Upsc Sample Booklet Online

7/27/2019 Upsc Sample Booklet Online

1/17

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SAMPLENOTES

i) CURRENTAFFAIRSii) CSAT-QUANT


3/17


Inflation,RBIandtheInterestRates

Theissue:Indiainthemidstofaninflationaryepisodesincethelast2years.Itbegan

December2009,whentheWPIinflationclimbedto7.15%,itcontinuedtorise,peaked

April2010,atjustshortof11%.Thereafter,ithassloweddownbutitisstillmuchhighe

than the comfort levelof less than 5%. High inflationmakesgoods and servicesle

affordable.RBIusesitsmonetarypolicytotrytobringdowninflation.

Inflation: Asustained rise inprices across the board, that is, a phenomenowhere theaverageprice of allgoods isonan increasing trajectory forsom

stretchoftime.

Independent Indias highest inflation occurred in September 197wheninflationreached33.3%

Monetary Policy: The process bywhichmonetary authority (RBI for Indiacontrols the supply of money in the economy by exercising its control ov

interest rates inorder tomaintain price stability andachievehigheconom

growth. RBI has been using monetary methods primarily to control inflatio

Thisinvolvesraisinginterestratesinordertocontroldemand.

Other methods to control inflation: (i) Fiscal Method Government cacontrolinflationby imposing or raisingtaxes,controlling expenditureetc.(i

Administrative Method It involves taking steps to control Hoarding

commodities by traders, Preventing Black Marketing etc. Government cainvokeEssentialServicesManagementActortheEssentialCommoditiesActi

caseofevidenceofHoarding.

WhatareInflationaryExpectations?Incaseinflationisconsistentlyhigh,atleasti

the short run, the actual inflation rate depends, in part, onwhat people expect th

inflationratetobe.Inflationcangetworsenedbytheveryfactofhigherinflationar

expectations.e.g.Expectingthatthepriceswillincreasemore,theunionsmaynegotia

for higher wage increase of the workers. Higher wage will lead to higher demand fo

goods,whichinturnwillcausethepricestorise.

Twocausesof inflation:(i)CostPushThepricesincreaseofcommoditiesincreabecauseoftheincreaseinthecostsofproduction.(ii)DemandPullThepricesincrea

becausetheincreaseindemandisnotbeingmetbyacorrespondingincreaseinsupply.

WhathasRBIdonesofar? RB,throughitsmonetarypolicy,targetsthedemandside

By increasing thekey short term interest rate (repo rate),it leaves lessmoney inth

hands of the people, thereby reducing liquidity. With less money chasing the sam

numberofgoods,thisissupposedtodecreasetheprices.However,iftheproblemiso

thesupplyside,thereislittlethatRBIcando.

RBIreviewsthemonetarypolicy8timesinayear(twiceeveryquarter) RBI had increased the reporate13 timessinceMar 2010,before relaxing

moderatelyin2012.

Two types of inflation: (i) Headline inflation: total inflation within an econom

including items which can undergo spikes like food and energy. (ii) Core inflatio

inflationwhichexcludescertainitemswhicharesubjecttovolatilepricemovementsli

foodandenergy.

Stagflation: A condition of slow economic growthandrelativelyhighunemployme

accompaniedbyinflation.Thisisatoughsituationforpolicymakersbecausemonetar

policytargeting inflationmayreducegrowthfurther.Afeweconomists feelthatIndia

facingasimilarsituationnow.

TheIndicestomeasureinflation

WholesalePriceIndex

-The price of a representative basketof

wholesalegoods.

- Focuses on the price of goods traded

betweencorporations,ratherthangoods

boughtbyconsumers(measuredbyCPI)

-IndiausesWPItomeasureinflation(on

a monthly basis), with base year 2004-

05(annual%change=inflation)

-WPIfailstoreflecttheactualpricerise

of essential commodities (EC) because

the weightage given to EC is just 20%.

Remaining is Manufactured Products

(65%)andFuel(15%)

ConsumerPriceIndex

- Measureschangesin the pricelevel of

consumer goodsand services purchased

byhouseholds.

-It differs from WPI due togovernment

subsidies, sales and excise taxes, and

distributioncosts

QuickNotes

KeyRates

Repo(Repurchase)rateistherateatwhich

the banks borrow shot-term money from

RBI,againstsecurities.

Reverse Repo rate is the rate at which

banks deposit their short-term excess

liquiditywiththeRBI.

MarginalStandingFacility(MSF)istherate

at which banks can borrow funds when

thereisaconsiderableshortfallofliquidity

Cash Reserve Ratio(CRR) is the minimum

deposit(in %)thatbanksare supposedto

parkwithRBI(theycannotuseit)

Statutory Liquidit y Rat io (SLR)is t he

minimum % of deposits that the banks

haveto maintain withthemselvesin form

ofgold,cashorotherapprovedsecurities

The reverse reporateis alwayskept100

basis points (=1%) lower than the repo

rate.MSF iskept100basispoints higher

thanthereporate.


