(www.entrance exam.net) ma economics entrance question paper 1

8/6/2019 (Www.entrance Exam.net) Ma Economics Entrance Question Paper 1

1/15

pages umber;d drrough 'f i \ lso check hat heAiOf . Br inganymiss ing agcso theat tent ionf ther r r g i l l t t t t l ' .

. ' l ' l r i sp l r r . t l . t l rc x l t r t t i l t l t t i r t t ' r0 t l s i s ts f 20 rn t r l t i p le ' -c l ro iccl t i cs t i0 t ts 'i l t c l t l t t cs t io t ti s t i r l i o rvc r l ry oLr r oss ib lc l l swcrs , neof w5 ic5 s c . t ' t c t t l ' t l i cn tc thc co l - rcc tanswcr n thc bubb le-shec t ' OT on th isbook le t '

Ins t t t t ons :. Ir irst hcck hat hisbooklet asb01lotnf cvcrY agcsmarkcd

. Eaclr orrcct hoicewil l earn ou 1incot ' t ' t 'c l c l t t l icc. I l ' \ ' t . l t t l t l t t lc t t l t tcgct0 for thatqtrcstion.

PART : Onc 'mark ucs t i< tns

mark.Horvcver, 'ottu' i l l ose1/3mark for eacho f t l r c r t r h t l l cs l l l l ( ) l ( ' l t l t t l r l l c h t t l r l r l c ' o t r r v i l l

You nl tv cg i t t orv .Good uck.

I Consider consumer avinga utility function J=2x+)'tvhcrer and1'a.rewoconrmodi t ics.upposchat ihc r ice f x^ndy are othRs.5 cach nd heconslrmcr'sncomesRs,1C0.n equii ibrium,heconsuinervi l l consumehebundle( a ) 1 0 . 1 0 )(b) 0.20)(c) 20,0)(d)none f thcabovc

2. With qr.rantityf r on thehorizontal xis, heEngeicurve or commoditycorlcspondingo theuti l i ty unctionf,=y+flx)will be(a) a raY hrough heorigin(b) a vertical ine(c) a horizontaline(d) a curvewith an nflexionPointhasa fixedcoefficientechnologyQ=Min(2K' 3L)' rvhereQ isare h.enputs,At equilibrium

i t r r lctct ' t t t i t tntc4. A rnonopolist i l l never roduce quantityvherehepriccelastici ty f demandsi r t c l l r s l i ccca t t sc :(a) P > MC in such case(b) MR > MC in sucha case(c) MR < 0 in sucha case( d l P < A T C i n s u c h a c a s e

3. SupposeProduceroutpLrtndK andL(a) K=L. (b) K=(312)L(c) K=(2/3) l -

( t l ) K r t t t l L i r r c

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5, In the igurebelog'g,henhebudgetine drawn n bold)wasoriginal ly F + 10c =200,Anitapurchased0 unitsof F and5 unitsof C' At two ate dates'ines i ) Irtd(2 ) were heUuOlet ines, Anitahad hesame referencesn al l three nstances' s arational onsumer, hichma-rketaskets ighishehavepurchasedt he ater lrtes?

6

7 .

(a) A, B(b) A , D(c) IJ ,c(d)c, I)

Clorhing,C)

original udgetine

d | / r \f o o a t ' )

Nr \ l l l L I in rp l i cs( ; . r )l rc t t tc t t tp l t rY t t l c l l ti l (c s zcro(b) int lat ion s corlstal l li . j t t t . ratc f growth f rcalCDP sconstant(d)none f theabove

I p ug ( )pc r tgg111191) l ) ' r v i t Il c t ' [ cc tcap i t l r l l l ob i l i f y a l d f i xcd cxc l ra t tgcl t t cs ' t t t opc t t

rnu'kct oPct 'at ior t v i l l(a) ncrease ulPLIl nd educenterestate(b) ncrcasehe ttoneYuPPlY(c) iolver he radedeficitioi .r,'*g, the compositionof themonetarybase

If a persons a borrotver' rise'in he nterestatewill(a)alwaYseduce onowng8 .

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(b)alwaysncreaseonowing(c) could ncreaseonolvingdependingnsubsti tutionffects.(cl)noncof thcabovc.

the elative trengths f incomeand

.q Thc .I-cttrvesuggests ha t th e effect of ant r i t t l c r lancc s to :(a) irnProve t in th e short un(b) worsen t in the short ru n(c) leave t unchanged(d ) imProve t in th e long run'

appreciationf thc exchangeateon

10.Jnclcrlassicalupply onclitions,iscal xpansion(a)only aiseshepriceeveland he nterestate(b)cxpanclsupply tconstantrices(c)cxpanclsuppiy t ising ricesiO) .ou.t both upplyandpriceevelunchangedl l .Cons ider the fo l lo rv ing funct ions/ :r -+g t , rvheret deno tes these to fea lnumbers. hich f t ire ollorvin-qunctionssquasi-convex?2( a ) ( r )= . t(b),(r) = cos r

