Friday, 30 September 2016

The Solar System - Geography

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The Solar System - Geography for Bank PO, Clerk, SSC CHSL, CGL and other competitive exams| Universe, Galaxy, Stars, Solar System, Sun, Planets, Pluto


• The universe is commonly defined as the totality of everything that exists including all physical matter and energy, the planets, stars, galaxies and the contents of intergalactic space.

• The study of universe is known as Cosmology.
→ Literal meaning of Cosmology
cosmos (universe) + logos (science)


• A galaxy is a collection of billions of stars, dust, gas, clouds that hold together by force of gravity. Examples are the Milky Way, Andromeda galaxy etc.

• Milky Way or Akashganga is our home galaxy. It is spiral in shape.

• There are about 100 billion galaxies (1011 galaxies) in the universe, and each galaxy has, on an average, 100 billion stars (1011 stars).


• Stars are formed by clumps of dust and gas in a nebula come together due to gravity.

• Due to high temperature hydrogen converts to helium and heat and light is emitted and form stars.

• Stars emit light of their own (self luminous bodies).

• Light takes about 4.3 years to reach us from the next nearest star proxirna centauri.


• A constellation is a group of stars that forms a recognizable pattern in the night sky.

• Usually, they are named after mythological characters, people, animals and objects.

• Ursa Major or the great bear is a such constellation.
→ Big dipper or Saptarishi is a group of seven stars visible in the northern hemisphere is a part of Ursa Major.

Solar System

• The sun along with its eight planets, asteroids and comets form 'solar system'.

The Sun:
→ The Sun contains 99.85% of the solar system's mass.
→ It is in the center of the solar system.
→ It is made up of extremely hot gases particularly hydrogen.
→ The Sun has a diameter of roughly 14 lakhs kilometers which is almost 110 times the diameter of the Earth.
→ The sun weighs 2 × 1027 tonnes.
→ The sun is about 150 million km away from the earth.
→ It takes 8 minutes for light reach Earth from the Sun.
→ The surface temperature of sun is 6000° C.
→ Temperatures inside the Sun can reach 150 lakhs degrees Celsius.
→ The shining surface of the sun is called 'Photosphere' which look like a disc and acts as a source of energy.
→ The outer layer of sun's atmosphere made up of thin hot gases, is called Corona.

→ Asteroids are minor planets lying between the orbit of Mars and that of Jupiter.
→ These revolve around the sun in the same way as the planets.
→ These are made up of rock and metal.
→ 'Ceres' whose length is about 1000 km is the largest one.
→ More than 5000 asteroids have been identified.

→ Comets are small, icy objects that orbits the sun.
→ Comets have highly eccentric elliptical orbits
→ When passing close to the Sun, solid frozen part heats up and vaporizes to form a gaseous luminous coma and sometimes also a tail.

Meteors and Meteorites:
→ The meteors are the remains of comets which are scattered in the interplanetary space of the solar system.
→ On contact with the earth's atmosphere, they burn due to friction.
→ Those which completely burn out into ash are called meteors or 'shooting star.'
→ Those which do not burn completely and strike the earth in the form of rocks are called 'meteorites'.

→ Planets are opaque bodies which continuously revolve around the sun.
→ There are eight (8) planets in the solar system.
→ These planets move around the sun in fixed paths called orbits.
→ The sequence of planets according to their distance from the sun is: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune.
→ The sequence of planets according to their size is: Jupiter, Saturn, Uranus, Neptune, Earth, Venus, Mars and Mercury.

