problem sets ce review 2014

8/9/2019 Problem Sets Ce Review 2014

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ENGINEERINGECONOMICSSET 1

SIMPLE INTEREST1. Find the interest on

P6800.00 for 3 years at11 % simple interest.Ans. P2,244.00

2. A man borrowedP10,000.00 from hisfriend and arees topay at the end of !0days "nder 8 % simpleinterest rate. #hat isthe re$"ired amo"ntAns. P10,200.00

3. Annie b"ys a tele&isionset from a mer'hantwho o(ers P2),000.00at the end of 60 days.Annie wishes to payimmediately and themer'hant o(ers to'omp"te the re$"iredamo"nt on theass"mption that moneyis worth 14 % simpleinterest. #hat is there$"ired amo"ntAns. P24,42!.!*

4. #hat is the prin'ipal

amo"nt if the amo"ntof interest at the end of2 + year is P4)00 for a

simple interest of 6 % perann"mAns. P30,000.00

). ow lon m"st a P40,000note bearin 4 % simpleinterest r"n to amo"nt toP41,3)0.00Ans. 304 days

6. -f P16,000 earns P480 in! months, what is theann"al rate of interestAns. 4 %

*. A time deposit ofP110,000 for 31 daysearns P8!0.3! onmat"rity date afterded"'tin the 20 %withholdin ta oninterest in'ome. Find therate of interest perann"m.Ans. 11.*) %

8. A ban/ 'hares 12 %simple interest on aP300.00 loan. ow m"'hwill be repaid if the loadis paid ba'/ in one l"mps"m after three years.Ans. P408.00

!. A pri'e ta of P1200 is

spe'ied if paid within 60days b"t o(ers a 3 %dis'o"nt for 'ash in 30

days. Find the rate ofinterest.Ans. 3*.11 %

10.-t is the pra'ti'e ofalmost all ban/ in thePhilippines that whenthey rant a loan, theinterest for one year isa"tomati'ally ded"'tedfrom the prin'ipalamo"nt "pon release onmoney to a borrower. et"s therefore ass"methat yo" applied for aloan with a ban/ and theP80000 was appro&ed atan interest rate of 14 %of whi'h P11200 wasded"'ted and yo" werei&en a 'he'/ ofP68800. in'e yo" ha&eto pay the amo"nt ofP80000 one year after,what then will be thee(e'ti&e interest rateAns. 16.28 %

11.r. . de la 5r"borrowed money from aban/. e re'ei&ed fromthe ban/ P1,340.00 andpromised to payP1,)00.00 at the end of

! months. 7eterminethe simple interest rateand the 'orrespondindis'o"nt rate or often

referred to as the9an/ers dis'o"nt:.Ans. 1).!2 % ;13.*3 %

12.A man borrowed from aban/ "nder a promissornote that he sined inthe amo"nt pfP2),000.00 for a periodof one year. e re'ei&edonly the amo"nt ofP21,!1).00 after theban/ 'olle'ted thead&an'e interest and anadditional amo"nt ofP8).00 for notarial andinspe'tion fees. #hatwas the rate of interestthat the ban/ 'olle'tedin ad&an'eAns. 13.64 %

13.Anes Abanilla wasranted a loan ofP20,000 by heremployer 5P -nd"striaFabri'ator and5onstr"'tion 5orporatiowith an interest at 6 %for 180 days on theprin'ipal 'olle'ted inad&an'e.


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the pro'eeds on thenote.Ans. P18,800

14.P4000 is borrowed for*) days at 16 % perann"m simple interest.ow m"'h will be d"e

at the end of *) daysAns. P4133.33

1).r. Almaro made amoney mar/etpla'ement ofP1,000,000 for 30 daysat *.) % per year. -f thewithholdin ta is 20 %,what is the net interestthat r. Almaro willre'ei&e at the end ofthe monthAns. P)000


16.A bill for motorboatspe'ies the 'ost asP1200 d"e at the endof 100 days b"t o(ers a

4 % dis'o"nt for 'ash in30 days. #hat is thehihest rate, simpleinterest at whi'h the

b"yer 'an a(ord toborrow money in order tota/e ad&antae of thedis'o"ntAns. 21.4 %

1*.-n b"yin a 'omp"terdis/, the b"yer was

o(ered the options ofpayin P2)0 'ash at theend of 30 days or P2*0 atthe end of 120 days. Atwhat rate is the b"yerpayin simple interest ifhe aree to pay at theend of 120 days.Ans. 32 %

18.Find the dis'o"nt if P2000is dis'o"nted for 6months at 8 % simpledis'o"nts.Ans. P80.00

1!.5omp"te the dis'o"nt ifP2000 is dis'o"nted for 6months at 8 % simpleinterest.Ans. P*6.!2

20.>n ar'h 1, 1!!6 r.Almaro obtains a loan ofP1)00 from r. Abellaand sins a notepromisin to pay the

prin'ipal anda''"m"lated simpleinterest at the rate of ) %at the end of 120 days.

>n ay 1), 1!!6, r.Abella dis'o"nts thenote at the ban/ whosedis'o"nt rate is 6 %.#hat does he re'ei&edAns. P1)13.)6

21.A deposit of P110,000

was made for 31 days.


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31.-f yo" borrowedP10,000 from a ban/with 18 % interest perann"m, what is thetotal amo"nt to berepaid at the end ofone year

Ans. P11,800.0032.#hat is the e(e'ti&e

rate for an interest rateof 12 % 'ompo"nded'ontin"o"slyAns. 12.*) %

33.ow lon will it ta/e foran in&estment to&efold its amo"nt ifmoney is worth 14 %'ompo"nded semi =ann"allyAns. 12

34.An interest rate of 8 %'ompo"nded semi =ann"ally is how manyper'ent if 'ompo"nded$"arterlyAns. *.!2 %

3).A man is epe'tin tore'ei&e P4)0,000.00 atthe end of * years. -fmoney is worth 14 %'ompo"nded $"arterly,how m"'h is it worth at

presentAns. P1*1,*44.4)


36.A man has a will ofP6)0,000.00 from hisfather. -f his fatherdeposited an amo"nt ofP4)0,000.00 in a tr"stf"nd earnin 8 %'ompo"nded ann"ally,after how many years willthe man re'ei&e his willAns. 4.*8 years

3*.r. Adam depositedP120,000.00 in a ban/who o(ers 8 % interest'ompo"nded $"arterly. -fthe interest is s"b@e't to a14 % ta, how m"'h willhe re'ei&e after ) yearsAns. P1*0,14!.**

38.#hat interest'ompo"nded monthly ise$"i&alent to an interestrate of 14 % 'ompo"nded$"arterlyAns. 13.84 %

3!.#hat is the present worthof two P100.00 paymentsat the end of the thirdand the fo"rth year


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years in a 'ontin"o"sly'ompo"nded a''o"ntAns. P6,*)0.00

4!.A mer'hant p"ts in hisP2,000.00 to a smallb"siness for a period ofsi years. #ith a i&en

interest rate on thein&estment of 1) % peryear, 'ompo"ndedann"ally, how m"'h willhe 'olle't at the end ofthe sith yearAns. P4,626.00

)0.A person in&estsP4,)00.00 to be'olle'ted in 8 years.i&en that the interestrate on the in&estmentis 14.) % per year'ompo"nded ann"ally,what s"m will be'olle'ted in 8 yearsAns. P13,2!4.02

)1.-n year ero, yo" in&estP10,000.00 in a 1) %se'"rity for ) years.7"rin that time, thea&erae ann"alinBation is 6 %. owm"'h, in terms of yearero pesos, will be in

the a''o"nt at themat"rityAns. P1),030.00

)2.A 'ompany in&estsP10,000.00 today to berepaid in &e years in onel"mp s"m at 12 %'ompo"nded ann"ally. -fthe rate of inBation is 3 %'ompo"nded ann"ally,

how m"'h prot inpresent day pesos isrealied o&er &e yearsAns. P),202.00

)3.5omp"te the e(e'ti&erate for an interest rate of16 % 'ompo"ndedann"ally.Ans. 16 %

)4.5omp"te the e(e'ti&erate for an interest rate of16 % 'ompo"nded$"arterly.Ans. 16.!8 %


)).5on&ert 12 %'ompo"nded semi =

ann"ally to %'ompo"nded $"arterly.Ans. 11.83 %

)6.5on&ert 12 %'ompo"nded semi =ann"ally to %'ompo"nded monthly.Ans. 11.*1 %

)*.A ban/ is ad&ertisin !.)% a''o"nts that yield

!.84 % ann"ally. owoften is the interest'ompo"ndedaC 7ailybC onthly'C 9i = monthlydC D"arterlyAns. $"arterly

)8.9y the 'onditions of awill, the s"m ofP2),000.00 is left to airl to be held in a tr"stf"nd by her "ardian"ntil it amo"nt to P4),000.00. #hen will theirl re'ei&e the money ifthe f"nd is in&ested at 8% 'ompo"nded$"arterlyAns. *.42 years

)!.#hat is the e(e'ti&erate 'orrespondin to 16% 'ompo"nded daily


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6).-f money is worth 6 %'ompo"nded ann"ally,how m"'h 'an beloaned now if P6,000.00will be repaid at theend of 8 years.Ans. P3,*64.)0

66.A person in&est P4,)00to be 'olle'ted in 8years. i&en that theinterest rate on thein&estment is 14.) %per year, 'ompo"ndedann"ally, what s"m, inpesos, will be 'olle'tedeiht years hen'eAns. P13,2!4.00

6*.-f P)00,000 is depositedat a rate of 11.2) %'ompo"nded monthly,determine the'ompo"nded interestafter * years and !months.Ans. 6!0,84!

68.P200,000 wasdeposited on an"ary 1,1!88 at an interest rateof 24 % 'ompo"ndedsemi = ann"ally. owm"'h wo"ld the s"m on

an"ary 1, 1!!3Ans. P621,1*0.00

6!.Find the nominal ratethat if 'on&erted$"arterly 'o"ld be "sed

instead for 1) %'ompo"nded semi =ann"allyAns. 14.*3 %

*0.#hi'h of the followinhas the least e(e'ti&e

ann"al interest rateaC 12 % 'ompo"nded

$"arterlybC 11.) % 'ompo"nded

monthly'C 11.* % 'ompo"nded

semi = ann"allydC 12.2 % 'ompo"nded

ann"allyAns. 11.* %'ompo"nded semi ann"ally

*1.>ne h"ndred tho"sandpesos was pla'ed in atime deposit that earns !% 'ompo"nded $"arterly,ta free. After how manyyears wo"ld it be able toearn a total interest offty tho"sand pesosAns. 4.)6

*2.


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amo"nt fa'tor is e$"alto 1.34!86Ans. 3 %

102. Ameri'an Hpress5orp. 'hares 1 + %interest per month,'ompo"nded

'ontin"o"sly on the"npaid balan'ep"r'hases made on this'redit 'ard. 5omp"tethe e(e'ti&e rate ofinterest.Ans. 1!.*2 %

103. -f the nominalinterest is 12 %'ompo"nded'ontin"o"sly, 'omp"tethe e(e'ti&e ann"alrate of interest.