( c ) / ( - t )= c - *(d) ( . r ' ) r ' ' i l . t l0 ; / ( . t ) = 0 i f r = 0

12.Considc annx n matrixA with realentries.f matrixB is clcrived y addinghe irstcolumn f A to the astcolumn f A, then(a)dctA < dctB(b)detA > detB(c ) lc t11= 0 for cvcrY; e 9i

14. f thestatement.,Therexists egislaturendapartysuch hatevery egislatornthatpartypays axes"s false, henwhichof the oliowingstatemcnts us tbe true?(a) n cvery egislature ndeveryparty,al l legislatorso no tPa), axes.(h) l ' l rc lccx is ts lcg is la turcr rCl rhat vcry cg is la torn cvcrY ar ty ocs otpaytaxcs.(c) r rcvcry cg is l l l t t rc ,l tc rc x is ts pf l r ty nc l cg is ln to ll l thntpnr ty v l to locs

the

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n o t p a y t u x c s . . _ , ^(d) In every egislaturcnrievery alty, l iere xists egislator hodocs lotPaytaxes.15. f l : 9 i" -+! l is rv ice r f lbrent iab le ,oncavendhomogeneous

f deg|cc ' t i l c r tthc l css i l r r lt t i t t t ' i xl ' / s( a . t r c g l t i v cl c I t r l l c(b)Posi t ivee l ' in i tc( r ' ) s i r t l " t r l l t t

1 i l t t t l t t - . r t t l q r t' r t

16,Consider nexpcrinrenrn which ive ibers aving ifferentengths restlbjectinq'rr rc,sringroccsso lcrutr 'hic5 iU.r*i ir break iri t ' The engths f the ivc fibeLs t'cl i t r e l r , i t r t ' l t t ' s ' . ' lr r t ' l t c s " lr t c l t c st t t t l5 r t c l t c s 't t p l l t l s cl t cp t o l r i t l r i l i l \ ' l l r r t lt t t Vf iber wi i l bc t l rc irst to brcal i s ploport iol)al o thc lengthol t l t i l t ibcr., l ' l teprobabil i tyf.,arir. ' i , igrh of tfre'f iUlr i tratreaksirst s

not 'norcha.3 irtc'cs s:(a)3/5(b)2t5(c) 1/3(d)2/3

17.Whichol thc ol lowr'g staternentss WRONG:A probabil i ty lcnsity'urtctio(x

(a) canbe used o r-nodel continuousariable(b) nregratcso I over he ange f x(c) ncrcasesteaci i lYrom0 to I(d) mustbegreaterhanor equal o 0 ovcr he ange f x

l s . A p r i n r u y s c h o o l h a s 6 c l a s s e s , n u m b e r e d f r o m l t o 6 ' C l a s s l h a s t w i c e s s m a l ] ystudentsseach f theother lasse' 'wrt" i ' trteprobabil i tyhata randorrlyclectcd

studettts fronral ror'Jci-trutnberedlass?(a ) 0 /21(b)3/7(c) 8l2l(d) 4t719.A uaffic ighton heway o theUniversity'- ot"f Uility-of etting red ight i)2 days(a ) i )0 .16 ;i i )0 '20(b) i )0 '1 ( r ;i i )0 '29(c) i )0 '?.a;i i )O' le(d) none of the above

is rcd40Vo f the ime'What's hein a row; (i i) any2 outof 3 daYs'

coins re ossed' hevariance f Y- is20. *tY den3tehenunlberf headsbtainedhen(a)5.5(b)7'0(c )7 '5(d )8 ,0ASOl


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PART II: Trvo'markqucst ionsI r rs ' t t l t l l t s :. ' l ' l t i s1r : r r l f l l rcc r l t t t t i t t r t t i o t lr l t t s i s tsf 40 mrr l fp lc -c l ro icc t rcs t io r ts l l l nc l rr res t ionis [6l l t l rvct l V I '6ttr rossiblc l lswel 'S,neof rvhicI is ct l t ' tcct ' nt l icatc l tccorrcctnns\\ ' ]crn t l rc lrrbblc-shcct, OT on thisbooklct '. I lachcOr'rccthoicc rvi l l carnyou 2 ntarkS. {orvcvcr, yorr tYi l l osc 2/3 tnnrk ft l rc i lch ncor.rcct hoicc. f you shaclc oneof thc trubblcs r l l lorc t l tnnottc rtrbblc '

r r r rwi l l get0 for thatquestion'