4/17


CAGReports

Theissue:CAGtabled3reports intheParliament,whichpertainedtoPrivatizationofDel

Airport (T3 terminal), theUltra-MegaPowerProjects (UMPPs) and theCoalBlockallocatio

Project.TheCAGreportoncoalblockallocationswhichamountstoalosstotheexchequera

Rs1.86 lakh croremakesit evenbiggerthan the 2Gscamloss.Mediahasnamedthis scam

Coal-gate.

DelhiAirport:With cash contribution tothe tune of Rs1, 813cr, DIAL got 4,799.0acresofprimelandfor60yrsonleasewithearningcapacityofRs1.63lakhcr.

UMPPs:Coalbasedpowerprojectsthatareabletogeneratemorethan4,000MWofpower.TheCAGhas foundmajorpost-bid violation byallowing Reliance PowersLt

(RPL)touseexcesscoalfromthethreecoalblocksallocatedtotheSasanUMPP.

Coal Block Allocation: CAG has pointed out that since the blocks were randomassignedandnotauctioned;ithasresultedinalossofRs1.8lakhcr.

WhoisCAG?HeistheComptrollerandAuditorGeneralofIndia.Thisisaconstitutionalpos

similartotheSupremeCourtJudge.ThedutiesoftheCAGarementionedinArticle149ofth

Indianconstitution.Thebasicdutyistoaudittheaccountsofthegovernment.

CurrentCAGVinodRai

CanthegovernmentignorethereportsofCAG?Apart fromthehuge figurethat therepoestimates as loss, the report in itself is important because it is a report from a Neutra

Constitutional authority, andwhich is scrutinized by PAC,which includes Opposition par

members.Hencethegovt.cannotignorethereport.Thegovernmentiscurrentlyfinalizingth

biddingprocessofcoalblocksinpartnershipwithCRISIL.

CRISIL, which provides ratings, research, and risk and policy advisory services,preparing the coal auctionmethodology todetermine the reserve price ofblocks th

coalministryhasidentifiedforauction.

PresumptiveLoss: Whetheritis2GscamortheCoalgatescam,thefigurethatisportrayeda

loss is a presumptive loss. It is a notional loss which occurs due to not following the be

practices like e-auctioning, competitive bidding in case of allocation of scarce naturaresources.Thisisnottheactualloss.

Ashok Chawla Committee: Set upto in early2011 tosuggest transparent and corruptio

process forallocationofnatural resources. Itsimportantrecommendationsare(i)following

competitivebiddingrouteforallocationofcoalblocks,(ii)switchingtoopenacreagelicensin

policy forallocationofoilandgasblocks,(iii)makingpublictheminutesofthemeetingofth

Standing Linkage Committee (Long Term) pertaining to allocation decisions on coal, (iv

putting inpublic domain theminutes of themanaging committee(MC) foroilandgasblock

and(v)makingtheDirectorateGeneralofHydrocarbons(DGH)anindependententity.

Summary Overall, the committee has recommended "open, transparent ancompetitive"mechanismsofsaleinthecaseofmineralblocks,and"suitablemarket-

relatedprocesses"forthesaleofspectrum.

Impact-69outof81recommendationofthecommitteewereacceptedbytheGroupofMinisters(GOM)butitwasleftfortheindividualministriestoimplementthem.

2G scam: Spectrum allocation

was undercharged leading to a

presumptivelossofRs1.76lakh

cr. Currently, JPC is conducting

investigation (Chairman P C

Chacko)

DifferencebetweenPACandJPC

JointParliamentaryCommittee

- Ad-hoc committee, set up for

specificobjective&duration

- Set-up by a motion passed by

onehouse&agreedtobyanother

-Membership&subjectsdecided

by the Parliament (LS membersalwaystwicethatofRS)

-4JPCsbefore2G:Bofors(1987),

Securities&BankingDeals(1992),

Share Market Scam (2001),

Pesticide residue in soft drinks

(2003)

PublicAccountsCommittee

-Standingcommittee,constituted

everyyear

- To examine how the money

granted (budget) by Parliament

has been spent by the

government

- Consists of 15 to 22members.

Notmorethan15membersfrom

LS,&notmorethan7fromRS

- Notsupposed to go into policy

issues(UnlikeJPC)

- Depends on the inputs of the

CAG, the friend, philosopher &

guideofPAC

-1st

ChairmanofPAC:WMHailey

(1921)

-CurrentChairmanMMJoshi

(PACChairmanisalwaysfromthe

Opposition,unlikeJPC)

QuickNotes


5/17


ArabSpringandtheSyrianCrisis

Theissue:InDecember2010,amaninTunisiaburnedhimselftodeathinprotesto

treatmentbypolice.Verysoon,manycountriesoftheMiddleEast(Tunisia,Egypt,Li

Bahrain,Yemen andSyria)witnessed pro-democracy rebellions.Collectively, they

called ArabSpring. In2012, Syria has been atthe center ofthisrevolutionwith

SyrianPresidentBasharAlAssadgettingintoamilitaryconfrontationwiththerebe

therestoftheworlddiscussinghowtoputanendtothissituation.

