upsc sample booklet online
TRANSCRIPT
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SAMPLENOTES
i) CURRENTAFFAIRSii) CSAT-QUANT
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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.
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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,¬morethan7fromRS
- 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
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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
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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
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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%
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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
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=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,
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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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