Ans. 12.*) %104. 5omp"te the

di(eren'e in the f"t"reamo"nt of P)00'ompo"nded ann"allyat nominal rate of ) %and if it is 'ompo"nded'ontin"o"sly for ) yearsat the same rate.Ans. P3.8*

10). -f the e(e'ti&einterest rate is 24 %,what nominal rate ofinterest is 'hared for a

'ontin"o"sly'ompo"nded loanAns. 21.)1 %

106. #hat is the nominalrate of interest'ompo"nded'ontin"o"sly for 8 years if

the present worth fa'toris e$"al to 0.618*83)Ans. 6 %

10*. #hat is the di(eren'eof the amo"nt 3 yearsfrom now for a 10 %simple interest and 10 %'ompo"nd interest peryearAns. P1))

108. Find the dis'o"nt ifP2,000 is dis'o"nted for 6months at 8 % 'ompo"nd

$"arterly.Ans. P**.66

10!. -f a s"m of moneytriples in a 'ertain periodof time at a i&en rate ofinterest, 'omp"te the&al"e of the sinlepayment present worthfa'tor.Ans. 0.333

110. -f the sinle paymentamo"nt fa'tor for aperiod of ) years is1.33822. #hat is thenearest &al"e of theinterest rate

Ans. 6 %

111. -f the sinle paymentpresent worth fa'tor fora period of 8 years ise$"al to 0.)8201,'omp"te the nearest

&al"e of the rate ofinterest for that period.Ans. * %

112. -f money is worth 8 %'ompo"nded $"arterly,'omp"te the sinlepayment amo"nt fa'torfor a period of 6 years.Ans. 1.60844

113. A s"m of P1,000.00 isin&ested now and left for8 years, at whi'h timethe prin'ipal is

withdrawn.


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at a rate of 0.20 mJs2.7etermine the mass ofthe body in / and insl"s.

Ans. )00 /, 34.3sl"s

4.


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101.!2 /Pa. K E 20*!J/ L.

Ans. 0.4!6) /Jm3

24. 5al'"late thedensity of water &aporat 3)0 /Pa abs and20o5 if its as 'onstant

K is 0.462 /Pa m3J / L.Ans. 2.)! /Jm3

2). At 32o5 and 20) /Paae, the spe'i'weiht of a 'ertain aswas 13.* IJm3.7etermine the as'onstant of this as.Ans. *18.8* J/ L

FLUID MECHANICS andHYDRAULICSSET 2

26. #hat is the spe'i'weiht if air at atemperat"re of 30o5and a press"re of 4*0/Pa abs.Ans. 0.0)2! /IJm3

2*. Air is /ept at apress"re of 200 /Pa absand a temperat"re of30o5 in a )00 liter'ontainer. #hat is themass of airAns. 1.1) /

28.A as at 40o5 "nder apress"re of 21.868 bar

abs has a "nit weiht of362 IJm3. #hat is the&al"e of K for this as

Ans. 1!.3 mJLABSOLUTE ANDKINEMATIC VISCOSITY2!. -f the &is'osity of water

at 68oF is 0.01008 poise,'omp"te its absol"te&is'osity in po"ndse'ondper s$"are foot. -f thespe'i' ra&ity at 68oF is0.!!8, 'omp"te its/inemati' &is'osity ins$"are feet per se'ond.Iote? 1 lb.sJft2E 4*8.8poises.Ans. 2.1110)lb.sJft2,1.0!10) ft2Js.

30.-f the &is'osity of water at

*0o5 is 0.00402 poise andits spe'i' ra&ity is0.!*8, determine itsabsol"te &is'osity in Pasand its /inemati'&is'osity in m2Js and insto/es.

Ans. 0.000402 Pas,4.1110*m2Js, 4.11103sto/e

31.5on&ert 1).14 poises to/inemati' &is'osity in ft2Jsif the li$"id has a spe'i'ra&ity of 0.!64.

Ans. 0.016! ft2Js

32.


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3!. A &erti'al, 'ylindri'altan/ with a diameter of12.00 m and a depth of4.00 m is lled to thetop with water at 20o5G!.*! /IJm3C. -f thewater is heated )0o5

G!.6! /IJm3C, howm"'h water will spillo"tAns. 4.* m3

40. -f ! m3of an idealas at 24o5 and 1)0/Paa is 'ompressed to2 m3, GaC what is theres"ltin press"reass"min isothermal'onditions, GbC whatwo"ld ha&e been thepress"re and

temperat"re if thepro'ess is isentropi'.Nse / E 1.3.Ans. 6*) /Paa, 1060/Paa, 466.4 L or1!3.4o5

41.eli"m at 14! /Pa absand 10o5 isisentropi'ally'ompressed to oneforth of its oriinal&ol"me. #hat is its nal&ol"me / E 1.66Ans. 1488 /Pa abs

42. -f 12 m3of nitroen at30o5 and 12) /Pa abs is

permitted to epandisothermally to 30 m3,what is the res"ltinpress"re #hat wo"ldha&e been if the pro'esshad been isentropi' / E1.40

Ans. )0 /Paa, 34.*/Paa

SURFACE TENSION ANDCAPILLARITY43. #hat is the &al"e of the

s"rfa'e tension of a smalldrop of water 0.) mm indiameter whi'h is in'onta't with air if thepress"re within thedroplet is )61 PaAns. 0.042 IJm

FLUID MECHANICS andHYDRAULICSSET 3

44. A small drop of waterat 80oF is in 'onta't withthe air and has adiameter of 0.02 in. -f thepress"re within thedroplet is 0.082 psireater than theatmosphere, what is the&al"e of the s"rfa'etension

Ans. 0.004!2 lbJft

4). An atomier formswater droplets 4) m indiameter. 7etermine thee'ess press"re withinthese droplets "sin E0.0*12 IJm.Ans. 632! Pa

46.


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between the inside ando"tside of a b"bble ofdiameter 0.003 inAns. 80.0 lbJft2

)4.At 30o5, what diameterlass t"be is ne'essaryto /eep the 'apillary

heiht 'hane of waterless than 2 mm"rfa'e tension is0.0*12 IJm.Ans. 14.6 mm

)).#hat for'e is re$"iredto lift a thin wire rin 6'm in diameter from awater s"rfa'e at 20o5"rfa'e tension is0.0*28 IJm.Ans. 0.02*4 I

)6.#hat is the press"re

di(eren'e between theinside and o"tside of a'ylindri'al water @etwhen the diameter is2.2 mm and thetemperat"re is 10o5"rfa'e tension is0.0*42 IJm.Ans. 6*.) Pa

)*.7istilled water stands ina lass t"be of ! mmdiameter at a heiht of24 mm. #hat is thetr"e stati' heiht NseE 0.0*42 IJm.Ans. 20.64 mm

)8.Find the anle the s"rfa'etension lm lea&es thelass for a &erti'al t"beimmersed in water if thediameter is 0.2) in andthe 'apillary rise is 0.08in. Nse E 0.00) lbJft

)!.7istilled water at 10o5stands in a lass t"be of!.0 mm diameter at aheiht of 24.0 mm. #hatis the tr"e stati' heihtNse E 0.0*42 IJm.

FLUID STATICS60.A depth of li$"id of 1m 'a"ses a press"re of */Pa, what is the spe'i'ra&ity of li$"id

Ans. 0.*14

61.#hat is the press"re 12.)m below the o'ean Nsesp. r. E 1.03 for saltwater.Ans. 126.3 /Pa

62. -f the press"re 23 mbelow a li$"id is 338.44)/Pa, determine its "nitweiht, mass density,and spe'i' ra&ity.Ans. 14.*1) /IJm3,1)00 /Jm3, 1.)

63.-f the press"re at a point

in the o'ean is 60 /Pa,what is the press"re 2* mbelow this point

Ans. 332.82 /Pa64.-f the press"re in the air

spa'e abo&e an oil Gs E0.*)C s"rrfa'e in a'losed tan/ is 11) /Paabsol"te, what is thepress"re 2 m below the

s"rfa'eAns. 28.41) /Pa

6).Find the absol"tepress"re in /Pa at adepth of 10 m below thefree s"rfa'e of oil of sp.r. E 0.*) of thebarometri' readin is*)2 mm.Ans. 1*3.! /Pa

FLUID MECHANICS andHYDRAULICS

SET 4

66.A press"re ae 6 mabo&e the bottom of thetan/ 'ontainin a li$"idreads !0 /Pa.; anotherae heiht 4 m reads103 /Pa. 7etermine thespe'i' weiht of theli$"id.Ans. 6.) /IJm3

6*.An open tan/ 'ontains).8 m water 'o&eredwith 3.2 m of /erosene GE 8 /IJm3C. Find the

press"re at the interfa'and the bottom of thetan/.Ans. 2).6 /Pa, 82.4!8/Pa

68.-f atmospheri' press"reis !).* /Pa and the a

atta'hed to the tan/reads 188 mm&a'""m, nd theabsol"te press"re withithe tan/.Ans. *0.62 /Pa

6!. A weather reportindi'ates the barometripress"re is 2!.*) in ofmer'"ry. #hat is theatmospheri' press"re inpsiAns. 14.61 psi

*0.A press"re ae *.0 mabo&e the bottom of atan/ 'ontainin a li$"idreads 64.!4 /Pa, anotheae at heiht 4.0 mreads 8*.)3 /Pa.5omp"te the spe'i'weiht and mass densitof the B"id.Ans. *)60 IJm3, *86/Jm3

*1.An open tan/ 'ontains).* m of water 'o&eredwith 2.8 m of /erosene E 8.0 /IJm3C. Find thepress"re at the interfa'


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and at the bottom ofthe tan/. Nnit weiht ofwater E !.*! /IJm3.Ans. 22.4 /Pa, *8.2/Pa

*2.-f air had a 'onstantspe'i' weiht of 0.0*6

lbJft3and werein'ompressible, whatwo"ld be the heiht ofthe atmosphere if seale&el press"re were14.!2 psiaAns. 282*0 ft

*3.


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'ontent and the spe'i'ra&ity of soil solids aredetermined in thelaboratory to be 11 %and 2.* respe'ti&ely.5al'"late the followin?aC moist "nit weiht, bC

dry "nit weiht, 'C &oidratio, dC porosity, eCderee of sat"ration.Ans. aC 18; bC 16.22;

'C 0.63 ; dC 0.3! ; eC46.!2 %). -n its nat"ral state, a

moist soil has a &ol"meof 0.00!3) m3andweihs 1*8 I.


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7etermine thefollowin? aC sat. "nitweiht, bC moist"re'ontent when the moist"nit weiht is 1*.), 'Cshrin/ae limit.Ans. aC 20.)8; bC 2.1 %;

'C 20.0* %1).


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SET 3

24.


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of 18 % and a sp. r. of2.*0. 7etermine thefollowin? aC &oidratio, bC deree ofsat"ration, 'C air &oidratio.Ans. aC 0.6*; bC *2.)4

%; 'C 0.11

GEOTECHNICALENGINEERING

SET 4

34.


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/IJm3. -t has a spe'i'ra&ity of 2.6).