Whyisitrunningforsolong?InLibya,becauseoftheUnitedNationsSecuCouncil(UNSC)resolution,foreignpowersprovidedopensupportthathelpe

bringingthe regimedown.InEgypt,the countrystop leadersquitthemse

due to the uprising. However, in Syria, world powers are divided. T

ResolutionsbyUNSCwerevetoedbyChinaandRussia,becausetheyfeelitw

violateSyriassovereignty.

Indiasstand: IndiaisaNon-PermanentmemberinUNSCfor2yearsandhtovoteonresolutions

UNSCVoteonSyria IndiasVote

Oct2011 Abstained

Feb2012 VotedFOR

Jul2012 VotedFOR

AugUNGA2012 Abstained

Indiahasbeenchangingitsstand-IndiabelievesthataCountrysSovereigmustberespected.InOct,IndiaabstainedfromUNSCvote,toreflectthissta

butatthesametime,Indiaexpectedthattheviolenceshouldstop.Butin

2012, when the violence against citizens did not stop, India voted FOR

Resolution. However, in Aug 2012, India abstained from voting because

draftoftheresolutioncalledforPresidentofSyriatostepdownfrompowwhichIndiaconsidersasexternalinfluenceonacountry. UNSC, with 15 members, can take wide ranging decisions (power to

decisionsisheavilytiltedinfavourofpermanentmembers)thatmightinvo

militaryaction.UNGA,with193members,cantakedecisionsdemocratical

voting,buttheirvotewillhaveonlymoralpersuasioneffect.LikeinAug2

when133ofthe193membersvotedinfavoroftheresolutiondenouncing

violenceinSyria.CountryName Dateline Outcome

Tunisia 17Dec2010-14Jan2011 GovernmentOverthrown,Electionspeacefu

conducted.NewPresidentMocefMarzaou

Egypt 25Jan2011-11Feb2011 GovernmentOverthrown,Electionsheld

NewPresidentMohamedMorsi

Libya 17Feb2011-23Aug2011 GovernmentOverthrownafteracivilwar

NewPresident-MohammadMagarief

Syria 15Mar2011-Ongoing SignsofCivilWar,ManyCivilianCasualties.N

clearInternationalPlan

UNSC&India

- UNSC is the organ of United Nations

which is charged to maintain

InternationalPeaceandStability.

- 15 members including 5 Veto wielding

permanent members. Remaining 10 are

non-permanentanddonotwieldVeto.

- Indiais anon-permanent member for2yrs till Dec 2012. This is the 7th time

thatIndiahasbeenonUNSC.

- India has been seeking a permanent

seatontheUNSCasamemberoftheG4,

an organization composed of Brazil,

Germany, Japan, and India, all who are

currently seeking permanent

representation

- India has a permanent mission to the

UN, which is led by the Permanent

Representative,HardeepSinghPuri

-IndiaisafoundingmemberofUN.

- Vijaya Lakshmi Pandit was elected the

firstwomanPresidentoftheUNGeneral

Assemblyin1953

GCC: Gulf Cooperation Council is a

politicalandeconomicunionoftheArab

states bordering the Persian Gulf andlocatedonorneartheArabianPeninsula,

namely Bahrain, Kuwait, Oman, Qatar,

SaudiArabia, andUnited ArabEmirates.

AlongwiththeUN,itisplayingakeyrole

intryingtoresolvetheSyriancrisis.

QuickNotes

UNSCResolution1973: Itformed the legal

basis for military intervention in theLibyan

civil war, demanding "an immediate

ceasefire"and authorizingthe international

communitytoestablishano-flyzoneandto

useallmeansnecessarytoprotectcivilians.

10SecurityCouncilmembersvotedinfavor&

5 (Brazil, Germany, &India, and permanent

members China & Russia) abstained, with

none opposing. This led to the defeat &

deathofMuammarGaddafi,thedictatorof

Libya


6/17


EurozoneCrisis

Theissue:TheEuropeandebtcrisis(Eurozonecrisis)isthetermforEuropesstruggletop

thedebtsithasbuiltupinrecentdecades.FiveoftheregionscountriesPortugal,Irela

Italy,Greece,andSpain(calledPIIGS)have, tovarying degrees, failed togenerate enou

economicgrowthtopaybacktheirdebts.Althoughthesefiveareseenasbeingthecountries

immediatedangerof apossibledefault, thecrisishasfar-reachingconsequencesthatexte

beyond their bordersto theworld asawhole.The structure of theEurozone asamoneta

union (i.e., one currency) without fiscal union (e.g., different tax and public pension rul

contributedtothecrisisandharmedtheabilityofEuropeanleaderstorespond.