:1. A firmhas heproductionunctionQ= ITL- L2, vhere.Ls abournputandQ iso L r r p l r r .f t h e f i r m i s a m o n o p o l i s tw i t h a d e m a n d c u r v e P ( Q) =0 0 - Q ' r v h a t i s t h elr4fip. MarginaiRevenue roduct f Labour) urve?ro l rzoo 288L zt-z tt(b) 1200 288L-72L2 + 4L3(c )1200-488L 72L2 4L3^(d) 200 488L 72L2 + 4L322.SLrdhirivcs n Gujarat.His totalwealth extyeal ' ncl lCrng ishotrse' ' i l l beRs'-5.00.000,lcrc i i ^ fOpcrcent hancchata 6ig eart6qtrrkc' i l l occttr tcxtvearand

contprlcrelyestroy is rouse,alued tRs'2'00'000'(i) \Vlat is SuOnii 's xpected ealth extyear f hechooseslot o buyhouseinsurance?(i i) Suppose udhir 's ti l i ty unctiontotalwealth n thousandsf rupees'neutral?is givenby U (W) = W05,whereW representsls Sudtrir isk-averse.isk-loving, r risk-

13 .Consirlcr nairport hatprodr-rccsoise N) thatd,ecliness hedistanced) it t' ki lorrrc'tcrs.rol11hcairportncrcases:(d)= I/d7' Prafvl vt-rrkst hcairport'I ' r r l l r l ,sl . r r ' rgc i .onr i ' l i scs l r rpec pct ' r t t i l I t to is t '. l t r r t ls lssr rc in tc t lv i t l t v l tcrcl , r . l r l ' r r li v cs . l i s cos ts .o l ' con t rn r r t i ngrcR t rpcc pcrk i l o r l r c l c t ' ( c i t c l tvnv ) ' l ' l t ccloscst ecan ive to theairport s d = 0'1 km'(i) wrar is thecl istanceraiulwil l l ive rom hcairportn thcabsencefcor t t l tc t ts l t t io t tot ' l rcno isc?(i i) suppose raful s compensatedor hisdamage, hcrever emay ive' HowrnLrchvi l lhc bccomPcnsatcd?

(a) ( i )Rs. ,50,000(b) ( i )R.s.4.50,000(c) ( i )Rs, ,80,000(d ) ( i )Rs.4 ,80 ,00C

and ii ) risk-averseand ii) r isk-neutraland ii) r isk-lovingand ii ) isk-averse

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(a) ( i ) I krn and i i ) Rs ' 100(b) i ) 0 '1 km and i i ) Rs ' 100(c) i ) 1km and i i ) Rs '(d ) i ) 0 ' 1km a ' rd i i )Rs '10024.Supposehecar market s perfectly ompetitiveindeach irm has he same ostsrntcrure. hcrcare1000 irms n the niustry,Themarketdemand ndcost

s e l t c t l t t l c st t c g i v c l t r c ' l r r r r ' '

Costs cr inr r l ts .?00r C S )250 300 350 400 450 500t 10,00 12.40 t2 .106 .40 1 .00 7.6s 8.40MC R 0 0 9.007 . 1 0 7.20 7 .504vqATC 7 ,801 2 . 8 0 7

( X ) t0.22 11 .00I 1 , 0 0 I043 10.06 r0.00

rd

l n t h e l o t r g r t t t t i ^ ^ . L - - , . . , , i l r r , , n r(a)Someirlusw'i l lexit hendustly' utothersvi l l enratniuj Sorn.111rn5villenterhe ndusryi.j ff,. number f firms vill emainhesameia) ftt. industryvillciose own

25.Abhik's ndBnnda's emanduves orapplesre iven yp = 2 0 - q ( A b h i k )p = 5 - ( q / 2 ) ( B r i n d a ),"0;i:'J:,iJ,:';:i:J:lt,y T,n:umersn he rarket,ndhatite rarkcrupprl'function s givenby ' p = 2 + Q'fnen ti'e equilibrium uantity n themarke is :(a) 12aPPIes(b)9 aPPles

(c)6 aPPles( t l )3 i rpp lcs26 . Afarttter's etnatldor rvheats givenby the uncttott:

-nJ;fir;ii"rKry incomendps he riceofvhear.et hearnrcr's.ror)cvinconrebeRs' l0O0.Supposethatrn i t ia l ly, thefarmerpurchaseswheatinthenrar.kforRs. 0 perkg.Now, onsider;ff i t ; ; ; . t t trtt f*'ntt obtainsBPLcardwhichatiows im o purchasep o'ii rt f or *rtt" l:t lt' 5 perkg' Whatwill be hcincreasen hisdertrandor wheat tt'ilui?U'fto heSlutsky ubstitutionficct'/

N,larket etnat 6 ,80 8.40 10.00 I 1 ,60 I 3 .? ( )200

Price iacs/oercar)3 . 6 5 5 20

350 300 250Quantity(thousandsr )