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sat"ration, 'C b"l/ sp.r..Ans. aC 0.64 ; bC 0.436 ;'C 1.66

)2.aboratory test data ona sample of sat"ratedsoil show that the &oid

ratio is 0.4) and thespe'i' ra&ity of solidsis 2.6). For these'onditions, determinethe followin? aC water'ontent, bC sat"rated"nit weiht, 'C dry"nit weiht.Ans. aC 1* %; bC 20.!*;'C 1*.!3

)3.A soil sample has a b"l/"nit weiht of 1!.6/IJm3at a water

'ontent of 10 %.7etermine the followinif it has a sp. r. sE2.*? aC &oid ratio, bCper'entae air in &oidsGair &oidsC, 'Cderee of sat"ration.Ans. aC 0.486; bC 14.)%; 'C )).6 %

)4.For a 'ompa'ted soil,spe'i' ra&ity sE2.*2, water 'ontent E18 %, dE 0.!0 zav.5omp"te the followin?aC ero air &oid "nitweiht, bC dry "nit

weiht, 'C deree ofsat"ration.Ans. aC 1*.!1 /IJm3;bC 16.12 /IJm3; 'C *4.18%

)).For a sandy soil, emaE0.*2, eminE 0.46 and sE

2.68.aC #hat is the moist "nitweiht of 'ompa'tion inthe eld if 7rE *8 % andwater 'ontent of ! %.Ans. 18.8! /IJm3

bC 5omp"te thesat"rated "nit weiht.Ans. 20.6* /IJm3

'C 5omp"te the dereeof sat"ration.Ans. 46.64 %

GEOTECHNICALENGINEERING

SET 6

)6.A soil at a 'onstantmoist"re 'ontent showsthe followin when'ompa'ted

7eree of 7ry"nit

at"ration#eiht

40 % 14. )0

/IJm3 *0 % 1*.8!

/IJm3

aC 7etermine thespe'i' ra&ity of soil.Ans. 2.64bC 7etermine themoist"re 'ontent of soil.Ans. 11.86 %'C 7etermine &oid ratio

of the 1*.8! /IJm3

soil.Ans. 0.44*)*.A soil sample has a

nat"ral water 'ontent of22.) % and it is /nownto ha&e a sp. r. of 2.6.-n order to determinethe moist density of thesoil, a portion of soilweihin 224 is p"t ina )00 'm3'ontainer. -t islled with 382 'm3ofwater to ll the

'ontainer. 7etermine thefollowin? aC moist "nitweiht of soil, bC dry "nitweiht of soil, 'C &oidratio.Ans. aC 18.62 /IJm3;bC 1).2 /IJm3; 'C 0.6*8

)8.Followin are the res"ltsof a eld "nit weihtdetermination test "sinthe sand 'one method.7ry "nit weiht of sand

E 16.36 /IJm3#t. of sand to ll the'one

E 1.1) I#t. of @ar O 'one O sanGbefore "seC E )8.! I#t. of @ar O 'one O sanGafter "seC

E 2*.6) I#t. of moist soil from

holeE 32.)) Ioist"re 'ontent ofmoist soil

E 11.6 %7etermine the dry "nitweiht of 'ompa'tion inthe eld.Ans. 1).8)4 /IJm3

)!.A 'lay sample was pla'ein a lass dish.


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60.


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6*.


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). Find two 'onse'"ti&epositi&e odd inteerswhose s$"are di(er by24.

Ans. ) and *6.


23/93

A. 20 5. 229. 21 7. 23

MATHEMATICSSET 2

DIGIT PROBLEMS

24.-n a twodiit n"mber,the "nitMs diit is 3reater than the tenMsdiit. Find the n"mber ifit is 4 times as lare asthe s"m of its diits.Ans. 36

2).


24/93

Ans. 12.)*

AGE PROBLEMS

41.ne pipe 'an ll a tan/in ) ho"rs and anotherpipe 'an ll the sametan/ in 4 ho"rs. Adrainpipe 'an empty thf"ll 'ontent of the tan/in 20 ho"rs. #ith all thethree pipes open, howlon will it ta/e to ll thtan/Ans. 2.)0 hrs

)).A swimmin pool is llethro"h its inlet pipeand then emptiedthro"h its o"tlet pipe i8 ho"rs. -f water entersthro"h its inlet andsim"ltaneo"sly allowedto lea&e thro"h itso"tlet, the pool is lledin *.) ho"rs. Find howlon will it ta/e to ll thpool with the o"tlet'losed.

Ans. 3 hrs)6.


25/93

hrs, 4 hrs, and 6 hrs,respe'ti&ely. #hatfra'tion of the @ob 'anthey nish in one ho"rwor/in toetherAns. 3J4

)*.A father and his son

'an di a well if thefather wor/s 6 hrs andhis son wor/s 12 hrs orthey 'an do it if thefather wor/s ! hrs andthe son wor/s 8 hrs.ow lon will it ta/e forthe son to di the wellaloneAns. 20 hrs

)8.Peter and Pa"l 'an do a'ertain @ob in 3 hrs. >na i&en day, they wor/

toether in 1 hr thenPa"l left and Peternishes the rest of thewor/ in 8 hrs. ow lonwill it ta/e Peter to dothe @ob aloneAns. 12 hrs

)!.7elia 'an nish a @ob in8 hrs. 7aisy 'an do it in) hrs. -f 7elia wor/edfor 3 hrs and then 7aisywas as/ed to help hernish it, how lon will

7aisy ha&e to wor/ with7elia to nish the @obAns. 1.!2 hrs

60.Hle&en men 'an nish the@ob in 1) days. Fi&e menwere wor/in at the startand after 6 days fo"r menwere added. ow manydays will it ta/e to nishthe @ob

Ans. 21 days61.


26/93

remainin wor/for'e to'omplete the @obAns. 80 days

*0.


27/93

Ans. 360 mph83.An airplane Byin with

the wind too/ 2 hrs totra&el 1000 /m and 2.)hrs in Byin ba'/. #hatwas the wind &elo'ity in/phAns. )0 /ph

84.


28/93

Ans. )00 /

MATHEMATICSSET 6

!).A 40ram alloy'ontainin 3)% old tobe melted with a 20ram alloy 'ontainin)0% old. ow m"'hper'entae of old isthe res"ltin alloyAns. 40%

!6.


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110. Find the thirdproportional to thes$"are of 2 and the'"be root of 8Ans. 1

111.


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ENN DIAGRAM

122. An enineerinprofessor 'ond"'ted as"r&ey reardin thefa&orite s"b@e'ts of thest"dents. nly 1)st"dents li/e all thethree s"b@e'ts. ow

many st"dents weres"r&eyedAns. !)

123. -n a 'lass of 40st"dents, 2* li/es5al'"l"s and 2) li/e5hemistry. ow manyli/e both 5al'"l"s and5hemistryAns. 12

124. n one h"ndredparti'ipants in aseminar? 80 are 5H, 30are H, 20 are HH, 1!are both 5H and H, 2are both H and HH, 10are both HH and 5H, and1 is a 5H, H, and HH.aC ow many

parti'ipants are 5Honly

Ans. )2

bC ow manyparti'ipants are Honly

Ans. 10

'C ow manyparti'ipants are HHonly

Ans. !

12!. -n a s"r&ey'ontainin the smo/inhabits of 'ons"mer, itwas fo"nd that ))%smo/e 'iarette A, )0%smo/e 'iarette 9, 40%smo/e 'iarette 5, 30%smo/e 'iarette A and 20% smo/e 'iarette A

and 5, 12% smo/e'iarette 9 and 5, only10% smo/e all three

3


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'iarettes. #hatper'entae of thepop"lation did notsmo/eAns. *%

130. ta/en 3at a timeAns. 60 ways

133. ow manyperm"tations 'an bemade o"t of the letters in

the word -HAI-AAns. 4)3,600 ways134. ow many

perm"tations 'an bemade o"t of the letters inthe word -AI7 ta/info"r letters at a timeAns. 360 ways

13). ow many 4 diitn"mbers 'an be formedwitho"t repeatin anydiit, from the followindiits 1, 2, 3, 4 and 6.

Ans. 120136. ow many

perm"tations 'an be

made o"t of the lettersof the wordHI-IHHK-IAns. 2**,200 ways

13*. ow many ways 'an3 men and 4 women beseated on a ben'h if thewomen are to betoetherAns. )*6 ways

138. -n how many ways'an ) people line "p topay their ele'tri' billsAns. 120 ways

13!. -n how many ways'an ) people line "p topay their ele'tri' bills iftwo parti'"lar personsref"se to follow ea'hotherAns. *2 ways

140. ow many ways 'an* people be seated at aro"nd tableAns. *20 ways

141. -n how many relati&eorders 'an we seat *people at a ro"nd tablewith a 'ertain 3 peopleside by side.Ans. 144

142. -n how many ways'an we seat * people in

a ro"nd table with a'ertain 3 people not in'onse'"ti&e order

Ans. )*6 ways143.


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Ans. 3,628,80014*. -n how many ways

'an 4 persons beseated in a ro"nd tablewith 4 seatsAns. 6

148. A lare horiontal'ir'"lar rin has 8hoo/s aro"nd its'ir'"mferen'e. -n howmany ways 'an 8di(erent lanterns beh"n with one lanternon ea'h hoo/Ans. ),040

14!. P,I>P, >PIand PI>.ow manyperm"tationsare there for! lettersta/en ! at atime

Ans. !

1)6.ow manyperm"tationsare their ifthe lettersPIK5H areta/en si at atime

Ans. *20

1)*.Fo"r di(erent 'oloredBas 'an beh"n in a rowto ma/e a'oded sinaow manysinals 'anbe made if asinal'onsists ofthe display oone or moreBas

Ans. 64

1)8.A perm"tation is anorderedarranemenof anyn"mber ofthins.