Classification of Planets:
→ The solar system's eight planets is divided into two groups according to some common features:
◘ Terrestrial Planets or Rocky Planets: Mercury, Venus, Earth and Mars.
◘ Jovian Planets or Gaseous Planets: Jupiter, Saturn, Uranus and Neptune.
→ Planets are classified into two groups: inner and outer planets as per separation by Asteroid Belt.
→ Difference Between Inner Planets and Outer Planets:

Inner Planets  Outer Planets 
These are nearer to the sun. These are far away from the sun.
These include Mercury, Venus, Earth, Mars. These include Jupiter, Saturn, Uranus Neptune etc.
These are made up of dense metallic minerals. These are made up of hot gases, mainly hydrogen and helium.
These move faster and have a shorter period of revolution. These move rather slowly and have a longer period of revolution.
These have thin, rocky crust.  These are all gaseous bodies.
These have a mantle rich in iron and magnesium.  These are made of gases. 
These have a core of molten metals and have thin atmosphere. These have ring systems around them.
These have very few natural satellites (or moons) or no satellites  These have a large number of natural satellites (or moons). 

→ Mercury is the smallest and the nearest planet to the Sun.
→ It is extremely hot planet.
→ This planet has no water in it.
→ It has no atmosphere and no satellite.
→ Its days are scorching hot and nights are frigid.

→ Venus is second planet according to distance from the sun and also very close to earth.
→ It is considered as 'Earth's-twin' because its size and shape are very much similar to that of the earth.
→ It is also the brightest planet.
→ It is also called the 'morning' or 'evening star'.
→ It is probably the hottest planet because its atmosphere contains 90-95% of carbon dioxide.
→ The day and night temperatures are almost the same.
→ Venus has no water in it also there is no sufficient oxygen present.
→ It has no satellite.

→ The earth is the third nearest planet to the Sun.
→ Earth is the only known planet which provides sustenance or life on it.
→ It takes 23 hours 56 minutes and 4.091 seconds to rotate on its axis.
→ It takes 365 days, 5 hours and 48 minutes to revolve around the Sun. 
→ he earth is called 'blue planet' because because its two-thirds surface is covered by water. From the outer space, the earth appears blue 
→ It has a large quantity of oxygen which supports life.
→ The earth has all the essential elements like carbon (in the form of CO2), hydrogen (H2), nitrogen (N2) and oxygen (02) which act as building blocks for the origin of life. ›
→ The earth is neither too hot nor too cold. It has Goldilock Zone

Goldilock Zone is the habitable zone of solar system where all conditions are available for life to sustain. 

→ The earth has a protective layer of ozone which save life from the harmful ultraviolet radiation of the sun.
→ The earth has a satellite: Moon
◘ The moon is the only satellite of the earth.
◘ Its size is approximately one-fourth (27%) that of the earth.
◘ It has a diameter of 3475 km.
◘ The moon moves around the earth in about 27 days. It takes exactly the same time to complete one spin. As a result, only one side of the moon is visible to us on the earth.
◘ The moon's surface is covered with dead volcanoes, impact craters, and lava flows.
◘ The moon has no atmosphere, no twilight and no sound.
◘ The bright parts of the moon are mountains whereas the dark patches are low-lying plains.

→ Mars is considered as 'Red Planet' because of iron-rich red soil and pink sky.
→ It is marked with dormant volcanoes and deep chasms where once water flowed.
→ It has a thin atmosphere comprising of Nitrogen and Argon.
→ The highest mountain name of Mars is Nix Olympia which is three times higher than Mount Everest.
→ 'Phobos' and 'Demos' are two satellite of the earth.

→ It is the largest planet of the solar system.
→ Its atmosphere contains hydrogen, helium, methane and ammonia.
→ It is also known as winter planet as its average temperature is very low (-148° C).
→ It also contains dusty rings and volcanoes.
→ It has 16 satellites.
→ Ganymede, satellite of Jupiter is the largest satellite in the Solar system.

→ Saturn is the second largest planet of the solar system.
→ It has a bright concetric rings composed of thousands of rippling, spiraling bands of icy rock and dust just 200 feet thick and 270,000 km in diameter.
→ It has 21 known satellites. Titan is the largest among them.