What is the problemwithGreece?Greece,which spent a lotof years and failedgenerate income, was the first to feel the impact of weaker growth. When grow

slows,sodotaxrevenuesmakinghighbudgetdeficitsunsustainable.Theresultw

that Greecewasforced toannouncethat its debtswere so large thatthey actua

exceedthesizeofthenationsentireeconomy.SinceGreeceisapartoftheEurozon

its problems became theproblemsof Eurozone. Investors responded by demand

higheryieldsonGreecesbonds,whichraisedthecostofthecountrysdebtburdena

requiredaseriesofbailoutsbytheEuropeanUnionandEuropeanCentralBank(ECB

WhathavetheEuropeanGovernmentsdoneaboutthecrisis?Theprimarycouofaction thus farhas been a series of bailouts forEuropes troubled economies.

early2010,whentheEuropeanUnionandInternationalMonetaryFunddisbursed1billioneuros ($163billion) toGreece.Greecerequireda secondbailoutinmid-20

for about $157 billion. OnMarch 9, 2012, Greece and its creditors agreed to a de

restructuring that set the stage for another round of bailout funds. Ireland a

Portugalalso received bailouts, inNovember 2010andMay2011, respectively. T

EurozonememberstatesalsocreatedtheEuropeanFinancialStabilityFacility(EFS

toprovideemergencylendingtocountriesinfinancialdifficulty.

EFSFwas created bythe euromember states following the decisionstaken on9 May 20

withintheframeworkoftheEcofinCouncil(comprisingofEconomicsandFinanceMinisters

the Member States). The EFSFs mandate is to safeguard financial stability in Europe

providing financial assistance to euro area Member States. It is backed by guaran

commitments from the euro areaMember States for a total of780 billion(approx. $10

billion or 1 trillion) and has a lending capacity of 440 billion.Its headquarter is

Luxembourg.

EuroTroika:TheEuropeanCommission,EuropeanCentralBankandInternationalMoneta

Fund,inthecontextofworkingtogethertoresolvetheGreekcrisis,arecalledtheEuroTroika.

EffectofEurozonecrisisonIndia :Duetothiscrisisworldtradehascomedown&thish

alsoimpactedIndiasexportstoEurope.Investorconfidenceisalsolow,whichhasledtoles

ForeignDirectInvestment(FDI)&ForeignInstitutionalInvestment(FII)toIndia.

FDI - investment directly into production in a country by a company locatedanothercountry,eitherbybuyingacompanyinthetargetcountryorbyexpand

operationsofanexistingbusinessinthatcountry.Ithelpsinthegrowthofthecoun

whereinvestmentisdone.

FII-investmentmadebyaninvestorinthemarketsofaforeignnation.Itcanbeeaswithdrawn.However,exitingfromFDIistougherbecauseitsalongterminvestme

intoactualassets.FIIisthemodethroughwhichforeigninvestorsputtheirmoney

stockmarkets.

Schengen Area comprises the

territories of 26 European countries

thathaveimplementedtheSchengen

Agreement signed in the town of

Schengen, Luxembourg,in 1985. The

Schengen Area operates very much

like a single state for international

travel with external border controls

forthosetravellinginandoutofthe

area, but with no internal border

controls when travelling between

Schengencountries.

QuickNotes

What is the difference between

European Union and Eurozone?

European Union is a political union,

consisting of 27 countries. These

countries share common external

tarif fs and have free trade area

amongthem.Eurozoneisamonetary

union where they have a common

currencyEuro,whichpromotestrade,

tourism.17 membersof EUare part

ofEuro.

The Maastricht Treatyestablished the European Union

under itscurrentname in 1993.

The latest amendment to the

constitutional basis of the EU,theTreaty ofLisbon, came into

forcein2009

Estonia isthe latestmember ofEurozone(2010)

UK is a part of EU, but not ofEurozone

The European Parl iament iselected every five years by EU

citizens.

The current President ofEuropeanCouncilisHermanVan

Rompuy Free Trade Agreement (FTA)

betweenIndiaandtheEuropean

Union (EU) is expected to be

signedsoon


7/17


CSAT-QUANTTECHNIQUESFROMINDIAsNo.1APTITUDETRAINERBYJU

INDEX

1)CONSTANTPRODUCTRULE

2)POWERCYCLE

3)MINIMUMOFALLREGIONSINVENNDIAGRAMS

4)LAST2DIGITSTECHNIQUE

5)SIMILARTODIFFERENTGROUPING(P&C)

6)APPLICATIONOFFACTORIALS

7)GRAPHICALDIVISIONFORGEOMETRY

8)ASSUMPTIONMETHOD

1)CONSTANTPRODUCTRULE &

Thisrulecanbeappliedwhenwehavetwoparameterswhoseproductisconstant,orinotherwords,when

theyareinverselyproportionaltoeachother.

eg)TimexSpeed=Distance,Pricexconsumption=Expenditure,Lengthxbreadth=Area

A increaseinoneoftheparameterswillresultina decreaseintheotherparameteriftheparametersare

inverselyproportional.