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$po, 24perm"tations of theletters r, s, t,& ta/en fo"rat a time.ow manyperm"tation

s are thereof the siletters r, s, t,", &, w ta/ensi at atime

Ans. *20

1)!.A fa'tory b"ildin has8 entran'edoors. -nhow manyways 'o"ld aperson enterand lea&e.

by any door

Ans. 64 ways

by di(erent door

Ans. )6 ways

160.ow many

perm"tations 'an bemade o"t of

the letters inthe word5>PN


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herself, inhow manyways 'anshe assinseats to theother

Ans. 144 ways

1*0.ow many di(erentways 'an )people line"p to paytheirtelephonebills at theeral'ooQ'e in anyorder

Ans. 120 ways

1*1.i boys @oin hands. -nhow manyways 'anthey formstraiht line

Ans. *20 ways

5>9-IAI

1*2.ow many ways 'anyo" draw 3

DNHHIs and2 L-Is

from a de'/ of)2 'ards

Ans. 24 ways

1*3.ow many ways 'an yo"in&ite any oneor more of

yo"r &efriends to yo"rbirthdayparty

Ans. 31 ways

ow many ways 'an a'ommittee of&e besele'ted fromanoraniation

with 3)members

Ans. 324,632 ways

ow many line sements'an be formedby 13 distin'tpoint

Ans. *8

-n how many ways 'an a

hostess sele'tsi l"n'heon"ests from 10

women if sheis to a&oidha&in aparti'"lar twoof themtoether atthel"n'heon

Ans. 140 ways

A semi'ond"'tor 'ompanywill hire *men and 4women. -nhow manyways 'an the'ompany'hoose from! men and 6women who

$"alied forthe position

Ans. )40 ways

178.How many two digit

combinations can be o!med"sing digits 0 to 9#$ns. 45

179.How many t%!ee digitcombinations can be o!med o"t

o digits 0 to 9#$ns. 120

180.How many o"! digit

combinations can be o!med"sing digits 0 to 9#

$ns. 210

181.ow many &e = diit'ombinations 'an beformed o"t of diits 0 to !Ans. 2)2182.ow many si = diit'ombinations 'an beformed o"t of diits 0 to !Ans. 210183.ow many three =letter 'ombination 'an beformed "sin all the lettersin the alphabetAns. 2,600

184.ow many fo"r = lette'ombinations 'an beformed "sin all the lettersin the alphabetAns. 14,!)018).ow many eiht =letter 'ombination 'an beformed "sin all the lettersin the alphabetAns. 1,)62,2*)186.ow many ten = letter'ombinations 'an beformed "sin all the letters

in the alphabetAns. ),311,*3)

3


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18*.ow many twel&e =letter 'ombinations 'an beformed "sin all the lettersin the alphabetAns. !,6)*,*00188.ow many'ombinations 'an be madeo"t of the letters A957

and H ta/en two at a time.Ans. 1018!.ow many trianlesare determined by 8points, no three of whi'hare 'ollinearAns. )61!0.9A9--ne'ard is drawn, followed byanother. #hat is theprobability of ettin an A'then a LinAns. 4 J 66320).A sinle de'/ of playin'ards is sh"Sed well. >ne'ard is drawn, followed byanother. #hat is theprobability of ettin D"eethen another D"eenAns. 1 J 221

206.A sinle de'/ of playin'ards is sh"Sed well. >ne'ard is drawn, followed by

3


36/93

another. #hat is theprobability of ettin twoA'esAns. 1 J 22120*.A ba 'ontains 3 whiteand ) red balls. -f two ballsare drawn in s"''essionwitho"t repla'ement, what

is the probability that bothballs are whiteAns. 3 J 28208.A ba 'ontains 3 whiteand ) bla'/ balls. -f twoballs are drawn ins"''ession witho"trepla'ement, what is theprobability that both ballsare bla'/Ans. ) J 14

20!.A ba 'ontains 3 whiteand ) bla'/ balls. -f twoballs are drawn ins"''ession witho"trepla'ement, what is theprobability that the twoballs are of the same'olorAns. 13 J 28210.A ba 'ontains 3 whiteand ) bla'/ balls. -f twoballs are drawn in

s"''ession witho"trepla'ement, what is theprobability that two balls aredi(erent 'olorsAns. 1) J 28211.-n lotto there are pinpon balls n"mbered from 1to 4). si balls are drawn,

one at a time, to determinethe winnin 'ombination inany order. 7etermine theprobability of winnin thislotto.Ans. 1 J 8,14),*86212.A ba 'ontains 4 redballs, 3 reen balls, and )bl"e balls. #hat is theprobability of not ettin thered ball in rst drawAns. 2 J 3213.


37/93

mar/ for a wron answer. -fthe probability that ary'orre'tly answers a$"estion in a test is 2J3,determine the probabilitythat ary ets two mar/s.Ans. 4 J !22).A mar/sman hits *)%

of all his tarets. #hat isthe probability that he willhit ea'tly 4 of his net 10shotsAns. 0.01622226.A two = diit n"mberis 'hosen randomly. #hatis the probability that isdi&isible by *Ans. 13 J !022*.>ne bo 'ontains fo"r'ards n"mbered 1, 3, ),and 6. Another bo'ontains three 'ardsn"mbered 2, 4, and *. >ne'ard is drawn from ea'hba. Find the probabilitythat the s"m is e&en.Ans. * J 12228.ne letter is ta/enfrom ea'h of the wordsPAKAH and HH at

random. #hat is theprobability of ettin thesame letterAns. 1 J )230.-n a shootin ame, theprobability that 9otoy and


38/93

repla'ement, what is theprobability that both ballsare bla'/Ans. ) J 14246.A ba 'ontains 3yellow and ) bla'/ balls. -f2 balls are drawn ins"''ession witho"t

repla'ement, nd theprobability that the to ballsdrawn are both yellow.Ans. 3 J 2824*.A ba 'ontains 3yellow and ) bla'/ balls. -f2 balls are drawn ins"''ession witho"trepla'ement, nd theprobability that the ballsdrawn are one yellow andone bla'/ ball.Ans. 1) J 28

248.From a ba 'ontainin4 bla'/ balls and ) whiteballs, two balls are drawnone at a time. Find theprobability that both ballsare bla'/. Ass"me that therst ball is ret"rned beforethe se'ond ball is drawn.Ans. 16 J 8124!.-n the H5H 9oardHaminations, theprobability that aneaminee will pass in ea'hs"b@e't is 0.80. #hat is theprobability that an

eaminee will pass at least 2s"b@e'tsAns. 0.64AK-I2)0.#hat is the )0thterm ofthe proression 3, ), *, !VVAns. 101

2)1.#hat is the s"m of therst )0 terms of theproression 3, ), *, ! VVVAns. 2,6002)2.#hat is the 30thterm ofthe proression =1), 13, 11,! V.Ans. 432)3.


39/93

Arth"r. ow m"'h isArth"rMs hareAns. P4, 00026!.P36, 000 is to bedi&ided amon Arth"r,9ernard and 5arlos s"'hthat their shares in sameorder form an arithmeti'

proression. 9ernardMsshare is 3 times that ofArth"r. ow m"'h is9ernardMs shareAns. P12, 000

2*0.ow many terms ofthe proression 3, ), * Vm"st be in order that theirs"m will be 2600Ans. )02*1.#hat is the s"m of the

proression 4, !, 14, 1! V"p to the 20thtermAns. 10302*2.A eodeti'Hnineerin st"dent ot as'ore of 30% on n the lastn"mber he ot !0% inwhi'h a 'onstantdi(eren'e more on ea'hn"mber than he had onthe immediately pre'edinone. #hat was his a&eraes'ore in "r&eyin

Ans. 602*3.-n a pile of los, ea'hlayer 'ontains one more lothan layer abo&e and the top'ontains @"st one lo. -f thereare 10) los in the pile, howmany layers are thereAns. 14 layers

2*4.Find the 30thterm of theA.P. 4, *, 10 V..Ans. !12*).-n a ra'in 'ontest,there are 240 'ars that willha&e pro&isions that will lastfor 1) ho"rs. Ass"min'onstant ho"rly 'ons"mptionfor ea'h 'ar, how lon willthe f"el pro&isions last if 8'ars withdraw from the ra'ee&ery ho"r after the rstAns. 2)

2*6.


40/93

n"mbers namely 8)0 and2)0 are remo&ed, what isthe arithmeti' mean of heremainin n"mbersAns. 42.31286.Find the s"m of these$"en'e 2), 30, 3) V.Ans. ) J 2 Gn2O !nC

28*.#hat is the s"m of thefollowin nite se$"en'eof terms 18, 2), 32V.6*Ans. 340288.Find the $"otient ofthe s"m of all odd inteersbetween 100 and 1000when it is di&ided by !.Ans. 2*)0028!.Find the $"otient ofthe s"m of all e&eninteers between !!! and!!!! when it is di&ided by

!.Ans. 2*4!)002!0.7etermine the s"m ofthe odd n"mbers from 1 to61 of the followininteers.Ans. !612!1.7etermine the s"m of the followin series E2 O ) O 8 O 11 V.. with100 terms.Ans. 1)0)02!2.Find the s"m of therst ne&en positi&einteers.

Ans. n Gn O 1C2!3.Find the s"m of the rstnpositi&e interal m"ltipliesof 4.Ans. 2nGnO 1C2!4.Find the s"m of then"mbers di&isible by 6 thatlie between *) and 1!0.

Ans. 2)082!).A sta'/ of bri'/s has 61bri'/s at the bottom layer,)8 bri'/s in the 2ndlayer, ))bri'/s in the 3rdlayer and soon, "ntil the last layer whi'hhas 10 bri'/s. 7etermine thetotal n"mber of bri'/s "sed"p.Ans. 63!2!6.#hi'h of the followinfra'tion is wron to form anA.P. 2*.)J14, 33J28, 4)J28,

and 1*.)J14.Ans. 33 J 282!*.-f !x, !", !zare in A.P.

then y is e$"al toAns. 2xzJ GxOzC

2!8.


41/93

Ans. 3313.1J), 1J8, )J and2)J)12 form a eometri'proression. #hat is the&al"e of Ans. 64314.2J*, 3J14, !J)6 and

2*J form a eometri'proression. #hat is the&al"e of Ans. 22431).#hat is the &al"e of in the eometri'proression 1J3, 4J, and16J2*Ans. !316.


42/93

the net se'ond? 144 mon the third se'ond andso on. Find how far thebody falls d"rin the *thse'ond.Ans. 11664333.Find the &al"e of

from the i&eneometri' Proression1J), 2J, 4J4)V.Ans. 1)334.


43/93

3)0.A ball is thrown&erti'ally "pward to aheiht of 100 m. Ha'htime the ball stri/es thero"nd the rebo"nd is+ of the pre&io"sheiht. ow far has theball tra&eled "p and

down when it stri/esthe ro"nd to the )thtimeAns. 38*.) m

3)1.


44/93

36!.A r"bber ball is madeto fall from a heiht of )0ft. and is obser&ed torebo"nd 2J3 of thedistan'e it falls. ow farwill the ball tra&el before'omin to rest if the ball'ontin"es to fall in this

mannerAns. 2)03*0.


45/93

3!0.


46/93

if the prod"'t of theroots is 4Ans. 1*J2

413.-f the roots in the$"adrati' e$"ation a2O b O ' E 0 are 3 and2, nd a O b O '.Ans. 2

414.


47/93

Ans. 1)J16440.-n the epansion of

G O 4yC12, what is then"meri'al 'oeQ'ient ofthe )thtermAns. 126,*20

441.#hat is the middleterm in the epansion

of G2

= 3C8

Ans. )6*0 8

442.


48/93

2C, what is theremainderAns. 2y

468.-f G)3= 14 O 3C isdi&ided by G = 2C, whatis the remainderAns. 1)

46!.


49/93

4!3.#hi'h of the

followin n"mber is not

a prime n"mber

aC 33 'C *bC 13 dC 1!

4!4.#hi'h of the

followin n"mber is not

a prime n"mber

aC 31 'C )bC 1! dC **

SIGNIFICANT FIGURES

4!).Ko"nd o( 12.048*!

to fo"r sini'ant

"res.

aC 12.0) 'C 12.0488bC 12.04!dC 12.048*!4!6.Ko"nd o( 0.002*86

to three sini'ant

"res.

aC 0.002*! 'C0.0028

bC 0.003 dC 0.002*864!*.Ko"nd o( 102.48886

to fo"r sini'ant "res.

aC 102.48! 'C102.48886

bC 102.) dC 102.48!

4!8.


50/93

Ans. *)13.#hat is the &al"e of

Glo ) to the base 2C O Glo

) to the base 3C

Ans. 3.*!