→ Uranus is the third biggest planet of the solar system. It is about four times the size of the earth.
→ The planet appear greenish in colour because of methane gas present in its atmosphere.
→ Uranus rotates from east to west axis, which is opposite to other planets except Venus.
→ It is one of the coldest planets because of having an average temperature of -223° C.
→ Its atmosphere is made of mainly hydrogen and helium
→ The Uranus appear blue-green colour due to presence of methane.
→ There are 9 dark compact rings around the planet and a corkscrew shaped magnetic field.
→ It has 15 satellites. Aerial, Ambrial, Titania, Miranda are important satellite.

→ It is the most distant planet from the sun.
→ The temperature on the surface of Neptune remains low.
→ There are five rings of Neptune. The outer ring seems to be studded with icy moonlets while the inner ring appears narrow and nearly solid.
→ It has 8 satellites like Titron, Merid, N-1, N-2, N-3 etc.

Why Pluto was demoted from Planets?

• Pluto, demoted from planet status in August 24, 2006 under new IAU (International Astronomical Union).

• Now, Pluto and other dwarf planets like it will be called plutoids. 

• Plutoids are celestial bodies in orbit around the Sun at a distance greater than that of Neptune that have sufficient mass for their hydrostatic equilibrium (near-spherical) shape. The two known plutoids are Pluto and Eris. It is expected that more plutoids will be named as science progresses and new discoveries are made.

Friday, 12 August 2016

प्राचीन भारतीय इतिहास - सूची

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प्राचीन भारतीय इतिहास की सूची। प्राचीन भारत का इतिहास

• प्राचीन भारतीय इतिहास के स्त्रोत
→ धर्म ग्रंथ
→ ऐतिहासिक एवं समसामयिक ग्रंथ
→ विदेशियों के विवरण
→ पुरातत्व सम्बन्धी साक्ष्य

• प्रागैतिहासिक काल

• पाषाणयुगीन संस्कृति

• ताम्र-पाषनिक काल

• भारत की जनजातियाँ

• हड़प्पा सभ्यता
→हड़प्पा सभ्यता के स्थल
→ विशेष इमारतें एवं कला
→ नगरों की विशेषताएँ 
→ आर्थिक क्षेत्र
→ राजनैतिक क्षेत्र
→ धार्मिक क्षेत्र
→ सामाजिक जीवन

• वैदिक युग

• ऋग्वेदिक काल
→ भौगोलिक क्षेत्र
→ राजनैतिक स्थिति
→ सामाजिक जीवन
→ आर्थिक जीवन
→ धर्म

• उत्तर वैदिक काल
→ राजनैतिक क्षेत्र
→ सामाजिक जीवन
→ आर्थिक जीवन
→ धर्म

• महाजनपदों का उदय

• मगध राज्य का उत्कर्ष
→ हर्यक वंश
→ शिशुनाग वंश
→ नन्द वंश

• जैन वंश

• बौद्ध धर्म

• ब्राह्मण धर्म

• वैष्णव (भागवत) धर्म

• शैव धर्म

• प्राचीन भारत पर विदेशी आक्रमण
→ ईरानी आक्रमण
→ यूनानी आक्रमण

• मौर्य साम्राज्य
→ स्त्रोत
→ चन्द्रगुप्त मौर्य
→ बिंदुसार
→ आशोक
♠ आशोक का धम्म
♠ अभिलेख
→ मौर्य प्रशासन
→ आर्थिक स्थिति
→ सामाजिक स्थिति

• ब्राह्मण राज्य
→ शुंग वंश
→ कण्व राजवंश
→ आंध्र-सातवाहन वंश

• कलिंग नरेश खारवेल

• वाकाटक

• मौर्यकालीन भारत पर विदेशी आक्रमण

• पार्थियन एवं शकों का भारत पर आक्रमण

• कुषाण साम्राज्य

• गुप्त साम्रज्य
→ प्रशासन
→ व्यापार एवं वाणिज्य
→ सामाजिक स्थिति
→ धार्मिक स्थिति
→ कला एवं स्थापत्य
→ राजनितिक स्थिति