500 .150 400

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(a) .5 g(b) '0kg(c ;4 .5 gtd)5 .0 gr\rrsr 'crhcncxt ourquestionssing he ollorvingnformation' netonomyaswo( l q c | l | r ( ] a n t | 2 ) a n c | 3 t t l t i t s e a c h o f w o g o o d s , X a n |Y , A n o | l o c a t i o n i n t h is e c o n o m yi . t , r t . f i t r c t lt , s r t t r r l t l t ' i f: a . i n ) . ( r r ' l ' r ) ' i t l ' . ) ' 2 ) ) o f n o n ' r t r " c ' t r r ! t ' c r a a lt t , n b c r ' s ' t v l t c r e( . r t . . )t ) r r r r r i ' \2 1 ,2) t t t . t ,l t c r t t t t t l t t t t t s{ 14or ld ' , ;nn t ! , ( . ( , | | . \ .1 ( | | t t ' (l l r . . , \ . ( t ' l r t . t

und 2rc.r l tect ivei t t ,r td (x0,!0) are t l teamounts f the nvo goods cft o" 'e aftcr thet ' o r t , s t t t n l t t i o n o J ' t t t c l w o a g c n t s ( i ' c ' ,g = 3 - x ] - x 2 ' y o = 3 - ) ' 1 - l z ) ' T h e a g e n t s '

u l t i l i t t , toonsun les in t i tec l ,o that fo r eac l tAgent=1,2 , ( r i . . r ' i ) rn t ts f a l i s f i i

. ; * r; < 12. Agcttt t is l t igttcr r t he socialadrterdr t r l t ' / ' r r( :}' /1()() ' f t 't is con' t t tntpt i t tr tbttndlr,(-rt . ,1 Jirst. Agent cl tooscster onsrtmption ttncl lerotr t n' l l r t rentains f t l rct\\,() oodsafter Agertt lns chosetr.At tequilibium fo r thiseconomv 's rrtallocatiort.ruclt lnt( ) (x1 ) maximiz.e'rgent 'sutiliry ubiecto thecotlstratnt's^ ) + y 3 < 1 2 , a n dr < 3 . ) r S 3 . i + Y , = I L ' a n u(2) . ( . r2 . . t '2 ) tax i rn izesgent 'sut i l i ry ubjecto hecot ts t rn l t l ts

r : < J - 1 1 . ' 1< 3 - ) ' t ' " t 3 ' r | < t Z 'I r sg ivet tlnt Age,t 'sut i l i ty f t t t lc t ion1( I1 ,y t) = x l1 '1anct gent 'sut i l i ty funct ior tn1(x2. : ) = ctx2 y2, whee 'a ' isa g iven osi t ive untber '

27.WSicho'c of t6c a l locat ions( ;16) '0 , r1 yr ) ' (xz .r ' : ) spcc i f icd c lorv s ancquil ibriLrrnor thiseconontY?

(a) (0, ), 3,6), 0,3 "6))

r t r )(0 .0) ,s . 2) . (3.6 ' t ) )28. Lct c=1, or Agent2'suti l i ty unction. hen, heequil ibrium llocationn theabovequestions(a ) Pareto fficient, ecauseheslopes f theAgents'indjfferenceurves retangcnt t hatal location'(b) NgtParcto fficicnt, ccauseheslopcs f thcAgcnts ndiffcrcnccurvcs rcnot angent t hatal location'

(c) I)urct. l ' f i i ic.t,bccnuschcrc s a bound nAgctrt 's lbi l i ty to consttl l lc '

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( c l )N o r P a r . c r o c t ' f i c i c n r . a s A g e n t 2 c i u t b e n r a d e b e t t e r o f fv i t h o u t t l l l t k i t l g ' A g c r r tI r i t r l : , c r l

29,Su1 l1 . r0 .scl r c r c i r \ to ro r t t t t ll t t J t c l r i l i t y l ' i l t r ylS0 l l toco l l s t l l l t c 't t t t l o r t o r t l i lchoosehevalueo1 ircpararneter'a'n Agent2'suti l i ty 'unctiotr 'rorwlti l tVitluc l'a' would theequilibriuin n Question be efficient?(a) I(b)""8t . l u6( t l )

30.Now Supposell lat \gertt is higheron hesocialadderharlAgertt ' sor\gcrtt - 'e:ro choose .,. nnru,t"tptionunile beforeAgent I do.es' il other eatures 1'thceconomy reunchangtA'f a =Z'which oneof theallocations( ( x o , ) ' o ) , ( r t , - l ' 1 ) , ( x z ' ) : ) ) b e l o w i s a n e q u i l i b r i u m fo r t h i s m o d i f i e d e c o n o n t ; " ?