)14.-f lo of 2 to the base

2 pl"s lo of to the base

2 is e$"al to 2, nd the

&al"e of .

Ans. 2)1). -f G2 lo to the base

4C = Glo ! to the base 4C E

2, nd .

Ans. 12)16.ol&e for the

simplied &al"e of"Elo 20e.Ans. y E lo eJ Glo

2 O 1C)1*.ol&e for the

simplied &al"e of y Elo 20e3.Ans. y E G3 lo eC

Glo 2 O 1C)18.Find the &al"e of ? lo 6

O lo 4 E lo 4 Olo G32 O 4CAns. 3

)1!.


51/93


52/93

Ans. !

)63.ol&e for if4n O 2= 24G4n = 1C

E10G4n O 1C

Ans. T)64.ol&e for if 8E 2y O 2

and 163 = y

E 4y

Ans. 2)6).-f 8E 3, nd the

&al"e of 26.Ans. !

)66.ol&e for ? 16= O 1 E 8Ans. T

)6*.-f !E ), what is the&al"e of 34Ans. 2)

)68.ol&e for y if y E GeOeC2= Ge= eC2

Ans. 4

)6!.-f to the U power

e$"als 8, nd the &al"e

of .

Ans. 16)*0.-f 42 O 1E 1024, nd

the &al"e of 4

Ans. 16)*1.-f 3 O 1E 81, nd 32 = 1

Ans. 243)*2.#hat is the &al"e of

102O1if 10E )Ans. 2)0

)*3.-f 8E 3, what is the&al"e of 83 O 1Ans. 216

)*4.ol&e for ? E G1J2*C2J3

Ans. !)*).ol&e for a in the

e$"ation?

a E 644y.Ans. 43 O y

MATHEMATICS

SET 24

)*6.implify 3= 3 = 1= 3 =2.Ans. ) G3 =2C

)**.#hi'h of the

followin is tr"e

a. 2 2 E 2b. 24 E 4 6'. 10 E ) O 2d. ))O ))O ))O ))O ))

E )6

An-. (!!" d.

)*8.ol&e for ? E 18

*2 O )0.

Ans. 2 2)*!.ol&e for ?

= 1 = E 1 Ans. 16J2) X 0

)80.implify324 3164O 2 3)44

Ans. )

3

24

)81.ol&e for ? 3 ) O 1E 6O 2

Ans. 2.1)44)82. Ga2b3C2

implify a2b1

Ans. a6b*

)83. G3Cis e$"al to?Ans. 3\2

)84.ol&e for ? 3* O 1 E6)61

Ans. 1

)8).-f 3a E *b, then 3a2

J*b2E Ans. * J 3

)86.ol&e for N ifN E 1 = 1 =1 V.Ans. 0.618

)8*.-f to the U power

e$"als 8, then e$"als?

Ans. 16)88.-f 33yE 1, what is the&al"e of yJ33

Ans. 0)8!.Find the &al"e of tha

will satisfy the followinepression?

= 2 E O 2Ans. E ! J 4

)!0.e3is e$"al to?Ans. 0.04!*8*

)!1.b to the mJnth

power ise$"al to?Ans. nthroot of b to

the m power)!2.Find from the

followin e$"ations?

2*E !y

81y3 E 243Ans. 1

)!3.ol&e for a if GamCGanC E100,000, anJamE 10 andamnE 100,000.Ans. 31.06

)!4. G2y32C3G3y3C1J2

implify

Gy3C)J2

1Ans.

2y*3

)!).implify the

followin?

5

*a O 2 = 8 G*a O 1C O ) G*aC Ans G1 O bC J G1 Ans 18 = i 616 -n the 'omple n"mbe


53/93

* = 8 G* C O ) G* CO 4! G*a = 2C.Ans. *a

)!6. implify?

(y1C4 G2y2C3

G2y3C4 G3y3C3

1

Ans. 3y

)!*.implify the followin?

) 3

) O 3Ans. 4 1)

)!8.#hi'h of the followinis e$"i&alent to m naAns. mna

5.S'(8 &'" 9 &"'# !%*$8n :a!$'n+

48 32 8 E 2 Ans. 2600.ol&e for if

8 34 4 E 4Ans. 16

601.Kationalie thedenominator anddetermine thetransformed fra'tion

a1J2

a1J2 a1J2b1J2

Ans. G1 O bC J G1 =bC

602.


54/93

Ans. *062*.Perform the indi'ated

operation? ! 3343Ans. 21i

628.#hat is the $"otientwhen 4 O 8i is di&ided

by i3

Ans. 8 O 4i

62!.#hat is theeponential form of the'omple n"mber 4 O3iAns. ) e i 36.8*

630.#hat is the alebrai'form of the 'omplen"mber 13 e i6*.38Ans. ) O 12i

631.ol&e for that satisfy

the e$"ation 2O 36 E! = 22.Ans. 3i

632.H&al"ate ln G) O 12iCAns. 2.)6) O1.1*6i

633.Find the &al"e of andy in the e$"ation? G3 OyC O G = yCi E G18 = 2iCAns. E 4, y E 6

634.#hat is the &al"e of and y in the e$"ation?

2 O )y O 3yi = 1) =3iE 0

Ans. ), y 163).#hat is the &al"e of

and y in the e$"ation? G3O 2yC = G3 O 3yCi E ) = !iAns. E 1, y E 4636.#hat is the &al"e of

and y in the e$"ation?

O 2y O G3 = 2yCi E G2 O

3iC = G1 O 2iC

Ans. E 0.), y E 263*.Find the &al"e of and y

in the e$"ation? = 4yi O) = 8i E 0Ans. E ), y E 2

638.Find the &al"e of and yin the e$"ation? G O yiCG1 = 2iC E * = 4i

Ans. E 3, y E 263!.Hpress 3 O 4i in

trionometri' form.Ans.

) G'os )3.130O i sin

)3.130C

640.Hpress 2 G'os 300O -sin 300C in alebrai' form.Ans. 3 O i

641.Hpress 4 'is 60 inalebrai' form a'omple n"mber.Ans. 2 O 23i

642.


55/93

pfra'tions?

O 2 2= * O 12Ans. 6 ) = 4 =3

MATHEMATICSSET 26

6)8.Kesol&e into partialfra'tions?

32= 8 O ! G = 2C3

Ans. 3 4) = 2 G = 2C2 G= 2C3

6)!.Kesol&e the followin

into partial fra'tionsand 'omp"te the s"mof A, 9, 5, 7 and H.

3O 42O ) O 3 AG O 1C G2O O 1C2

O 1 9 O 5 7 O H2O O 1 G2O O1C2

Ans. 3660.Nsin distin't

linear fa'tors, resol&e

its fra'tions into partial

,

9 and 5.

42= 2* O 20 AG = 3C G = 4C G O 2C =

3 9 5

= 4 O 2Ans. A E ), 9 E 4, 5E 3

661.Nsin repeated linearfa'tors, resol&e itsfra'tions into partialfra'tions and sol&e for A,9 and 5.

62= 11 = 32 AG O 6C G O 1C2

O 6 9 5 O 1 G O 1C2

Ans. A E 10, 9 E 4, 5 E3

662.Nsin distin't $"adrati'fa'tors, resol&e itsfra'tions into partialfra'tions and sol&e for A,9 and 5.

1 = 13 = 102 AG = 2C G22O 1C =

2 9 O 522O 2 O 1

Ans. A E ), 9 E 0, 5 E3

p$"adrati' fa'tors,resol&e its fra'tions intopartial fra'tions andsol&e fro A, 9, 5, 7 andH.

4= 63O !2= 10 O ) A G = 3C G2= 2 O 2C2

= 3 9 O 5 7 O H2= 2 O 2 G2= 2 O2C2

Ans. A E 1, 9 E 2,5 E 0, 7 E 1, H E3

MATRICES

664.i&en the (. matri'es X&e'tors?

1 2 3a E 4 , 9 E 0 2

3 0 1

4 6 25 E 6 0 3 , d E 43 0 2 3 1

H E 6 0 31 0 )

5al'"late the (.epressions or i&ereasons why they are

"ndened.

G CbC 3 G H O )9


56/93

1 410 2

668.Find 59if 5 E 2 0 3

2 1 4

9 E 2 3

1 14 2

Ans. 8 013 13

66!.-f Y a b ' Z E Y 2 13 Z,nd the &al"e of a, band '.Ans. 2, 1, 3

6*0.i&en the matrie$"ation, sol&e for X y?

1 1 23 2 y 0

Ans. E 4, y E 66*1.From the i&en matri

e$"ation, sol&e for , yand .

1 1 1 22 1 1y E 11 2 1 0

Ans. 1, 2, 3

ythe i&en matriepansion?

1 1 1 2y 2 2 2 6

Ans. ), )

6*3.ol&e for , y, , and wfrom the i&en matrie$"ation.2O1 y ) 3 O2 w1 4 2

Ans. 2, 3, 2, 16*4.ol&e for , y and from

the i&en matrie$"ation.

Y G2C y G23C Z EY GyOC 2 G1C Z

Ans. 10, 2, 6

MATHEMATICSSET 27

6*).Find the &al"e of AG95C? 2 0

A E 3 11 =2

9 E 1 32 1

5 E 4 3

Ans. 4 1216 1322 4

6*6.Find the matri : thatsatises the e$"ation?

) 1 2 6

2 6 0 4 E4 4 2 )0 2

Ans. 2 14 11 2

6**.Find A O 9? 2 6 2

if A E 1 1 3 ) * 2

* 6 )and 9 E 4 8 3 0 2 3

Ans. ) 0 3) ! 0) ) 1

6*8.Find A9?-f 1 4 01

2 0 3

2

1 6 0 2 1 3 0 2 4

Ans. ) 2) 28 1 13

6*!.Find 57?

2if A E 11

7 E Y 1 2 3Z

Ans. 2 4 61 2 31 2 3

680.Find A9? 1 1 0

3

-f A E 2 0 32 0 4 )

2

2 60 1

1 32 3

Ans. 4 4) !1 )

5

684.


57/93

681.Find the &al"es of a, b,' and d from the i&ene$"ation.

a 1 4 ' ! 8b 3 1 d 1 3

Ans. 2, 1, 3, 2DETERMINANTS

682.


58/93

&al"e of the

determinant whose

elements are?

2 1 )

6

0 3 3

2

0 0 1

1

0 0 0

3

Ans. 18

6!1.7etermine the

&al"e of the

elements are as follows?

3 0 0 0

) 2 0 0

2 1 6 0

1 4 * 8

Ans. 288

6!2.7etermine the &al"e

of the determinant whose

elements are?

0 0 0

2

0 0 1

6

0 2 3

)

2

Ans. 16

6!3.7etermine the &al"e

of the determinant

whose elements are as

follows?