Letsseetheapplicationwiththefollowingexamples

1)Amantravelsfromhishometoofficeat4km/hrandreacheshisoffice20minlate.Ifthespeedhadbeen6

km/hrhewouldhavereached10minearly.Findthedistancefromhishometooffice?

Solution:Assumeoriginalspeed=4km/hr.Percentageincreaseinspeedfrom4to6=50%or. increasein

speedwillresultin decreaseinoriginaltime=30minutes.(fromgivendata).Originaltime=90minutes=1.5

hoursAnswerisDistance=speedxtime=4x1.5=6km

2)Thereisa20%increaseinpriceofsugar.Findthepercentagedecreaseinconsumptionafamilyshouldadopt

sothattheexpenditureremainsconstant.

Solution:Herepricexconsumption=expenditure(constant)

Usingthetechnique,20%( )increaseresultsin16.66%( )decreaseinconsumption.Answer=16.66%


8/17


2)PowerCycle

Thelastdigitofanumberoftheformabfallsinaparticularsequenceororderdependingontheunitdigitof

thenumber(a)andthepowerthenumberisraisedto(b).Thepowercycleofanumberthusdependsonits

unitdigit.

Considerthepowercycleof2

21=2, 2

5=32

22=4 26=64 2

3=8 2

7=128

24=16 2

8=256

Asitcanbeobserved,theunitdigitgetsrepeatedafterevery4th

powerof2.Hence,wecansaythat2hasa

powercycleof2,4,8,6withfrequency4.

Thismeansthat,anumberoftheform

24k+1

willhavethelastdigitas2 24k+2

willhavethelastdigitas4

24k+3

willhavethelastdigitas8 24k+4

willhavethelastdigitas6(wherek=0,1,2,3)

Thisisapplicablenotjustfor2,butforallnumbersendingin2.

Thereforetofindthelastdigitofanumberraisedtoanypower,wejustneedtoknowthepowercycleofdigits

from0to9,whicharegivenbelow

Forexample

3) Findtheremainderwhen375isdividedby5.

1)Expressthepowerintheform,4k+xwherex=1,2,3,4.Inthiscase75=4k+3.

2)Takethepowercycleof3whichis3,9,7,1.Sincetheformis4k+3,takethethirddigitinthecycle,whichis7

Anynumberdividedby5,theremainderwillbethatoftheunitdigitdividedby5.Hencetheremainderis2.

Sometimes,youmaygetaquestioninthetermofvariables,whereyouneedtosubstitutevaluestogetthe

answerinthefastestwaypossible.

Forexample,

4) Findtheunitdigitof

Putn=1,theproblemreducesto73^4

,whichis781.

Since81=4k+1,takethefirstdigitinthepowercycleof7,whichis7.

5) Whatisthefirstnonzerointegerfromtherightin83301957

+83701982

?

a)3 b)1 c)9 d)noneofthese

83701982

willendwithmorenumberofzeroessoweneedtoconsideronlythefirstpart.Rightmostnon-zero

integeroftheexpressionwillbe=unitdigitof8331957

Unitdigit Powercycle Frequency

0 0 1

1 1 1

2 2,4,8,6 4

3 3,9,7,1 4

4 4,6 2

5 5 1

6 6 1

7 7,9,3,1 4

8 8,4,2,6 4

9 9,1 2


9/17


=unitdigitof31957.

Since1957=4k+1,takethefirstdigitinthepowercycleof3,whichis3.

6) IfN=(13)1!+2!+3!+..+13!

+(28)1!+2!+3!..+28!

+(32)1!+2!+3!+...+32!

+(67)1!+2!+3!+......+67!

,thentheunitdigitofN

is

(a)4 (b)8 (c)2 (d)noneofthese

BasedonPowerCycle

After4!Everynumberisoftheform4k+4,hereweneedtocheckthenatureofthepowertill4!Everytermspowerisoftheform4k+1.

Sotakingthefirstdigitfromthepowercyclesof3,8,2,and7wewillgettheunitdigitas(3+8+2+7=..0).

Ans=0

3)Usefultechniquetofindthelast2digitsofanyexpressionoftheformab

Dependingonthelastdigitofthenumberinquestion,wecanfindthelasttwodigitsofthatnumber.

Wecanclassifythetechniquetobeappliedinto4categories.

TYPE METHOD EXAMPLES

1)Numbersendingin1 Thelastdigitisalways1.

The2nd

lastdigit=productof

tensdigitofbase*unitdigitof

thepower.