• पुष्यभूति वंश
→ हर्षवर्धन
→ हर्ष का शासन प्रबन्ध

• प्राचीन काल के महत्वपूर्ण स्तूप

• प्राचीन भारत के महत्वपूर्ण चैत्यगृह

• प्राचीन काल में आए प्रमुख विदेशी यात्री

• दक्षिण भारत (550 से 750 तक)
→ पल्लव वंश
→ चालुक्य वंश

• भारत पर अरबों का आक्रमण

• गुर्जर-प्रतिहार वंश

• राष्ट्रकूट राजवंश

• पाल वंश

• त्रिपक्षीय संघर्ष

• शाकंभरी चौहान वंश

• गहड़वाल वंश

• चंदेल वंश

• कलचुरी वंश

• हिन्दूशाही वंश

• गुजरात का सोलंकी वंश

• काकोट वंश

• उतप्ल वंश

• लोहर वंश

• चेर वंश

• चोल वंश

• पांड्य वंश

• संगम साहित्य

• भारत पर अरबों का आक्रमण

हिंदी इतिहास के सूची जाएँ

Thursday, 11 August 2016

Sentence - General English

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Sentence (General English) for Bank PO, Clerk, SSC CHSL, CGL and other competitive exams| Sentence, Definition, Kinds, Phrase, Clause, Sentence Structures

Basic Things

Number of alphabets in English: 26 alphabets

• Alphabets are divided into two types:

Vowels: Those alphabets that can be pronounced without the help of any other alphabets are called
Vowels. There are five vowels: a, e, i, o, u.

Consonants: Those alphabets that can be pronounced with the help of vowels are called
Consonants.Remaining 21 alphabets are consonants.

Words: A word is formed by one or more alphabets. It has a meaning.

Syllables: A syllable is a single unit of a word pronounced in one instance. It is a way to split word into speech sounds.
Example: Car, Cat, Eat are one syllable words.
Again, Purple, Silver are two syllable words.
Similar, Animal, Attention are three syllable words.


Definition: A group of words which makes complete sense is called a sentence.
Example: This is my car.

Kinds of Sentence: There are four kinds of sentences:

◘ Assertive or Declarative Sentence: A sentence which states or declares a fact is called an Assertive sentence. It ends with a full stop.
Example: The sun rises in the east.
He is a student.

◘ Imperative Sentence: A sentence expresses a command, a request, an entreaty or wish is called an Imperative sentence.
Example: Close the door.
Please lend me your notebook.

◘ Interrogative Sentence: A sentence which asks question is called an Interrogative Sentence. It ends with a question mark.
Example: Where do you live?
Where did you find this book?

◘ Exclamatory Sentence: A sentence which expresses sudden and strong feelings such as surprise pleasure, sorrow or happiness is called an Exclamatory Sentence.
Example: What a shot!
Oh my God!

Phrase: A group of words that makes sense, but not complete sense, is called a phrase.
Example: extremely pleasant, The old man

Clause: A group of words which forms part of a sentence, and contains a subject and a predicate, is called a clause.
Example: I first met him in town where I lived earlier. Underlined part is a Clause.

Independent Clause: An independent clause is a clause that can stand alone as a sentence as it makes complete sense. It has a subject and verb.
Examples: I met him in train.
He read the book.

Structures of Sentence

• There are four sentence structures:

Simple sentence: A simple sentence contains one independent clause.
Example: I like to play football.
He is my friend.

Compound Sentence: A compound sentence has two independent clauses joined by a linking word such as and, but, so, or.
Example: He worked hard yet he did not achieve good marks.
They went to museum but found it closed.

Complex Sentence: A complex sentence has one independent clause and one or more dependent clauses.
Example: After she became old, she started going for morning walks.
He wanted to go to the cricket match, even though it was raining.