8 3 1

4

1 2 3

0

6 ) 0

0

2 0 0

0

Ans. 120

the determinant whose

elements are shown

below

1 ) 2

2 1 3

3 2 1

Ans. 46

6!).#hat is the &al"e o


elements are shown

below

! ) 2

6 1 3

11 2 1

Ans. !2

5

6!6.#hat is the &al"e 2 1 2 Ans. 3)


59/93

of the determinant

whose elements are

shown below

1 2 3

4 1 2

2 1 1

Ans. 3)

6!*.#hat is the &al"e

of the determinant

whose elements are

shown below

! 2 3

1 1 2

8 1 1

Ans. *0

6!8.#hat is the &al"e of


elements are shown

below

6 1 1

2 1 1

10 2 2

Ans. 28

6!!.Find the &al"e of the

determinant whose

elements are?

4 3 0

3

6 ) 1

3

2

8 1 )

3

Ans. *0

*00.Find the &al"e of the

determinant whose

elements are?

2 3 0

3

3 ) 1

3

1 1 2

2

4 1 )

3

*01.Find the &al"e of th

determinant whose

elements are?

2 3 0

3

3 ) 3

3

1 1 6

2

4 1 1)

3

Ans. 10)

*02.Find the &al"e of th

determinant whose

elements are?

5

2 6 0 2 ) 1 Ans. e)

*10 Find the determinants


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3

3 10 1

3

1 2 2

2

4 2 )

3

Ans. *0

*03.Find the &al"e of


elements are?

2 3 1

4

1

0 1 2

)

3 3 2

3

Ans. 3)

*04.H&al"ate the

determinant?

ln

1 1J

Ans. 1 = ln

*0).H&al"ate the

followin determinant

e2 e3

2e2 3e3

*06.H&al"ate the

followin determinant

'os sin

sin 'os

Ans. 1*0*.H&al"ate the followin

determinants se'

tan se' tan se'2

Ans. se' *08.H&al"ate the followin

determinants ln 1 1 O ln

Ans. O ln G = 1C*0!.-f the determinant of

the matri 5 E 1, sol&efor the &al"e of ?

1 2 )

Ans. 3

MATHEMATICS

SET 2

*10.Find the determinantsof ?

1 0 4 E 2 2 6

3 1 12Ans. 46

*11.Find the determinant o?

4 1 2 32 0 2 110 3 0 114 2 4 )

Ans. 28ADJOINT OF A MATRIX

*12.Find the ad@oint of

the matri, when it eis

nd the in&erse

1 2 4A E 1 0 3

3 1 2

Ans. 3 8

A1E 1J* * 14*

1 ) *13.Find the ad@oint matri

of

6

1 40 2

S0HERICALTRIGONOMETRY

6. -f tan 4A E 'ot 6A, ndthe &al"e of A

Ans. 20.!00, 6!.10


61/93

0 2Ans.

2 40 1

*14.Find the in&ersematri of

2 31 1

Ans.1 31 2

*1).7etermine the in&ersematri of

'os sin sin 'os

Ans.'os sin sin 'os

*16.Find the ad@oint of thematri

1 0 21 2 01 2 1

Ans. 2 4 4 1 3 2 4 2 2

0LANE

and

TRIGONOMETRY

PLANE TRIGONOMETRYTRIGONOMETRICIDENTITIES

1. -f tan a E 4J), determine4 sin a = 'os a3 'os a O sin a

Ans. 11J1!2.


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2nd$"adrant, sin 9 E

*J2), 9 in 1st$"adrant.

Find sin GA O 9C.

Ans. 3J)

1*. ow many di(erent

&al"es of lie between

00and 1800for the

e$"ation G2 sin =1C

G'os O 1C E 0

Ans. 3

18. -f Gsin O 1Jsin C E

2, then sin2 O 1Jsin2

, is e$"al to?

Ans. 0

1!. -f **0O 0.40 E ar'

tan G'ot 0.2)C, nd ?

20. H&al"ate 'os Gar' tan

1)J8 = ar' sin *J2)C

Ans. 2!*J42)

21. Ar' tan Y2'os Gar' sin

31J2J2CZ is e$"al to?

Ans. J4

22. H&al"ate

ar' 'ot Y2 'os Gar' sin

0.)CZ

Ans. 300

23. Find the &al"e in

derees of ar' 'os Gtan

240C

Ans. 63.)60

24. Find the &al"e of

Ans. 8J1*

MATHEMATICSSET 3

2). H&al"ate

tan ar' sin Y 3J2

G tan ar' 'ot 3 CZ

Ans. 1

26. H&al"ate ar' sin 'os

ar' tan 3.

Ans. 300

2*. -n the i&en

e$"ation below sol&e for

.

E Gtan O 'ot C2

sin2 tan2

28. -f tan A E + and tan

9 E 1J3, nd the anle

GA O 9C.

Ans. 4)0

2!. -f A O 9 O 5 E 180

and tan A O tan 9 O tan

5 E ).6*, nd the &al"e

of tan A tan 9 tan 5.

Ans. ).6*

30. ol&e for in the

e$"ation?

ar' tan G2C O ar'

tan GC EJ4

Ans. 0.281

6

31. -f ar' tan O ar' Ans. 0.862 Ans. 0.46!8 42. ol&e for if 'oth2


63/93

tan 1J3 E J4, nd the

&al"e of .

Ans. +

32. ol&e for if ar' tan

J2 O ar' tan J3 E 4)0.

Ans. 1

33.ol&e for from the

i&en trionometri'

e$"ation.

Ar' tan G1 = C O ar'

tan G1 O C E ar' tan

1J8

Ans. 4

34. -f ar' tan 4J3 O ar'

tan 12J) E ar' sin G O

yC, nd G O yC

3). -f sin E 3J), 'os E

)J13, nd GO C

Ans. 0.!6!

36. ol&e for the &al"e of

A: when sin A E 3.) and

'os A E ).).

Ans. 32.4*0

3*. -f sin A E 2.)11, 'os

A E 3.06 and sin 2A E

3.!3!, nd the &al"e of

Ans. 0.2)6

38. -f sin G O yC E 0.*66

and sin G = yC E 0.1*36,

nd sin 'os y.

3!. ol&e for the &al"e

of if?

Ar' sin G3 = 4yC E

J2

Ar' 'os G = yC E J3

Ans. 1

40. -f 'o&ersed sin E

0.134, nd the &al"e of

Ans. 600

41. Find if &ersed sin

E 0.423

Ans. )4.*60

= 's'h2 E ese'ant

Ans. 600

43. Find the &al"e of i

the e$"ation

'osh2 = sinh2 E 2

sin .

Ans. 300

44. implify the epression

se' Gse' C sin2

Ans. 'os

4). implify

4 'os y sin y G1 2 sin2y

6

Ans. sin 4y 48. i&en three anles A, )2. ol&e for 'os *20if )6. ow many di(erent


64/93

46. ol&e for ? sin

se' O 's' tan 2E

0.0866

Ans. 430

4*. #hat are the ea't

&al"es of the 'osine

and tanent

trionometri' f"n'tions

of a'"te anle A, i&en

that

sin A E 3J*

Ans. 'os A E 2

10J* ;

tan A E 3

10J20

9, and 5 whose s"m is

1800. -f the tan A O tan 9

O tan 5 E , nd the

&al"e of tan A tan 9

tan 5.

Ans.

4!. #hat is the sine of

8200

Ans. 0.!84

)0. 's' 2*00E

Ans. 1

)1. -n 'o&ersine is

0.134, nd the &al"e of .

Ans. 600

the i&en relationship is

'os 2A E 2 'os2A = 1

Ans. 0.30!

)3. Find the &al"e of

sin G ar' 'os 1)J1* C

Ans. 1*J!

)4. Find the &al"e of 'os

Y ar' sin G1J3C O ar' tan

G2J)CZ

Ans. G2J!C G10 = 1C

)). -f sin 400O sin , nd

the &al"e of .

Ans. 800

&al"e of from 00to

1800for the e$"ation

G2 sin = 1C G'os O 1C

E 0

Ans. 3

)*. Find the &al"e of i

the e$"ation 's' O 'o

E 3.

Ans. J)

)8. Find sin if

2 sin O 3 'os = 2 E 0

Ans. 1 X )J13

)!. -f 'os E 3J2, the

nd the &al"e of if E

1 = tan2

.

6

Ans. 2J3 63. -f 'os E J2 then 1 = MATHEMATICSSET 31

Ans. sinh 2


65/93

60. -f sin 'os E

1J3, what is the &al"e

if sin 2

Ans. 8J!

61. -f 'os O y sin

E 1 and sin y 'os

E 3, what is the

relationship between

and y

Ans. 2O y2E 10

62. -f O y E !00, then

sin tan y is

e$"al to?

sin y tan

Ans. 'ot

tan2is e$"al to?

Ans. G22= 4C J 2

64. ol&e for in the

e$"ation? ar' tan G2C O

ar' tan GC E J4

Ans. 0.281

6). ol&e for y if

y E G1Jsin = 1Jtan C G1

O 'os C

Ans. sin

66. ol&e for ?

E 1 = Gsin 'os C2

Ans. sin 2

6*. implify 'os4 sin4

.

Ans. 2 'os21

68. ol&e for ?

1 = tan2a

1 O tan2a

Ans. 'os 2a

6!. Find the &al"e of y?

y E G1 O 'os 2C tan

.

Ans. sin 2

*0.


66/93

than its sides

Ans. 2 times

*4. -f tan 9 E J 1 =

2, nd 'os 9 E

Ans. 1 = 2

*). -f 'os A E 2ab J Ga2

O b2C, nd 's' A E

Ans. Ga2O b2C

Ga2

= b2

C

*6. -f ar' tan G1 O C O

1J18, what is the &al"e of

Ans. 6

**. -f ar' sin G3 = 4yC E

J2 and ar' 'os G = yC

EJ3, what is the &al"e of

and y

Ans. 1.0 , 0.)

*8. ol&e for if

'os G6C E 1

's' G3O !C

Ans. !0

*!. 5o&ersed sin E 0.2,

nd the &al"e of

80. -f &ersed sin E

0.38, what is

Ans. )1.680

81. -f 2 'ot E1, what is

the &al"e of ) sin =

3 'os

2 sin

O 'os

Ans. 1.4

82. -f sin A E 4J) and sin

GA O 9C E , nd 'os 9.

Ans. 0.8

83. -f sin G O yC E

0.81!1)2 and sin G = yC

&al"e of sin 'os y.

Ans. 0.62

84. -f ar' tan )J3 O ar'

tan U E ar' sin G O yC,

nd G O yC.

Ans. 0.!!)

8). -f sin A 'os A O sin 2A E1, what is the &al"e of Ain dereesAns. 20.!

86. -f sin 2A E 2.6*18,sin A E 1.40) and'os A E 4.323, what isthe &al"e of and AAns. 0.22, 18

8*. -f ar' 'os Gsin 0.8C E 6O 0.4), what is the&al"e of in dereesAns. 24

88. -f ar' 'os Gsin 0.8C E 6O 0.4), what is the&al"e of tan

6

Ans. 0.44)8!. -f sin A E 1.*4*,

A 2 83! d

!3. A, 9 and 5 are anles ofa trianle. -f tan A O tan9 t 5 12 d th

the opposite ede of the

th l/ th d t l

distan'e of 120 m fromit. 5omp"te the heihtf th t


67/93

'os A E 2.83! andsin 2A E 2.!*), whatis the &al"e of A indereesAns. 31.6!0.