In2167

;2isthetensdigitof

baseand7istheunitdigitof

power

1)2167

=__41(2*7=__4_)

2)4187

=__81(4*7=__8_)

3)1261167

=__21(6*7=__2_)

4)31124

=__21(3*4=__2_)

2)Numbersendingwith5 Lasttwodigits:

always25or75

e.g.)155534

=__25

3)Numbersendingin3,7,9 Changethepowersothatthebaseendswith1andthenuse

thesametechniqueasforthose

numbersendingwith1.

eg)34,7

4&9

2allwillendin1.

e.g.)17288=(174)72(takingthepower4as7

4willendin1.

(172*17

2)

72

=(_89*_89)72

(aslast2digitsof172=89)

=(_21)72

(aslast2digitsof89*89=21)

Answer=__41(as2*2=4)

4)Forevennumbers(2,4,6,8) Usethepatternofthenumber

1024=210

i.e.

*210

raisedtoevenpowerendswith76and

*210

raisedtooddpowerends

with24.

e.g.)2788

=(210

)78

*28=

__76*__56=__56.

Itisalsoimportanttonotethat,


10/17


1.76multipliedbythelast2digitsofanypowerof2(>21)willendinthesamelast2digitsasofthatpowerof2

E.g.76*04=04,76*08=08,76*16=16,76*32=32

2.Thelasttwodigitsofx2,(50-x)

2,(50+x)

2,(100-x)

2willalwaysbethesame.Forexamplelast2digitsof

122,38

2,62

2,88

2,112

2.willallbethesame(..44).

Also,lasttwodigitsof112=39

2=61

2=89

2=111

2=139

2=161

2=189

2andsoon

3.Tofindthesquaresofnumbersfrom30-70wecanusethefollowingmethod

7)Tofind412

Step1:Differencefrom25willbefirst2digits= 16

Step2:Squareofthedifferencefrom50willbelast2digits= 81Answer=1681.

8):Tofind432

Step1:Differencefrom25willbefirst2digits= 18

Step2:Squareofthedifferencefrom50willbelast2digits= 49Answer=1849

4.Combiningallthesetechniqueswecanfindthelast2digitsforanynumberbecauseeveryevennumbercan

bewrittenas2*anoddnumber

4)MinimumofallregionsinVennDiagrams

9) Inasurveyconductedamong100meninacompany,100menusebrandA,75usebrandB,80use

brandC,90usebrandD& 60usebrandE ofthesame product.Whatistheminimum possiblenumberof

menusingallthe5brands,ifallthe100menuseatleastoneofthesebrands?

Sumofthedifferencefrom100=(100-100)+(100-75)+(100-80)+(100-90)+(100-60)=95

Againtakethedifferencefrom100= 5(answer)

5)SimilartodifferentGroupinginPermutation&Combination

AllquestionsinPermutationandCombinationfallinto4categories,andifyoumasterthese4categories,you

canunderstandallconceptsinP&Ceasily.

1)SimilartoDifferent

2)DifferenttoSimilar

3)SimilartoSimilar

4)DifferenttoDifferent

Inthisbooklet,wewilllookatthefirstcategory;i.e.SimilartoDifferent,whereIwillgiveauniqueapproachto

thenumberofwaysofdividingnidentical(similar)thingsintordistinct(different)groups


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a)NOLIMITQUESTIONS

Letmeexplainthiswithanexample.SupposeIhave10identicalchocolatestobedividedamong3people.

The10chocolatesneedtobedistributedinto3partswhereapartcanhave zeroormorechocolates.

Soletusrepresentchocolatesbyzeroes.Thestraightredlines(Callthenones)areusedtodividetheminto

parts.Soyoucanseethatfordividinginto3parts,youneedonlytwolines.

Supposeyouwanttogive1

stperson1chocolate,2

nd3chocolatesand3

rd6chocolates.Thenyoucanshowit

as:

Supposeyouwanttogiveoneperson1chocolate,anotherperson6chocolatesandanotherone3,thenitcan

berepresentedas:

Nowiffirstpersongets0,secondgets1andthirdgets9chocolatesthenitcanberepresentedas:

Nowsupposeyouwanttogivefirstperson0,secondalso0andthirdallof10thenyoucanshowitlike:

So,fordividing10identicalchocolatesamong3personsyoucanassumetohave12(10zeroes+2ones)thingsamongwhichtenareidenticalandrest2aresameandofonekind.Sothenumberofwaysinwhich

youcandistributetenchocolatesamong3peopleisthesameinwhichyoucanarrange12things,among

which10areidenticalandofonekindwhile2areidenticalandofonekindwhichcanbedonein Theabovesituationissameasfindingthenumberofpositiveintegralsolutionsofa+b+c=10.a,b,cisthe

numberofchocolatesgiventodifferentpersons.

b)LOWERLIMITQUESTIONS

Now supposewehave a restrictionthat the groups cannot beempty i.e. in the aboveexampleall 3personsshouldgetatleast1.