(a) (0,0),3, ,5) ,0,3 J3))(b) (0, ),3 ^,Tst,: ^[tus),(JN 5 'l-rusll( c l ( ( 0 ' ) ; , ( ) , JJr 1,.6)i(d) (0,0),2,3 " ' l ' (1, ' \6))

7'lte ollotvittg ittfttrttrutiottapplies o the rtext our questitttts'Cortsidcrdt I cL'()tt()ttt\)

t,,,herelrc totrtirtal vageate(W)is set y tl te o'k' i t ancl t clependsri thee'Ypactcd

ltr ice tat'ct(P" ttt i t l t l ta rale of unertrploVnterttu) irt the fol lott ' i r tg i! 'rr ') ' '\ \ / = P ' l I - c l u ) , w l r c r e a i s a p a r a t t v t c r ; 0 < a < l ' T l t e u c t r u t l p r i c e l e v c l ( P ) t t t t t l t totlwr utul is ssrb), tl teprodttcersltocharge markup over henoninaLwage ]ta

'eo- tnor ;p - ( l* ASW wht:rcA>0 isanother arat t te ter '

3 ' I f rhe rvorker:; re al\\,45,sble o colTectiy uess he price evel then he ri. l tel-

unenrploy,m.n,i ir t l rvays emaintainedta level vhichs givenby:Il ' r \ - _ '\ q, / L + A

al/h\ -_.-\ v / , r 't 1 - AIt r - )' " ' ( l - ) ) gI + a/ . t \ -- -\ " / . 1I - r n

32.Therevi l lbe alrvaY'se ful lonly f theexPectednd heemployment f theaggregatetocko[ Iabour orcc i arld..i . iur rice levelare elatedn thc ollowrngway:

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( a )(b)

+ =

D- =n cI'D/^ \ rP( c l ) - =

I1 +

( l + , i X l - a ),I'ltcfollox'irtgadditiottal rtforntationapplies o the next ttt'oquestiotts' rradditiott otlterttfcrtttarionwenfor tlteabove two^questions,upposeheproduction echnolo.gyssuclt lnt orrc etrtplol,eclorker o,,produreone tnito.fotttpur' et Y' N'::d.L denotetl tt:Lcvcl . f outl tut, ' t l tcevelof enlployntentnd the aggrcgatc tock 'f abour orcercsl)ectivc!\,.tt tlte basis f the wageand price inforntationgiven in ilrc previottsrlrtr:,sti,tt.s',+'rtrkrt ta rclation'rhip eweenP' P' and Y anr'lanstt'cr he ollotuingn+'o

tlrr ' str .s".33.An increasen output eteris aribuseadso(a)arr ncreasen theactual rice evel(b ) a decreasen theactual rice evel

i. j rt.r. ctual ricc cvclwil l rcmain nchanged(cl)givcn nfortnations not' ufficiento concluclc l l i ,thing bout hc changenItc lt l t lPr icccvc-1.1r\n irrc|cascn thcaggrcgatctock l ' labOrOrcc ctc|i 'r '7rri l i ,ttIci tt ls tr(a)an ncreasen theactuai rice evel(b ) a clecreasen the actual rice evel(c) heactuai rice evelwil i remain nchanged(rl)givcrr rt 'cir ation s not strff icicnto concltrdcrr 'r l t ingairotrthc changcnact t ta l r icccvc l'l'ltc.fttllrntittli nfortnaliortapplics o tltc next v'o qucslittns'Cottsitlcr he ollon'inrntctcrocL'onctpticorlel. The gooclsmarket is characteriZcds; ' thc following se t of

( ( / I tQt I ( ) t1s. '( ' - . d o l " d , \ 'I = ln+ p, \ ' -p . iC= e (cxogettouslYiven),,,, ' l rcreo,dt,ar, 00, r, 0, are l lpositiveonstantsnd z'+ F' < 1'' l ' l rcrnottcvttarkct qtri l ibri trmonditions givcnby:i7- : l = / t Y - Y r i : Y ,I'Ansrver hc follorving tlvo

, 7, positive onstants.questionsn hebasis f thismodel:

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3,5It ' utctcst lrc(i) i ttct 'etscs y otteutti t 'incor"neevel f hrs ttl decreaseynD "/ r ' l ' ' u l l l l s' - ' 1 - ( & t - r P t lI(b) --------;- ui)tts1 - ( c t t P t )

i( c ) ' - , - - L l l l l l sl ' - ( ( l r t 1 i , ) / ' 1 1 ,i ':

1(cl) ------- unlts1 ' ( d r + P t ) + * o ,T:

to l t ta in ta i t t qu i t ib r iu r l rn t l t c g t rods ' t t l l l t kc l '

3 6 .A u t t t tlevel ((a )

incrcuscl i gr rVcntr l lc l l txpendi tureG) wi l l incrcasehecqui l ib r i t ln rt tcot l tci') byfr- Lrnitsl - ( a t + p , )

LUllts' " ' 1 - 1a , P , ' )(. ) 1 -- - uni15I - ( q t * i , ) - t p ,161 I unitsI - ( u t . P , ) ' ; o ,/ 2