68/93

the tower obser&es itanle of ele&ation to beonly one half as m"'has the anle ofele&ation of the sametower when he mo&es )m nearer towards the

tower. ow hih is thetowerAns. 3 m

10).A man nds the anleof ele&ation of the topof a tower to be 30derees. e wal/s 8) mnearer the tower andnds its anle ofele&ation to be 60derees. #hat is theheiht of the towerAns. *3.61

106.Points A and 9 are 100m apart and are of thesame ele&ation as thefoot of the bld.


69/93

64.* /m dire'tly awayfrom 7, how lon inho"rs has it tra&eledAns. 2

11).-n a trianle A95, A9E 20 m and 95 E 8 m.>ne possible dimension

of 5A is?Ans. 2* ^ 12

116.-n trianle 957, 95 E10 m and 57 E 2) m.

ne possible perimeterof the trianle is?Ans. 3*

118.


70/93

Ans. after 2.13 hrs132.A stat"e 2 meters hih

stands on a 'ol"mnthat is 3 m hih. Anobser&er in le&el withthe top of the stat"eobser&ed that the

'ol"mn and the stat"es"btend the sameanle. ow far is theobser&er from thestat"eAns. 2 ) m

133.From the top of ab"ildin 100 m hih,the anle of depressionof a point A d"e Hast ofit is 300. From a point 9d"e o"th of theb"ildin, the anle ofele&ation of the top is600. Find the distan'eA9.Ans. 100 30J3

134.An obser&er fo"nd theanle of ele&ation ofthe top of the tree to be2*0. After mo&in 10 m'loser Gon the same&erti'al and horiontalplane as the treeC, theanle of ele&ation

be'omes )40

. Find theheiht of the tree.

MATHEMATICSSET 34

13).From a point A at thefoot of the mo"ntain, the

anle of ele&ation of thetop 9 is 600. Afteras'endin the mo"ntainone G1C mile at anin'lination of 300to thehorion, and rea'hin apoint 5, an obser&er ndsthat the anle A59 is13)0. #hat is the heihtof the mo"ntain in ftAns. 124!3

136.A )0 = m &erti'al tower'asts a 62.3 = m shadow

when the anle ofele&ation of the s"n is41.60. #hat is thein'lination of the ro"ndAns. 4.*20

13*.A &erti'al pole is 10 mfrom a b"ildin. #hen theanle of ele&ation of thes"n is 4)0, the pole 'ast ashadow on the b"ildin 1m hih. Find the heiht ofthe pole.Ans. 11 m

anle of ele&ation of thes"n is 610. -f the polehas leaned 1)0from the&erti'al dire'tly towardthe s"n, what is thelenth of the poleAns. )4.23 m

13!.An obser&er wishes todetermine the heiht ofa tower. e ta/es sihtsat the top of the towerfrom A and 9, whi'h are)0 ft apart, at the sameele&ation on a dire't linewith the tower.


71/93

P1, )00.00 per s$"aremeter, what is the 'ostof the roadway

40 m

30 m

Ans. P601, 3)0.0014).A man impro&ises a

temporary shield fromthe s"n "sin atrian"lar pie'e ofwood with dimensionsof 1.4 m, 1.) m, and1.3 m. #ith the lonerside lyin horiontally

on the ro"nd, he props"p the other 'orner ofthe trianle with a&erti'al pole 0.! mlon. #hat wo"ld bethe area of the shadowon the ro"nd when thes"n is &erti'allyo&erheadAns. 0.) m2

146.At 12?00 noon shipsailed from the port in

miles per ho"r. At 1?00P another ship left thesame port in the dire'tionI )00# at a speed of 20na"ti'al miles per ho"r.At what time will these'ond ship be ea'tly

Iorth of the rst shipAns. 2?4!.4 P..

14*.A ship sailed in thedire'tion of 420# at aspeed of 1) na"ti'almiles per ho"r.


72/93

p460. From the foot oftower 9 the anle ofele&ation of the top oftower A is 280. 9othtowers are on le&elro"nd. -f the heiht of

tower 9 is 120 m.aC ow hih is tower Ain mAns. 40.* mbC ow far apart are thetowers in mAns. *6.)* m

1)4.From the top of ab"ildin the anles ofdepression of points Aand 9 are 21 dereesand 32 derees,respe'ti&ely. Points A

and 9 are 100 m apartand are on the sameele&ation as the foot ofthe b"ildin.aC ow hih is theb"ildin in mAns. !!.) mbC ow far is A from theb"ildin in mAns. 2)!.2 m

1)).A 'ar tra&els frompoint 5 northwards for

'onstant speed of the 'aris 40 /ph, how far dire'tlyfrom point 5 will it beafter ea'tly 2 ho"rsAns. 64.* /m

1)6.A b"s tra&el northward

from point 7 for one ho"r,then eastward for 30 min,then shifted I 300H.


73/93

i&en?A E 40018M $E100010M5 E *)000M #E6)02)MFind side aand anle 9.

Ans. 41013M)1M63010M2*M

168.i&en the parts of thespheri'al trianle?A E 60030M #E 3801)M

aE 40030MFind the &al"e of side $.Ans. 46043M

16!.An airplane Bew from7a&ao whose latit"de is140I and lonit"de of121030M H on a 'o"rse 300# and maintainin

a "niform altit"de. Atwhat lonit"de will theplane 'ross thee$"atorAns. 113033M H

1*0.Iorthwest AirlinesBew from


74/93

*)0, 5 E 860and rE 40m.Ans. 3,3*! m2

184.-n the spheri'altrianle A95, A E11601!M, 9 E ))030M and

5 E 8003*M. Find the&al"e of side #:.Ans. )6.0320

18).-n the spheri'altrianle A95, aE 610, #E 430and $E 680. Findthe &al"e of A.Ans. *0.)230

186.-n riht spheri'altrianle A95, 5 E !00, 9E 3*0and #E 310. Findthe &al"e of a: inderees.

Ans. )2.88018!.A riht spheri'al

trianle A95, 5 E !00, 9E 3*0and #E 310. Findthe &al"e of A: inderees.Ans. 68.*0

MATHEMATICSSET 37

1!0.-n riht spheri'al

trianle A95, 5 E !00, A

Ans. *0.1)0

1!1.-n riht spheri'altrianle A95, 5 E !00, AE *4.*0and $E **.20.Find the &al"e of #: inderees.

Ans. 4!.260ANALYTIC GEOMETRYSTRAIGHT LINES

1.


75/93

18.


76/93

Ans. 3.*!4). Find the distan'e from

the point G4,)C to theline 3 O 2y O 6 E 0.Ans. 4.4

46. Find the anle between

the lines y O = 12 E 0and 4y = = 2 E 0.Ans. )!.040

4*. Find the anle betweenthe lines y = 2 O 6 E 0and 2y O 3 O * E 0.Ans. 11!.*0

48. Find the lenth of theline from point G),3C tothe y = ais if its slopeis 3J2.Ans. !.01

4!. #hat is the e$"ation of

the line bise'tin thebier anle formed bythe interse'tion of thelines 2 = y O 2 E 0 and2 O y = 4 E 0.Ans. y = 3 E 0

)0.


77/93

3y E 8.Ans. 4

*3. Find the distan'ebetween the lines, 3 Oy = 12 E 0 and 3 O y =4 E 0.

Ans. 8J10*4. #hat is the lenth of

the line with slope 4J3from a point G6,4C to they = aisAns. 10

*). Find the &al"e of y if aline ha&in a slope of2J3 and passinthro"h the point G6,2C interse'ts the y =ais.Ans. 2

*6. Find the &al"e of if aline ha&in a slope of)J2 and passinthro"h point G4,)Cinterse'ts the = ais.Ans. 2

**. A line of slope 3 passesthro"h the pointG*,10C. -f point on theline has an abs'issa 2,nd its ordinate.Ans. )

*8. -f the slope of the line4h O 6y O 8 E 0 is

*!. Find the y 0 inter'ept ofa line ha&in a slope of 3and passes thro"h G1,6C.Ans. !

80. Find the abs'issa of a

point ha&in an ordinateof 4 of a line that has a y= inter'ept of 8 and aslope of 2.Ans. 2

81.


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4y 12 E 0.Ans. )

!8.


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122.Find the lenth of the'hord 'ommon to the'ir'les 2O y2E 2) and2O y2= 10y E 0.Ans. 8.66

123.7etermine the lenth

of the 'hord 'ommon tothe 'ir'le 2O y2E 64and 2O y2= 16 E 0Ans. 13.86

124.Find the lo'"s of the'enter of the 'ir'le thatmo&es s"'h that it isalways tanent to the y= ais and another'ir'le whose 'enter ised at G4,2C withradi"s of 3.Ans. y2= 4y =14 O

11 E 012).


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G3,4C.Ans. G O 3C2O Gy O 4C2

E 64146.Find the area of a

'ir'le with 'enter at G

4,)C and tanent to theline y E = 4.Ans. 84.)

14*.Find the e$"ation of a'ir'le ha&in its 'enteron the line 3 = 2y = 22E 0 and tanent to they = ais at G0,1C.Ans. 2O y2= 16

= 2y O 1 E 0.148.Find the e$"ation of

the 'ir'le'ir'"ms'ribin a

trianle whose &erti'esare G0,0C, G0,)C andG3,3C.Ans. 2O y2= =)y E 0

14!.Find the e$"ation of a'ir'le 'ir'"ms'ribinthe trianle formed bythe lines y E 0, y E and 2 O 3y E 10.Ans. 2O y2= ) Oy E 0

1)0.A trianle has its sides

ha&in e$"ations e$"al

trianle.Ans. G = 2C2O Gy O 1C2E )1)1.A 'ir'le has its 'enter

at G0,0C and its radi"s is

10 "nits. 7etermine the

e$"ations of the lines

thro"h G1),1)C and

tanent to the 'ir'le.

Ans. = 0,303y E10.4) = 3.3y E 34.48

1)2.7etermine the lenth ofthe line @oinin theinterse'tion of thee$"ation 2O y2E 48 and2O 8y E 0.Ans. 11.31

1)3.Find the distan'ebetween the point ofinterse'tion of the line =2y O 2 E 0 and the 'ir'le2O y2O 6 O 6y O 8 E

0.Ans. 4.4* "nits

1)).


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y y18 respe'ti&ely.5omp"te the lenth of'hord of the o"ter 'ir'lethat is tanent to theinner 'ir'le.