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Youhavetodividetenchocolatesamong3personssothateachgetsatleastone.Startbygivingthemone

eachinitiallyandtakecareofthiscondition.Youcandothisin just1 wayasallthechocolatesareidentical.

Now,youareleftwith7chocolatesandyouhavetodividethemamong3peopleinsuchthatwaythateach

gets0ormore.Youcandothiseasilyasexplainedaboveusingthezeroesandones.Numberofways=

Theabovesituationissameasfindingthenumberofnaturalnumbersolutionsofa+b+c=10.(a,b,carethe

numberofchocolatesgiventodifferentpersons)

NowsupposeIchangethequestionandsaythatnowyouhavetodivide10chocolatesamong3personsin

suchawaythatthefirstpersongetsatleast1,thesecondatleast2andthethirdatleast3.

Itsassimpleasthelastone.Firstfullfilltherequiredcondition.

Givethe1st

person1,secondperson2andthethirdperson3chocolatesandthendividetheremaining4

(1012-3)chocolatesamongthose3insuchawaythateachgetsatleast1.

Thisissameasarranging4zeroesand2oneswhichcanbedonein6C2ways.

Theabovesituationissameasfindingthenumberofpositiveintegralsolutionsofa+b+c=10suchthat

a>1,b>2,c>3.a,b,cisthenumberofchocolatesgiventodifferentpersons.Inthiscasetheansweris9C2.

10)Rajeshwenttothemarkettobuy18fruitsinall.Ifthereweremangoes,bananas,applesand

orangesforsaletheninhowmanywayscanRajeshbuyatleastonefruitofeachkind?

a)17

C3 b)18

C4 c)21

C3 d)21

C4

ThisisaGroupingtype1SimilartoDifferentquestion,withalowerlimitcondition.M+B+A+O=18

Removeonefromeachgroup,therefore4issubtractedfrombothsides.

TheproblemchangestoM+B+A+O=14.Usingthelogicalshortcutyoujustlearnt,theanswerisbasedonthearrangementof14zeroesand3ones(i.e.17

C3)

11) Therearefourzeroestobeputinfiveboxeswhereeachboxcanaccommodateanynumberof

zeroes.Inhowmanywayscanonedothisif:

a)Zeroesaresimilarandboxesaredifferent

a)275 b)70 c)120 d)19

Whenthezeroesaresimilarandtheboxesaredifferent,itsagroupingtype1question

A+B+C+D+E=4,whereA,B,C,D,Earethedifferentboxes.Thenumberofwaysofselectionand

distribution=8C4=70

12) Thenumberofnonnegativeintegralsolutionsofx1+x2+x310

a)84 b)286 c)220 d)noneofthese

Bynon-negativeintegralsolutions,theconditionsimplythatwecanhave0andnaturalnumbervaluesforx1,

x2,x3,andx4.Toremovethesignaddanotherdummyvariablex4.Theproblemchangestox1+x2+x3+x4=10

Thisisanexampleofgroupingtype1(SimilartoDistinct).Itisthearrangementof10zeroesand3ones.

Usingtheshortcutofzeroesandones,Thereforetheansweris13

C3=286


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6)APPLICATIONOFFACTORIALS

AthoroughunderstandingofFactorialsisimportantbecausetheyplayapivotalrolenotonlyinunderstanding

conceptsinNumbersbutalsootherimportanttopicslikePermutationandCombination

DefinitionofFactorialN!=1x2x3x(n-1)xn

Eg1)5!=1x2x3x4x5=120 eg2)3!=1x2x3=6

LetusnowlookattheapplicationofFactorials

I) Highestpowerinafactorialorinaproduct

QuestionsbasedonhighestpowerinafactorialareseenyearafteryearinCAT.Questionsbasedonthiscanbe

categorizedbasedonthenatureofthenumber(primeorcomposite)whosehighestpowerwearefindingin

thefactorial,i.e

a) Highestpowerofaprimenumberinafactorial:

Tofindthehighestpowerofaprimenumber(x)inafactorial(N!),continuouslydivideNbyxandaddallthe

quotients.

13)Thehighestpowerof5in100!

=20; 4;Addingthequotients,its20+4=24.Sohighestpowerof5in100!=24

ALTERNATIVEMETHOD

=20+4=24(Wetakeupto52

asitisthehighestpowerof5whichislessthan100)

b) Highestpowerofacompositenumberinfactorial

Factorizethenumberintoprimes.Findthehighestpowerofalltheprimenumbersinthatfactorialusingthe

previousmethod.Taketheleastpower.

14)Tofindthehighestpowerof10in100!

Solution:Factorize10=5*2.

1.Highestpowerof5in100!=24 2.Highestpowerof2in100!=97

Therefore,theanswerwillbe24,becausetogeta10,youneedapairof2and5,andonly24suchpairsare

available.Sotakethelessernumberi.e.24&thisistheanswer.

15)Highestpowerof12in100!

Solution:12=22

*3.Findthehighestpowerof22and3in100!

