.

Syntax:

1. less <file name>  

Linux User Commands

17. su Command

The su command provides administrative access to another user. In other words, it allows access of the Linux shell to another user.

Syntax:

1. su <user name>  

18. id Command

The id command is used to display the user ID (UID) and group ID (GID).

Syntax:

1. id  

19. useradd Command

The useradd command is used to add or remove a user on a Linux server.

Syntax:

1. useradd  username  

20. passwd Command

The passwd command is used to create and change the password for a user.

Syntax:

1. passwd <username>  

21. groupadd Command

The groupadd command is used to create a user group.

Syntax:

1. groupadd <group name>  

Linux Filter Commands

22. cat Command

The cat command is also used as a filter. To filter a file, it is used inside pipes.

Syntax:

1. cat <fileName> | cat or tac | cat or tac |. . .   

23. cut Command

The cut command is used to select a specific column of a file. The '-d' option is used as a delimiter, and it can be a space (' '), a slash (/), a hyphen (-), or anything else. And, the '-f' option is used to specify a column number.

Syntax:

1. cut -d(delimiter) -f(columnNumber) <fileName>  

24. grep Command

The grep is the most powerful and used filter in a Linux system. The 'grep' stands for "global regular expression print." It is useful for searching the content from a file. Generally, it is used with the pipe.

Syntax:

1. command | grep <searchWord>  

25. comm Command

The 'comm' command is used to compare two files or streams. By default, it displays three columns, first displays non-matching items of the first file, second indicates the non-matching item of the second file, and the third column displays the matching items of both files.

Syntax:

1. comm <file1> <file2>  

26. sed command

The sed command is also known as stream editor. It is used to edit files using a regular expression. It does not permanently edit files; instead, the edited content remains only on display. It does not affect the actual file.

Syntax:

1. command | sed 's/<oldWord>/<newWord>/'  

27. tee command

The tee command is quite similar to the cat command. The only difference between both filters is that it puts standard input on standard output and also write them into a file.

Syntax:

1. cat <fileName> | tee <newFile> |  cat or tac |.....  

28. tr Command

The tr command is used to translate the file content like from lower case to upper case.

Syntax:

1. command | tr <'old'> <'new'> 

29. uniq Command

The uniq command is used to form a sorted list in which every word will occur only once.

Syntax:

1. command <fileName> | uniq  

30. wc Command

The wc command is used to count the lines, words, and characters in a file.

Syntax:

1. wc <file name>  

31. od Command

The od command is used to display the content of a file in different s, such as hexadecimal, octal, and ASCII characters.

Syntax:

1. od -b <fileName>      // Octal format  
2. od -t x1 <fileName>   // Hexa decimal format  
3. od -c <fileName>     // ASCII character format  

32. sort Command

The sort command is used to sort files in alphabetical order.

Syntax:

1. sort <file name>  

33. gzip Command

The gzip command is used to truncate the file size. It is a compressing tool. It replaces the original file by the compressed file having '.gz' extension.

Syntax:

1. gzip <file1> <file2> <file3>...  

34. gunzip Command

The gunzip command is used to decompress a file. It is a reverse operation of gzip command.

Syntax:

1. gunzip <file1> <file2> <file3>. .  

Linux Utility Commands

35. find Command

The find command is used to find a particular file within a directory. It also supports various options to find a file such as byname, by type, by date, and more.

The following symbols are used after the find command:

(.) : For current directory name

(/) : For root

Syntax:

1. find . -name "*.pdf"  

36. locate Command

The locate command is used to search a file by file name. It is quite similar to find command; the difference is that it is a background process. It searches the file in the database, whereas the find command searches in the file system. It is faster than the find command. To find the file with the locates command, keep your database updated.

Syntax:

1. locate <file name>

37. date Command

The date command is used to display date, time, time zone, and more.

Syntax:

1. date  

38. cal Command

The cal command is used to display the current month's calendar with the current date highlighted.

Syntax:

1. cal<  

39. sleep Command

The sleep command is used to hold the terminal by the specified amount of time. By default, it takes time in seconds.

Syntax:

1. sleep <time>  

40. time Command

The time command is used to display the time to execute a command.

Syntax:

1. time  

41. zcat Command

The zcat command is used to display the compressed files.

Syntax:

1. zcat <file name>  

42. df Command

The df command is used to display the disk space used in the file system. It displays the output as in the number of used blocks, available blocks, and the mounted directory.

Syntax:

1. df  

43. mount Command

The mount command is used to connect an external device file system to the system's file system.

Syntax:

1. mount -t type <device> <directory>  

44. exit Command

Linux exit command is used to exit from the current shell. It takes a parameter as a number and exits the shell with a return of status number.

Syntax:

1. exit  

After pressing the ENTER key, it will exit the terminal.

45. clear Command

Linux clear command is used to clear the terminal screen.

Syntax:

1. clear  

After pressing the ENTER key, it will clear the terminal screen.

Linux Networking Commands

46. ip Command

Linux ip command is an updated version of the ipconfig command. It is used to assign an IP address, initialize an interface, disable an interface.

Syntax:

1. ip a or ip addr  

47. ssh Command

Linux ssh command is used to create a remote connection through the ssh protocol.

Syntax:

1. ssh user_name@host(IP/Domain_name)</p>  

48. mail Command

The mail command is used to send emails from the command line.

Syntax:

1. mail -s "Subject" <recipient address>  

49. ping Command

The ping command is used to check the connectivity between two nodes, that is whether the server is connected. It is a short form of "Packet Internet Groper."

Syntax:

1. ping <destination>  

50. host Command

The host command is used to display the IP address for a given domain name and vice versa. It performs the DNS lookups for the DNS Query.

Syntax:

1. host <domain name> or <ip address>