The ollotvitrg rtfortrrtttioil pplies o the rtext tvo questiorts'uvitrilttts lrtl 0 lrtlt tt t t

housc:lrolt lor 2 rrt.ttt l ts tt, i t l twaSes IVt atuJ trz resPCCtivaly'lrc1;i t,r 'sl i trl ttr

co^surlptiott rt l te ^,y,Ltrtrttthsdenoted y,c, and c., respeci lvely)o tts ot)1(t ' \ttttt:L'

Ih e r u t i l i r y g i v e t t b s ' l o g c ' ' f f i r o g c z ' w h e r e d > 0 i s t h e t J i s c o u n l r a t a ' S l r c i : t t l s ' r tallotved o borrovt'fronther employ.ern the firstmonth'whichshe has o

reptit" tt'itlt

inrerest r tlrc ete , rott herseconclo' ' ' i ' 'La'nings'AhernativelyhecQtr\avc ottte

of her ly6rgc..,., , t i rr ' '1i irrtK)ntl t ,ra rf,) ' i ," in tne ":1,:: earnan i,rterest t tht sct,tcrale . It t rhis 'rutr" '"t ' ' ' ' tl ttsrrlarlrc ol lol i ttg twoquesltotts"

37.Savitr i vi l l optimallydecide o bonow trom her enrployerrt t l te irsttttottt l tl ' rrrrt l

-"tt iy i f t i*- ol io*' ingcondition

s satisfied:(a) rv"> (1-r )x ' ,( b ) ( 1 + 6 ) > ( I r r )( c ) (1 d ) r ' ' '> (1 r ) t v ,

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( d ) 1 + ) < ( 1 + )3 8 ' A s s t r r n i n g th a t t h e a b o v e c o n d i t i o n i s s a t i s f i e d ' .w h e n th e d i s c o u n therbonowtng(a)goes P(b) goes own

( c ) docs io t change( t l ) c l t t l t t o t l t y t ' " t ' t t ' ' " r l t s i s l t ' t l t c i vcn i t t f o t ' t t t l t t i o t r

I i/ / 1 iI

ra te d ) goes P'

3 9 considcr wo openeconomics ith fixedexchangeates' \ 'hcn ltc exchangeatc sru'i ty. l1-,c..onoti .,r-arc charact.r ir.dUy tftt iol lorving sct of cquations'wherei = L 2 ' . / . ' + \C = ( ' , , , ' C l , \ ) i - . { i /. ;l ' = l i7:U , = U i

T, = I,Y,M , = l l 1 n ' + m " Y '

c o r c o z 2 O O ; c r t = c r 2 = 0 ' 5 ; ' = l z = 2 5 0 : G ' = 7 1 ' 1 : ' = 1 2 0 ; t t = t : = 0 ' 4 := t t l r ' . 40;n t , r= 0 '05; i l1 t2 0 '3 thcnwhich f the ol lorv ings rue?

(n)coLrnrrv hasa higher quil ibriumevelof outptl t hancotrntry2 and t runsat l l ( l c l c f i c i ty i s - i \ - r ' i s t r t r t t t ry( t r )country I l tasa lorua,equi l ibr ium evcl of otrtptrt l t r t t t ottrt try ' arl t l t r t t t tsarmclc lf icitvis-ir-visountry(c1 iounr ryf ru ro t ' t ig f , . rcqu i l i | r iumlcve lfo l r tpu t t l t r t t tCo t tn t ryZandt runsatrade lrPlus is-i-visCountry(c.l)ountry t',o. to*erequilibriumevelof otttptrtltan ountry2 and t runsatt. i tt lcirrpltrsis-tr-vis otl l l tryIn tl ic Mundcll-Fleming oclel f a smallopeneconorny 'i th flcxible xchangeatesa'd pcrfccr apital .,"fr i i i i ' , upposetreeconomys initial ly n equil ibrium'f iumpsLrmaxes re ncreased. ha t ttnppenso the eqidlibrit,n cvclsof the country's i)GDP; ii ) interestateand iii) exchangeate?(a) (i) fal ls, i i) fal ls, i i i ) appreciatesiui ii i and ii) remainnchanged;iii)depreciatesi.j i i j falls,ii)anclii i) emninnchanged'(d) All thrcccmain nchangcd'

. : 9i ' + 9i isconvexf and nlYf(a ) (x , ) 9 t 'xg f / ( . r )S r } isconvex(b){(,r, ) 91'x9i | /( 'r) 2 r} isconvex(c){ x tl ' I fG)