Firstfindoutthehighestpowerof2.

Listingoutthequotients: ; ; ; ; ;

Highestpowerof2=50+25+12+6+3+1=97.Sohighestpowerof2 2=48(outof972s,only48are2 2)

Nowforthehighestpowerof3. ; ; ; ;

Highestpowerof3=48.Thus,thehighestpowerof12=48


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II) Numberofzerosintheendofafactorialoraproduct

Findingthenumberofzeroesformsthebaseconceptforanumberofapplicationquestions.Inbase10,

numberofzerosintheenddependsonthenumberof10s;i.e.effectively,onthenumberof5s

InbaseN,numberofzeroesintheendhighestpowerofNinthatproduct

16)Findthenumberofzeroesin13!Inbase10

Solution:Weneedtoeffectivelyfindthehighestpowerof10in13!=Highestpowerof5in13!Asthispower

willbelesser.

17)Findthenumberofzeroesattheendof15!inbase12.

Solution:Highestpowerof12in15!=highestpowerof22*3in15!=Highestpowerof3in15!=5

III) Numberoffactorsofanyfactorial

Letuslookatanexampletounderstandhowtofindthenumberoffactorsinafactorial

18)Findthefactorsof12!STEP1:Primefactorize12!i.e.findoutthehighestpowerofallprimefactorstill12(i.e.2,3,5,7,11).

12!=210

*35*5

2*7*11

STEP2:UsetheformulaN=am*b

n(a,baretheprimefactors).Thennumberoffactors=(m+1)(n+1)

Thenumberoffactors=(10+1)(5+1)(2+1)(1+1)(1+1)=792.Answer=792

APPLICATIONQUESTIONBASEDONFACTORIAL

20)Howmanynaturalnumbersaretheresuchthattheirfactorialsareendingwith5zeroes?

10!is1*2*3*4*(5)*6*7*8*9*(2*5).Fromthiswecanseethathighestpowerof5till10!is2.Continuinglike

this,10!-14!,highestpowerof5willbe2.Thenext5willbeobtainedat15=(5*3).

Therefore,from15!To19!-Thehighestpowerof5willbe3.

20!-24!HighestPower=4,In25,wearegettingoneextrafive,as25=5*5.Therefore,25!to29!,wewillget

highestpowerof5as6.Theanswertothequestionistherefore,0.Therearenonaturalnumberswhose

factorialsendwith5zeroes.

7)USEOFGRAPHICALDIVISIONINGEOMETRY

Letslookatatechniquewhichwillhelpyousolveageometryquestioninnotime

21) ABCDisasquareandEandFarethemidpointsofABandBCrespectively.

FindtheratioofArea(ABCD):Area(DEF)?


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LetsdividethefigureusingdottedlinesasshowninFigureB.AreaofABCD=100%.AreaAEDG=50%.ThenArea

inshadedregion1(AED)=25%.Similarly,DCFH=50%.Areainshadedregion2(DCF)=25%.NowAreaofEOFB=

25%..Areaofshadedregion3(BEF)=12.5%.Totalareaoutsidetriangle=62.5%.Areainsidetriangle=100-

62.5=37.5%.requiredratio=100/37.5=8:3.TolearnthisdirectlyfromBYJU,referthevideointheCDgiven

8)ASSUMPTIONmethod

This involves assumingsimple values for thevariables in thequestions, and substitutingin answer options

basedon thosevalues.Assumption helps totremendouslyspeeduptheprocess ofevaluatingtheansweras

shownbelow.

22)k&2k2arethetworootsoftheequationx

2px+q.Findq+4q

2+6pq=

a)q2b)p

3c)0d)2p

3

Solution:Assumeanequationwithroots1&2(k=1)

=>p(sumofroots)=3andq(productofroots)=2.

Substituteinq+4q

2

+6pq=54.Lookintheansweroptionsfor54onsubstitutingvaluesofp=3andq=2.weget2p3=54.=>Ans=2p

3.

23)ConsiderthesetS={2,3,42n+1),wherenisapositiveintegerlargerthan2007.DefineXastheaverage

ofoddintegersinSandYastheaverageoftheevenintegersinS.WhatisthevalueofX-Y?

a)1 b) c) d)2008 e)0

Thequestionisindependentofn,whichisshownbelow.

Taken=2.ThenS={2,3,4,5).X=4andY=3.X-Y=1,Taken=3.thenS={2,3,4,5,6,7}.X=5andY=4.X-Y=1

Henceyoucandirectlymarktheansweroption(a).Youcansolvethequestioninlessthan60seconds.

Thereweremorequestionswhichcouldbesolvedusingsimilarstrategies.

Themethodsgivenaboveclearlyshowthatforsomeonewithgood

conceptualknowledgeandrightstrategiesthequantsectionisacakewalk.


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Howarewedifferent?

TypicalProblem UsualApproach TheBYJUsClassesApproach

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