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Letter-A

Ravi Kumar Singh — Sat, 08 Mar 2008 03:41:31 +0000

A/a art. 1.one, any
2. first letter of english alphabet.

A 1 or A-one first rate, first class, informal excellent.

aback adv. towards the back,
taken~ surprised

abandonvt. give up
abase vt. degrade.
abash vt. embarras, disconcert, put shame.
abate vt.,vi. make or become less; ~ment n. reduction.

abattoirn. a slaughter house.
abbotn. head of community of monks.
abdicatevt. renounce the throne or responsibility.
abductvt. kidnap, carry off illegally.
abedadv. in bed

Abstract Algebra :The Group

Ravi Kumar Singh — Thu, 06 Mar 2008 10:50:10 +0000

Def. A non-empty set ‘G’ is called a group w.r.t. the binary operation’o', iff it satisfies the following axioms-
G1)Closure axiom
¥ a, b € G => aob € G.
G2)Associative axiom
¥ a, b, c€ G
ao(boc)= (aob)oc
G3)Identity axiom
if ‘e’ be identity of ‘G’
then aoe=eoa=a, ¥ e€G
G4)Inverse axiom
if ‘p’ be inverse of ‘a’
then aop=poa=e, ¥ a€G.

Abelian group : If G is commutative too,is called ‘abelian group’.
i.e. aob=boa

subgroup :a non-empty subset ‘H’ of a group G is called a subgroup of G is itself a group w.r.t. the binary operation defined on G.
Properties of Subgroups:-
If H is subgroup of G then,
i)H=inverse of H, but converse in not always true.
ii)square of H= HH= H.

Complex :-A non-empty subset ‘H’ of G is called Complex of G.
Properties of Complex:-If H,K,L be three complexes of G, then
i)HK is also a complex.
ii)inverse of H is also a complex.
iii)inverse of (HK)=(inverse of K)*(Inverse of H)

Conditions of H to be a Subgroup :-
1)(i) a, b€ H => ab €H,
(ii)a€ H =>(inverse of a) € H.

2)a, b€ H=>a*(inverse of b) €H.

3)H(inverse of H)=H.

4)a, b€H => ab€H

5)H & K are two subgroup them ‘HK’ is a subgroup iff ‘HK=KH’

A Counting Principle :-If H and K are subgroup, then the subset HK need to be a subgroup of G. We want to determine the number of distinct elements in the subset HK and we denote it by ‘o(HK)’ and
o(HK)=o(H)o(K)/o(HcapK).

Not:coset,modulo,Lagrange’s theorem,

Normalizer:-If G is a group and a€G, then normalizer of a is the set of all those elements of G which commute with a.
Symbolically,Normalizer
N(a) ={xa=ax:x€G}

Normal Subgroup:- A subgroup H is said to be ‘Normal Subgroup’ iff ¥ x€G, and ¥ h€H =>xH(inv of x)€H

Indian State: Karnataka

Ravi Kumar Singh — Fri, 29 Feb 2008 15:44:27 +0000

I’m starting a new topic in geography named “Indian State”
today’s state is “Karnataka”

General Facts
Original Name : State of Mysore
Present Name : Karnataka(renamed in 1973)
Formation : Nov 1, 1956
Capital : Bangluru
Area : 191,791 sq km, it is 8th largest state by area.
Official Language : Kannada
Population : 52,850,562 persons, it is 9th largest state by population.
Districts : 29

Meaning of ‘Karnataka’ : this name is derived from the Kannada words KARU, NADU meaning ‘elevated land’.
Geography
Boundaries : Karnataka is bordered by the Arabian see to the West, Goa to the North- west, Maharastra to the North, Andhra Pradesh to the East, Tamilnadu to the South-East and Kerala to the South-West.

River : the Kaveri, the Tungbhadra,the Krishna and the Sarswati.

Highest Points : the Mullayanagiri hills in (1,929 metre, Chikkamagaluru district)

Do you know? That…

Ravi Kumar Singh — Mon, 25 Feb 2008 14:48:50 +0000

1.south America continent is also known as Latin America because of speaking of the Latin Languages Portugese & Spanish

Rigveda

Ravi Kumar Singh — Mon, 25 Feb 2008 05:43:28 +0000

Rigveda is the oldest book of the world.With the time of its construction, historiests are not agree totally.But generally it is considered between 3000 to 2500 bc.
It is said that there were 21 branches of Rigveda,but nowadays there are only 5 branches available.There are- Shâkal, Åshwalâyan, Shânkhåyan, Vâkal, Mândukâyan.

Top Books For IAS Competition

Ravi Kumar Singh — Wed, 20 Feb 2008 16:36:56 +0000

Here I’m giving you a “List Of Great Books” for IAS Pre :-

These Books can be bought from “Pratiyogita Darran, 2/11 A, Swadeshi Bima Nagar, Agra-282002, website:http://www.pratiyogitadarpan.org

Yours

Ravi Kumar Singh

UPSC Examination: IAS & IPS

Ravi Kumar Singh — Wed, 20 Feb 2008 14:23:28 +0000

IAS(Indian Administrative Service) is India’s best post of civil service where you get money and respect together.