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12.I f: 9 i , +9i isdei incdyf ix) f ' e 'dt , henhe erivat ivef/atx > 0 s_ t ,(a ) 2xc ' - c '- 1( b ) 2 x e ' + e '

tc) ( } - - i ) . " '( d ) ( 2 r - l ) . '43 .Thesequencex , , ) ,vherexn ( -1 ) " (1+n - ' )and = l ' 2 ' " '(a)corlvcrgcso I(b)convergeso -1(c)convergeso I ru td-- i(d) convergeso neither nor 1-14 . hesc r l l= r *1 - r r - ' , 1+t - ' ) i s den t i ca lo

( a ) - 1 ' l( b ) - 1 , )( c ) -1 ' 1 )( d ) - l 1 l1 5 . ' l - h cc tU i . , * 1 ' ' r - ' , 1 - t - r l s d c n t i c a lo

t a ) - 1 ' l( b ) - 1 , 1 )( c ) - i ' l )( d ) -1 ,1 ]

4 6 , F o r , y e 9 1 " , l e t l ( " r ,' ' 1 = m a x { l x , - y ' li = 1 " " ' n } ' w h i c h o f t h e t o l l o r v t n gre,r t ions olds or ai l r , : e S'?(a )ri(.r, ) = ri('r, "'1 d$' z)(b)d(r, z) > cJ(x' ; + dU' z)(c ) c/(.r,) > ri('r'1' ;+ d(l' z)(d ) /(.r, i) < ri(.r, ') d(Y'z)47,Given ets Y,

{ . r e X l ' v a } ' } .l t t t t l C" /(a) (r \ - d) x( b ) ( A - B ) x( c ) ( A : B ) x( . ' j ) , ' \ ' - iJ) *

i e rX x l = { ( x , y ) l , r e a n d e Y i ' a n d l c t - Y =\Vhichof the ollowing ormulaes general lyon'ector scts

A' D6 ' = 1 1 j x c ) - ( A x c )f = ( , . l x c ) ' ( B x c )C = ( A x C ) - B( l =,.1 (i l x C)

48,Suppose/: 12 ! i isdcf ined 'by= r" j 'At (0 '0) th is unct ion(a)At ta ins t t rax inrum

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. 1 0- /

5 0 .

(b)At ta i r rs min imum(c)Attains saddle oint(d) sundcf incd

\Vhat s themaximumralueof the unctionn theprevious uestion' ubjecto theconstraints> 0,) > 0, and2x+Y 6?(a)2 .5( l r )4( ' ) l 5( r l )"Bcautiful i t ies epel eople' ookat ndia'smostbeautiful i t ies theyaleamongthc east opulated itiesoi thecountry".Whichof the ollo*'ing statementsi l lustratcsmethod f reasoning ostsimilar o theone n theargument bove?-(a)chi ldrenwhoarespankedend o bemorenaught"v'hanother hi ldren'Henceif achi ld s notspanked,hat hi ld s ess ikeiy o benaughtl"(b)Pesticidesreknown o cause sthma mong onte eople'Ho$'ever'mostasthmat iccoplecnd o ive n reg ions here cstc ic lcs renotcontmonlyused.(c)Thissoftrvarerogram elpsncreasehe$'orkelficicncl ' f i tsusers' s are ult, h.s. ui.rs*have ore ree ime or otheracrivit ies.(d) Duringwarm veather. y crops uffer rompestsmore handuring oolerri ,cathcr.hercforea varm nuironment usthclppcstso multipl l ' '

\ I ' l l r t ' r r v t ' r ' ; t r ' . ( ' l t ' i l v c l t i t l l ( ' l ( ) ; t t l i s t l t t t l c i t y i s r v l t t l t t t ' s l r Y t t l r i r l r ' tl t t ' l l l s l r 1 ' l r t t s\ t t t l t l te i i l i l t ( ) [ l cc i t l cu ,hc thc r o takc thc t ra in o r thc b t r s ,s o l t c t ( ) \ \ cs L t t l i t t \ \ ' l t l t t s l t t scxpectcd travel t ime?( a )Z ( w + z )(l>)Z(w+z)lw-z(c) (tv+z+2)12(d) Noncof theabove

two tcams,A andB, fo r a race. \trat isA wil l comc n first,sccond nd hird?? A classtas rstudents'andonrly ividedntothcprobabilityha t he luee unnersn team(a)3 /6(b )1 /6 !( c ) 31 )2 /61(c l ) /61Supposchat ach ersonutof agroup f4ckisscs. hats heprobabilityhat oclassgroLrp?h) 6 t t4 l( b t / 18k) 4t6(cl)614t.

fr iendss randomly ssigncdo oneof 6hasmorc iran rtcpcrsonrorrrhisi

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5.1. contir luousa*dor:r ariable ashe probabil i ty ensityunction (x) ='113'or:rbetween I and+2, and0 elsewhere.ts mean, ariance ndnredian re:( a ) 1 , 3 / a , V z )(b) ( 'h,3/t,Vz)( c ) ( th , , 1 )(d) (V7,, th)