Compound-Complex Sentence: A compound-complex sentence contains two independent clause and at least one dependent clause.
Example: Mahesh had a headache after the party was over so suresh cleaned the house.
After I graduated from college, I wanted to do travel, but I had to work immediately.

Go To Index of English

Tuesday, 14 June 2016

UPSC CSE Syllabus and Study Material of General Studies III (Paper IV)

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UPSC CSE Detailed Syllabus and Study Material of General Studies III (Technology, Economic Development, Bio diversity, Environment, Security and Disaster Management) (Paper IV)

Syllabus for GS III (Paper IV)

• Indian Economy and issues relating to planning, mobilization of resources, growth, development and employment.

• Inclusive growth and issues arising from it.

• Government Budgeting.

• Major crops cropping patterns in various parts of the country, different types of irrigation and irrigation systems storage, transport and marketing of agricultural produce and issues and related constraints; e-technology in the aid of farmers.

• Issues related to direct and indirect farm subsidies and minimum support prices; Public Distribution System- objectives, functioning, limitations, revamping; issues of buffer stocks and food security; Technology missions; economics of animal-rearing.

• Food processing and related industries in India- scope and significance, location, upstream and
downstream requirements, supply chain management.

• Land reforms in India.

• Effects of liberalization on the economy, changes in industrial policy and their effects on industrial growth.

• Infrastructure: Energy, Ports, Roads, Airports, Railways etc.

• Investment models.

• Science and Technology- developments and their applications and effects in everyday life
• Achievements of Indians in science & technology; indigenization of technology and developing new technology.

• Awareness in the fields of IT, Space, Computers, robotics, nano-technology, bio-technology and issues relating to intellectual property rights.

• Conservation, environmental pollution and degradation, environmental impact assessment
• Disaster and disaster management.

• Linkages between development and spread of extremism.

• Role of external state and non-state actors in creating challenges to internal security.

• Challenges to internal security through communication networks, role of media and social networking sites in internal security challenges, basics of cyber security; money-laundering and its prevention.

• Security challenges and their management in border areas; linkages of organized crime with

• Various Security forces and agencies and their mandate.

 Study Material for GS III (Paper IV)

Indian Economy

• Planning
• Mobilization of resources
• Growth and Development
• Employment
• Inclusive growth and issues
• Government Budgeting
• Cropping Pattern
• Irrigation: Types and systems
• Agriculture production, marketing and issues
• E-technology in the aid of farmers
• Farm subsidies and MSP
• Public Distributions System (PDS)
• Food Security
• Buffer Stock
• Technology missions
• Economics of animal rearing
• Food Processing
• Land Reforms in India
• Liberalization
• Industrial policy and growth
• Infrastructure
• Investment Models

Science and Technology

• Development
• Applications in daily life
• Achievements of Indians
• Developing new technology
• Indigenization of Technology
• Information Technology
• Space Technology
• Computer Science
• Robotics
• Nanotechnology
• Bio-technology
• Intellectual property rights


• Conservation
• Environmental pollution and degradation
• Environmental impact assessment

Security and Disaster Management

• Disaster and Disaster Management
• Development and spread of extremism
• Security Challenges
• Internal Security challenges through communication networks
• Cyber Security
• Money laundering and its prevention
• Border Security Challenges
• Security forces and agencies

Monday, 13 June 2016

UPSC CSE Syllabus and Study Material of General Studies II (Paper III)

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UPSC CSE Detailed Syllabus and Study Material of General Studies II (Governance, Constitution, Polity, Social Justice and International relations) (Paper III)

Syllabus for GS II (Paper III)

• Indian Constitution- historical underpinnings, evolution, features, amendments, significant provisions and basic structure.

• Functions and responsibilities of the Union and the States, issues and challenges pertaining to the federal structure, devolution of powers and finances up to local levels and challenges therein.

• Separation of powers between various organs, Dispute redressal mechanisms and institutions.