Ans. 14.*016*.A 'ir'le has ane$"ation 2O y2= 20 =44 E 0. -f the lenth of'hord is 22.62 "nits,'omp"te the distan'eof the 'hord from the'enter of the 'ir'le.Ans. 4.01

168.5omp"te the lenth of'hord of a 'ir'le ha&inan e$"ation 2O y2=16 E 0 if the distan'e

from the 'hord to the'enter of the 'ir'le is 4"nits.Ans. 13.86

16!.Find the e$"ation ofthe radi'al ais of thetwo 'ir'les ha&ine$"ations of 2O y2O4 O 6y = 3 E 0 and 2O y2O 12 O 14y O 60E 0.Ans. 8 O 8y O63 E 0

y0 and 2O y2= 4 O 2y =4 E 0.Ans. 4 = y O 2E 0

1*1.Find the radi'al 'enters

of the radi'al ais of thethree i&en 'ir'les. 2Oy2= 12 O 11 E 0, 2O y2

= 4 = 21 E 0, and 2O y2= 4 O 16y O 43 E 0.Ans. G2,4C

PARABOLA1*2.#hat is the lenth of the

lat"s re't"m of theparabola 2= 8 = 20y O)6 E 0.Ans. 20

1*3.#hat is the lenth of the

lat"s re't"m of theparabola 2O 8 = 16y O32 E 0 Ans. 16

1*4.#hat is the lenth of thelat"s re't"m of theparabola 2E 4Gy = 2CAns. 4

1*).#here is the fo'"s ofthe parabola 2E 4 Gy =2CAns. 0,3

y1**.#here is the fo'"s of

the '"r&e 2E 12yAns. 0, 3

1*8.ow far is the dire'triof the parabola G =4C2E

8Gy = 2C from the =ais.Ans. 6

1*!.Find the distan'e fromthe 'enter of theparabola G = 3C2E12y to the line 2 = 3y =12 E 0.Ans. 1.*

180.ow far is the dire'triof the parabola G = 4C2E 8Gy = 3C.Ans. 1

181.Find the distan'e of the&erte of the '"r&e G =2C2E 4y to the line 2 =3y = 8 E 0.Ans. 1.1

182.A parabola has its&erte at G2,3C and itsdire'tri is y E *. Findthe lenth of its lat"sre't"m.Ans. 16

183.A parabola with ais onthe ais passes thr" G

3,6C and its &erte is at

184.


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abo&e the bottom, thewidth a'ross the ar' is12 m. #hat is theheiht of the ar' in mAns. ).4

1!0.


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its ais, the se'tion is aparabola ha&in theliht 'enter as a fo'"s.-f the liht is 18 mmfrom the &erte and the

diameter of the liht is2)0 mm, nd the depthof the headliht.Ans. 21* mm

21).An ar'h is 18 m hihhas the form of aparabola with &erteais.


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parabola with &erte atG3,2C and the fo'"s atG0,2C.Ans. y2= 4y = 12 = 32E 0

236.Find the e$"ation of aparabola ha&in itsdire'tri of y E * andits &erte at G2,6C.Ans. 2 4 O 4y =20 E 0

23*.Find the e$"ation ofthe ais of symmetry ofthe f"n'tion y E 22=* O ).Ans. 4 = * E 0

238.A parabola has ane$"ation of 2E 9y O 5

whose &erte is at G0,2C and passes thr"G8,6C. 7etermine the&al"e of 9 and 5 andthe lat"s re't"m.Ans. 16, 32, 16

23!.A '"r&e has ane$"ation of 2E 5y Od.


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that the s"m of itsdistan'e from G4,0C andG4,0C is always 10. Findthe lenth of the minorais of the '"r&e

form"la.Ans. 62)!.A 'losed '"r&e is

formed by the lo'"s ofa point whi'h mo&ess"'h that the s"m of itsdistan'es from G4,0Cand G4,0C is always 10.Find the distan'e fromone dire'tri to the'enter of the '"r&e.Ans. 6.2)

260.A point mo&es s"'h

that the s"m of itsdistan'es from G8,0Cand G8,0C is always 20.Find the distan'e fromone &erte to the'enter of the '"r&eformed.Ans. 10

261.


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lon and lies on the =ais with its 'enter atthe oriin. 7eterminethe e$"ation of theellipse.

Ans. 16

2

O 2)y

2

=400 E 02*8.


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&erti'es is e$"al to 12.Find the distan'ebetween the dire'tri.Ans. 36

301.A point mo&es so that

the s"m of thedistan'es from thepoint G2,2C and G4,2C is8. Find the e''entri'ityof its lo'"s.Ans. 0.*)

302.Find the ma@or ais ofthe ellipse 2O 4y2= 2= 8y O 1 E 0.Ans. 4

303.An ellipse has a lenthof semi = ma@or ais of)00 m and a semi =

minor ais of 300 m.5omp"te the se'onde''entri'ity of ellipse.Ans. 1.333

304.#hat is the'ir'"mferen'e of anellipse whosediameters are fo"rteenand ten metersAns. 38.22

30).#hat is the areaen'losed by the '"r&e!2O 2)y2= 22) E 0.

Ans. 1)

306.Find the area in these'ond $"adrantbo"nded the '"r&e 2J 4O y2J ! E 1 and the'oordinate aes.

Ans. 3J230*.Find the area bo"ndedby the ellipse 2O 16y2=16 O !6y O 144 E 0.Nse area E ab.Ans. 16

308.Find the area en'losedby the '"r&e !2O 18 O2)y2= 100y E 116Ans. 1)s$. "nits

30!.A semi = ellipse and aparabola rest on thesame 60 meters wide and

20 meters hih. Nsin the'ommon base as = ais,'omp"te the di(eren'e ofordinates at points 2)meters from the 'enter ofthe base.Ans. 4.!) m

310.A satellite orbits theearth in an ellipti'al pathof e''entri'ity 0.6 andsemi = minor ais oflenth 12,000 miles. -fthe 'enter of the earth isat one of the fo'i, nd the

ellipse with the s"m asone fo'i. -f the farthestdistan'e of the s"n fromthe earth is 10).)0million /ilometers and

the nearest distan'e ofthe s"n from the earth is*8.2) million /ilometers,nd the e''entri'ity ofthe ellipse.Ans. 0.148

312.Point P G,yC mo&eswith a distan'e frompoint G0,1C one half of itsdistan'e from line y E 4,the e$"ation of the lo'"sis.Ans. 42O 3y2E 12

313.An ellipse has ane$"ation of 162O 2)y2E 400. 5omp"te theshortest lenth of thefo'al radi"s from pointG2,3.3*C.Ans. 3.8

314.Find the area formedby the points ofinterse'tion of the'"r&es 2O 3y2= 24 O36 E 0 and y2E 3Ans. 81

HYPERBOLA

Gy O 4C J16Ans. 4 = 3y = 2E 0

316.


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3 e 'oo d a e a esare asymptotes of thee$"ilateral hyperbolawhose &erte in therst $"adrant is 62

"nits from the oriin.#hat is the e$"ation ofthe hyperbolaAns. y E 36

322.


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its distan'es from G0,)Cand G0,)C is 8. Findthe e$"ation of thelo'"s.Ans. !y = 162E144

343.Find the e$"ation ofthe hyperbola ha&in'enter at oriin withtrans&erse ais on the = ais a E 4 and lat"sre't"m E 32.Ans. 42= y2E 64

344.Find the e''entri'ity ofa hyperbola whosetrans&erse and'on@"ate aes are

e$"al in lenth.Ans. 234).For what &al"e of /

will the line y E O /be tanent to thehyperbola 2= 4y2E48Ans. 6346.Find the e$"ation

of the hyperbola whose

asymptotes are y E

Ans. 42= y2E 1634*.#hat is the e$"ation of

the asymptote of thehyperbola 2J y = y2J 4 E1

Ans. 2 = 3y E 0348. 5omp"te the a'"te

anle formed by theasymptote of thehyperbola 2= 3y2= 8 =14 E 0.Ans. 600

34!.5omp"te the lo'ation ofthe fo'i of an e$"ilateralhyperbola 2= y2E !.Ans. G32,0CandG32,0C

3)0.5omp"te the lo'ation ofthe &erti'es of thee$"ilateral hyperbola y2=2E 16.Ans. G0,4C and G0,4C

3)1.o'ate the &erti'es ofthe e$"ilateral hyperbolay E 18.Ans. E 32 ; y E32

3)2.


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'ir'le 2O y2E 2)passin thr" G2)J3,0C.Ans. 3 O 4y E2) ;

3 = 4y E 2)366.Find the e$"ation of

the normal to thetanent of the parabola2E 16y at G8,4C.Ans. O y E 12

36*.Find the slope of the'"r&e 2E 6y O 10 atpoint G4,1C.Ans. 4J3

368.Find the e$"ation ofthe tanent to a 'ir'le2O y2E 2) ha&in a

slope of 1.Ans. y E )236!.Find the e$"ation of

the tanents to the'"r&e !2O 2)y2E 22)ha&in a slope of 2.Ans. y E 2 10!

3*0.Find the lenth of thes"b = tanent and s"b =normal of the '"r&e 2O y2E 2) at point G3,4C.Ans. G3,16J3C

tanent from point G*,8Cto the 'ir'le 2O y2= ! E0.Ans. 226

3*3.Find the &al"e of / forwhi'h the lenth of thetanent from point G),4Cto the 'ir'le 2O y2O 2/yE 0 is one.Ans. )

3*4.Find the lonestdistan'e from G10,*C tothe 'ir'le 2O y2= 4 = 2y= 20 E 0.Ans. 1)

DIAMETER OF CONICS3*).i&en the e$"ation of

ellipse 642

O 2)y2

E1600 and the slope of the'hord is 1J). Find thee$"ation of the diameterof ellipse.Ans. 64 O )y E 0

3*6.Find the e$"ation of thediameter of the ellipse2J 2) O y2J ! E 1 whi'hbise'ts all 'hords of slopem E 2.Ans. ! O )0y E 0.

3**.Find the e$"ation of the

diameter of a parabola

diameter of thehyperbola y E ! whi'hbise't 'hords whoseslope is =3.Ans. y E 3

3*!.Find the slope of the'hords whi'h arebise'ted by thediameter of ellipsewhose e$"ation is 2 =3y E 0 if the ellipse hasan e$"ation of 42O !y2E 36.Ans. 2J3

380.Find the slope of the'hords whi'h arebise'ted by the

diameter of hyperbolawhose e$"ation is 3 =2y E 0 if the e$"ation ofthe hyperbola is !y2=42E 36.Ans. 8J2*

381.Find the slope of the'hords whi'h arebise'ted by thediameter of a parabola E 3 if the e$"ation ofthe parabola is 2E 6y.Ans. 1

e$"ation of 22= )y2E10.Ans. 0

383.Find the e$"ation of thdiameter 'on@"ate tothe diameter 3 O y E 0of the hyperbola y E 0Ans. y E 3

384.Find the e$"ation of thpolar of the point P G1,)with respe't to thehyperbola 42= !y2E36.Ans. 4 = 4)y = 3E 0

38).Find the e$"ation of thpolar of the point A G

),)C with respe't to theellipse 162O 2)y2E400.Ans. 16 = 2)y O 8E 0

POLAR COORDINATES386.Nsin re'tan"lar

'oordinates, a point islo'ated at G3,4C. Find itspolar 'oordinates.

Ans. ), )3.130

9


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G,yC of a point in the'"r&e when E 300.Ans. G2.1*,1.2)C

DIAMETER OF ELLIPSE410.7etermine the

i f h

CENTROIDS ORINTERSECTION OFMEDIANS OF A TRIANGLE

414.


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e$"ation of thediameter of the ellipse!2O 2)y2 E 22) whi'hbise'ts all 'hordsha&in e$"al slopes of3J).Ans. ! O 1)y E 0

411.


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G4,4C. ow far is its

'entroid from the y =

ais

Ans. *.68

9

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