55.The oint probabil i ty istr ibutionf A andw for a givenpopulationsas fol lols'rvhereA is thc ndividual'sage n yearsandw is theweightshecan ift'AI 5 Years10ki los 0 '03W 20 ki los 0.0230k i i os 0 '01

25 years 40 Years 60 Years 80 Yearso.16 o . t4 o . r2 o '010 , l3 0 .1 0 ,09 0 '000.09 0.08 0.0i 0 00The expcctat iort 1 he tl largi t laldistr ibut ion f A is:(a)36.7Years(b )37 ,6Ycus(c)35 '6Ycats(d )38 .6Yca rs5 ( r . ' , sL r r ' cy t {00 l i kc l l ' vo tc r s ,2 l 5cspo .dcc l ^ t ' a ll t cy 'o r r l d ' t c to t l r c t r l i r r gpu.rya'ci lB5r.rpo,,..tcihat ireywouldvote or theopposition u'ty'Lct.7r cttotcihe racrio,.,"t;;i;k;l), ,;;;t"io prer..reo

he ulingpart)'at tlte trrtcol'tirc

s*.vey,a'd Ietp Ue h! 1'ractionf surveyesponclentshoprefcrrcdhc trl i rtgl i tL'v

Thestatldarcjnor of P is:(a)0 '02:(b) .03s(c)0'0a5(d)0 .0555 T , L . e t X a n dY b e t w o r a n do m va r i a b l e sw i t h E [ X] = 3 , 8 [ Y ] _ 0 , V [ X l ^= t , Y | ) ] ' : , ' 'andE[Xy] = 5

-;; l i i ) cov[x, y]; (i i) hePearsonianoefficientf conelattottbetrveen andY (px.v);i i i) VIX+YI'(a ) .5 ' ' 39

( b )5 '0 . 5 , J( c )5 ,5 , 9(d)5 ,0 .5 , 95g. f y isabinonrialancjomariaibleithparameterst = 4 andP= 0'78' alculateProb(Y 3) o decinrr l laces'(a)0 '15( b ) . 21(c)0 '64(d)0 .?9

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For tlte ollowirtg wo questiortsleas.eote hat hewo'tailert 7ocritical valueor a

.srarrurcliae normal lis;tribution's il:,96and heCorrespondingalueor a one-tailedtc,rr.r 1.645,At the 7o leveLf si.gnificance,hecrit icalvalueor a wo-tai led est s4.58 ontt hc corresponclingituiTo' a one-tailedes t s Q"33' )-5g. n cxaminatroltasgivcn o trvoclassesonsistingf 40 and50 studentsr .cs ' ( .c t ivc ly .n t6c i is tc l l i ssl tcntcan rac lcvns r ' i t1 . s tn t tdardc ' in t ior r f 3 'r r , l r i l c, t l rc cc. ' t rcr ,ss 'c , rc l r r gr .cr i vas s rv i t 'u str r r r r r r r ' r ll c ' i . t i ( ) *of 7 ' or rrhcbasis f a nvo-tailedesi, s there significant ifferulccLrct\r'cclllt cpcrformaltceof the wo classes ta levelof significancef 5Voand17o?(a) There s no significant ifferencen theperformancef thenvo classes t

the570and17aeveis f significance(b) rir.r.l, o rignificantdiffer"encen theperfornrancef theclasses t the57c evelbuino significanti fferencet hc 1q6s'el of significance(c) There s a significant i fferencen theperfonttartcef theclassest helVo levelbuinosignificant ifference r he 5% levelof significancerd) fnere is a significintdifferencen performancet both he590and7Vol cvcs(r0.A sanrpleol lof'300 otersromDistrictA and200voters romDistrictB shorvedtlrat (;% anc] o/orcspecl ivelyveren favour f a giYen andidatc' t a lcvelofsigrri f icancef 5Vo,teit|e hlpolhesishat a) heres a dif ' fcrenceet*'cenhc

11i* . t r . ic ts .b) hccancl ic la tcsprcferrcdn Distr ic t '( . ) - t . t rcrcisnosign i f icantl i f fc rcncecnvecnhc l is t r ic ts r td hcc l tnc i ic la tcis notPreferredrrDistrictA( b ) T h c r e i s n o s i g n i f i c a n td i f f e r e n c e b e tw e e n th e c j i s t r i c t s a n d th e c a n d i d a tels Preferredn DistrictA(c) Th"r;l ;^; Jgnii i .nn,differenceetrveethedistricts nd hecandidatesnotPrcfcn'cdn DistrictA(cl) f-f l"r.- ir-^ igni l ' icant i ffcrcncc ctrvccrthc l istr icts nd hccaltdiciatcsPreferredn DistrictA

lou finish, lmnd in thisbookletalong x'itlt )'our bubblc-tottie invigilators before eaving the exotttination mll'tlJ'tu'shc t t

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