• Comparison of the Indian constitutional scheme with that of other countries.

• Parliament and State Legislatures- structure, functioning, conduct of business, powers & privileges and issues arising out of these.

• Structure, organization and functioning of the Executive and the Judiciary Ministries and Departments of the Government; pressure groups and formal/informal associations and their role in the Polity.

• Salient features of the Representation of People's Act.

• Appointment to various Constitutional posts, powers, functions and responsibilities of various Constitutional Bodies.

• Statutory, regulatory and various quasi-judicial bodies

• Government policies and interventions for development in various sectors and issues arising out of
their design and implementation.

• Development processes and the development industry- the role of NGOs, SHGs, various groups and associations, donors, charities, institutional and other stakeholders

• Welfare schemes for vulnerable sections of the population by the Centre and States and the performance of these schemes; mechanisms, laws, institutions and Bodies constituted for the protection and betterment of these vulnerable sections.

• Issues relating to development and management of Social Sector/Services relating to Health,
Education, Human Resources.

• Issues relating to poverty and hunger.

• Important aspects of governance, transparency and accountability, e-governance- applications, models, successes, limitations, and potential; citizens charters, transparency & accountability and institutional and other measures.

• Role of civil services in a democracy.

• India and its neighbourhood relations.

• Bilateral, regional and global groupings and agreements involving India and/or affecting India's interests.

• Effect of policies and politics of developed and developing countries on India's interests, Indian diaspora.

• Important International institutions, agencies and fora- their structure, mandate.

Study Material of GS II (Paper III)

Indian Constitution and Polity

• Historical Ideas
• Framing of the Constitution
• Features of the Constitution
• Amendments of the Constitution
• Provisions of the Constitution
• Basic Structure of the Constitution
• Union (Functions and responsibilities)
• States (Functions and responsibilities)
• Federal System and Challenges
• Devolution and Challenges
• Separation of Powers
• Dispute Redressal (Mechanisms and institutions)
• Comparison of Indian constitution with others
• Parliament and State legislatures

→ Structure
→ Functioning
→ Conduct o Business
→ Power and Privileges
→ Issues

• Judiciary
• Executive
• Ministries and Departments of the government
• Pressure Groups and their roles
• Features of Representation of People's Act
• Constitutional Bodies
• Statutory Bodies
• Regulatory Bodies
• Quasi-Judicial Bodies

Governance and Social Justice

• Government developmental policies and issues
• NGOs, SHG's and charities role in development
• Schemes of Central and State government for vulnerable sections of society
• Social Sector issues
• Poverty and Hunger Issues
• Governance and e-governance
• Role of civil service

International Relations

• India and its neighbourhood
• Bilateral grouping
• Regional Grouping
• Global Grouping
• Policies affecting India's interest
• International organizations

Sunday, 12 June 2016

UPSC CSE Syllabus and Study Material of General Studies I (Paper II)

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UPSC CSE Detailed Syllabus and Study Material of General Studies I (Indian Heritage and Culture, History and Geography of the World and Society) (Paper II)

Syllabus for GS I (Paper II)

• Indian culture will cover the salient aspects of Art Forms, Literature and Architecture from ancient to modern times.

• Modern Indian history from about the middle of the eighteenth century until the present significant events, personalities, issues

• The Freedom Struggle - its various stages and important contributors/contributions from different
parts of the country.

• Post-independence consolidation and reorganization within the country.

• History of the world will include events from 18th century such as industrial revolution, world wars,
redrawal of national boundaries, colonization, decolonization, political philosophies like communism,
capitalism, socialism etc.- their forms and effect on the society.

• Salient features of Indian Society, Diversity of India.

• Role of women and women's organization,  population  and associated issues, poverty and developmental issues, urbanization, their problems and their remedies.

• Effects of globalization on Indian society

• Social empowerment, communalism, regionalism & secularism.

• Salient features of world's physical geography.