The System Of Exam

The present system of recruitment of civil service was adopted by “Union Public Service Commission” in 1979, three decades back.
Around December every year the Notification for the next year’s examination appears in all leading newspapers.
This examination is held in two successive stages (¡)Preliminary Examination, and (¡¡)Main Examination.
(i)Preliminary Examination:- it is an aptitude test based on multiple choice objective type questions.It may be negative marking.It is normally conducted on 2nd or 3rd sunday of may every year.
This is qualifying kind of examination and its marks are not considered for preparation of final result.
It consists of two question papers
*Paper I:General Studies, 150 marks, 2 hours duration.
*Paper II:Optional Subject, 300 marks, 2 hours duration.

(ii)Main Examination:- This is held in October/November.The candidate who has cleared Pre. will be eligible for this.The candidates qualified for Main compete for selection for the various services and posts.

Eligibility Criteria

For IAS & IPS a candidate must be an Indian between 21-30 age group, holding a degree of any recognized universities or possess an equivalent qualification and physically fit according to physical standard for admission to CSE.
A general category candidate is permitted to avail maximum of 4 attempts.

The Syllabus

*Pre. Exam :The question papers are set in both in Hindi and English. The candidate is to choose one optional subject from the list of given subjects-
‘Agriculture, Animal Husbandary and Veterinary Sciences, Botany, Chemistry, Civil Engineering, Commerce, Economics, Electrical Engineering,Geography, Geology, Indian History, Law, Mathematics, Mechanical Engineering, Medical Science, Philosophy, Physics, Political Science, Psychology, Public Administration, Sociology, Statistics, Zoology’.
General studies is a compulsory subject for all candidates at both Pre. and Main. The syllabus at Pre Level is broadly divided in 7 components-

Current Events of national and internationa importance
Indian Economy
indian History and National Movement
Indian and World Geography
Indian Polity
General Science
General Mental Ability

*Main Exam :There are 2-2 papers on two optional subjects of 300-300 marks and an Essay,two on general studies,one one English, one on other choosed Language. Total marks =2000.
And Interview of 300 marks.
After all this Merit is prepared.

Vector Analysis-2

Ravi Kumar Singh — Sat, 16 Feb 2008 17:53:33 +0000

In this section we will study on multiplication(Product) of vectors.

PRODUCT OF TWO VECTORS:-

this is of two types

i)Scalar Product

ii)Vector Product

=>>Scalar Product-

When product of two vectors is a scalar quantity,it is called ‘Scalar Product’.

If a & b be two vectors then their scalar product is denoted by ‘a.b’ and

a.b=|a||b|cos@ or

a.b=lmcos@

(`.`|a|=l etc.)

Important for a.b

i)a.b=b.a

ii)a.a=|a|2=l2

iii)a.b=0 =>a¿b

iv)i.i=j.j=k.k=1

i.j=j.k=k.i=0

v)if a=pi+qj+rk and

b=si+tj+uk ,

then

a.b=ps+qt+ru

vi)cos@=a.b/lm

=>>Vector Product-

when product is a vector quantity,it is called ‘Vector Product’.

It is written as ‘a*b’ and

a*b=|a||b|sin@ñ

a*b=lmsin@ñ

where ñ is u.v. along

a*b

Important for a*b

i)a*b=-b*a i.e. a*b is not equal to b*a

ii)a*a=0

iii)a*b=0 =>a || b

iv)i*i=j*j=k*k=0 ,and

i*j=k

j*k=i

k*i=j

v)a*b=

[i j k]

|p q r|

[s t u]

vi)if a & b are adjacent sides of ||gm, area of ||gm= |a*b|, and if sides of triangle then area=half of |a*b| i.e. Area=|a*b|/2

vii)if a and b are diagonals of ||gm ,area=|a*b|/2

viii)sin@=|a*b|/lm

Essay on COMPUTER

Ravi Kumar Singh — Sat, 16 Feb 2008 10:57:19 +0000

http://ravisclass.wordpress.com

1.Introduction, 2.What’s Computer, 3.Works of Computer, 4.Parts of Computer, 5.Language of Computer, 6.Types of Computer, 7.Computer in India, 8.Conclusion

1. introduction

The 20th century is the period of rapid developments in science and technology influencing aspect an human life. One of the greatest things that man has created is, perhaps, ‘the Computer’.The computer is truely an amazing machine. Computer is used in areas of administration, medicine, education, sports, home, defence, shops, markets, and many more. Computer and IT, in recent years, has become an integral part of our life. We can see it almost everywhere.

2.What’s Computer

Equation representing two straight lines through origin

Ravi Kumar Singh — Sat, 16 Feb 2008 08:26:45 +0000

This equation is generally written as aX2+2hXY+bY2=0 __(i)

Now we know that a line through origin is y=mx, let two represented by (i) be
y=m1x and
y=m2x
then
aX2+2hXY+bY2=b(y-m1)(y=m2x)
this gives
m1+m2=-2h/b and m1.m2=a/b

Also angle between (ii) is @ then
tan@=m1~m2/1+m1.m2
tan@=(h2-ab)1/2/(a+b)