• Distribution of key natural resources across the world (including South Asia and the Indian sub-continent); factors responsible for the location of primary, secondary, and tertiary sector industries in various parts of the world (including India)

• Important Geophysical phenomena such as earthquakes, Tsunami, Volcanic activity, cyclone etc., geographical features and their location- changes in critical geographical features (including water-bodies and ice-caps) and in flora and fauna and the effects of such changes.

Study Material of GS I (Paper II)

Indian Heritage and Culture

• Introduction

• Visual Arts
→ Architecture
→ Sculpture
→ Pottery
→ Paintings

• Performing Arts
→ Dance forms
→ Music
→ Theatre and Drama
→ Puppetry

• Miscellaneous Arts
→ Religion
→ Language and Literature
→ Cinema
→ Festivals
→ Philosophy
→ Foods
→ Handicrafts

Modern History

• Arrival of the Europeans in India
• British conquest of India
• Famous Battles
• Structure and Policy of British Empire
• Social and Cultural developments in India
• Revolt of 1857
• Rise of Indian Nationalism (1858-1905)
• Nationalist Movement (1905-1918)
• Struggle for Swaraj under Gandhi's Leadership
• Press under British rule
• British Education policy and growth of Modern education system
• Governor-Generals of India
• Freedom Movements
• Freedom Fighters
• India Post Independence

World History

• Industrial Revolution
• World war I
• World war II
• Redrawal of national boundaries
• Political Philosophies (Forms and effect on the society)
• Colonization and decolonization


• Introduction
• Diversity of India
• Role of Woman and women's organization
• Population and related issues
• Poverty and developmental issues
• Urbanization, problems and remedies
• Globalization and its effects
• Social empowerment
• Communalism
• Regionalism
• Secularism


• The Earth and the Universe
• Landforms
• Climate
• Continents
• Water
• Natural Resources and its distribution
• Factors behind location of industries
• Geological Phenomena

→ Earthquakes
→ Tsunami
→ Volcanic activity
→ Cyclone

• Geographical features and its changing face
• Biodiversity

Friday, 10 June 2016

Number System - Quantitative Aptitude

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Number System (Quantitative Aptitude) for Bank PO, Clerk, SSC CHSL, CGL and other competitive exams| Face Value and Place Value and Various types of numbers

Indian numeral system consist of ten digits namely 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. In words, zero, one, two, three, four, five, six, seven, eight, nine, ten.

Numeral: Number is represented by group of digits called numeral.

Face Value and Place Value:

Face Value: It is the value of the digit itself. For example, 7 is always 7 whether it at 578 or 5887888. The face value of digit not change with the place it appears in numeral.

Place Value: It is the place value of the digit multiplied by the place value at which it appears in the numeral. For example:
♦ In numeral 85269
◘ The place value of 9 is (9 × 1) = 9
◘ The place value of 6 is (6 × 10) = 60
◘ The place value of 2 is (2 × 100) = 200
◘ The place value of 5 is (5 × 1000) = 5000
◘ The place value of 8 is (8 × 10000) = 80000

Various Types of Numbers:

Natural Numbers: Counting numbers are called natural numbers. Example: 1, 2, 3, 4, ... etc. are all natural numbers. Smallest natural number is 1 and largest natural number is ∞.

Whole Numbers: All counting numbers together with zero are called whole numbers. Example: 0, 1, 2, 3, 4, ... are whole number.
◘ All natural number are whole number.

Integers: All counting numbers, 0 and -ve of counting numbers are called integers. Example: -∞..., -4, -3, -2, -1, 0, 1, 2, 3, 4 ... ∞ are integers.
◘ Set of Positive integers: [1, 2, 3, 4, ....]
◘ Set of Negative integers: [-1, -2, -3, -4, ...]
◘ Set of all Non-Negative integers: [0, 1, 2, 3, 4, ....]

Real Numbers: Positive or negative, large or small, whole numbers or decimal numbers are all Real Numbers.

Rational Numbers: Any number which can be expressed in the form of p/q where p and q both are integers and q 0 are called rational numbers. Example: 3/7, -2/8, -5 etc.
◘ There exists infinite rational numbers between any two rational numbers.

Irrational Numbers: Non-recurring and Non-terminating decimals are called irrational numbers. Example: √3, √5, etc.

Even Numbers: Numbers which are exactly divisible by 2 are called even numbers. Example: -4, -2, 0, 2, 4 etc.
◘ Sum of first n even numbers = n(n + 1)

Odd Numbers:  Numbers which are not exactly divisible by 2 are called odd numbers. Example: -5, -3, 1, 3, 5 etc.
◘ Sum of first n odd numbers = n2

Prime numbers: Numbers which have exactly 2 factors, 1 and number itself is called Prime Numbers. Example: 2, 3, 5, 7, 11, etc.
◘ 1 is neither prime nor composite.
◘ 2 is only even prime number.
◘ There are 15 prime numbers between 1 to 50 and 10 prime numbers between 50 to 100.

Composite numbers: Numbers which have more than 2 factors. Example: 4, 6, 8, 10, etc.

Relative Prime Numbers: Two numbers are said to be relatively prime if they do not have any common factor other than 1.Example: (3,5), (7,20), (11,15), etc.

Twin Prime Numbers: Two prime numbers which differ by 2 are called twin prime numbers. Example: (3.5), (5,7), (11,13) etc.

Co-Prime Numbers: Two natural numbers a and b are said to be co-prime if their HCF is 1. Example: (2,3), (4,5), (7,9) etc.

Divisibility Rules

• Divisibility rules let you test if one number is divisible by another, without doing calculations.

• Divisibility by 2: A number is divisible by 2 if its digit at ones place (unit digit) is 0, 2, 4, 6 or 8. Example: 5896, 8572, 4856, etc.

• Divisibility by 3: A number is divisible by 2 when sum of its digits is divisible by 3. 
Example: 5496 = 5 + 4 + 9 + 6 = 24; 24 is divisible by 3 therefore, 5496 is also divisible by 3.

• Divisibility by 4: A number is divisible by 4 if the sum of its last two digits is divisible by 4. Example: 58975 = 7 + 5 = 12; 12 is divisible by 4 therefore, 5496 is also divisible by 4. (In 58975, 7 and 5 are last digits).

• Divisibility by 5: A number is divisible by 5 if its digit at ones place (unit digit) is 0 or 5.
Example: 8565, 25840, 50, etc.

 Divisibility by 6: A number is divisible by 6 if it is divisible both by 2 and 3.
Example: 18, 24, 48, etc.

• Divisibility by 7: A number is divisible by 7 if its digit at ones place (unit digit)  or last digit is multiplied by 2 and subtracted from the rest of the number and result is either 0 or divisible by 7.
Example: 672 = 2 × 2 = 4, 67 - 4 = 63, 63 ÷ 7 = 9; Here, result 63 is divisible by 7 therefore 672 is also divisible by 7. 

• Divisibility by 8: A number is divisible by 8 if the number formed by the last 3 digits of the number is divisible by 8.
Example: 589160, 698552, 58256, etc. whose last three digits is divisible by 8. 160 ÷ 8 = 20.

• Divisibility by 9: A number is divisible by 9 if sum if all the digits of a number is divisible by 9.
Example: 585 = 5 + 8 + 5 = 18; 18 is divisible by 9 therefore, 585 is also divisible by 9.

• Divisibility by 10: A number is divisible by 10 if its digit at ones place (unit digit) is 0.
Example: 580, 5690, 63210, etc.

• Divisibility by 11: A number is divisible by 11 if the the difference between the sum of its digits in odd places and in even places is either 0 or divisible by 11.
Example: 2728 = 2-7+2-8 = -11. Here, -11 is divisible by 11 therefore, 2728 is also divisible by 11.