TCs QUestion

7/23/2019 TCs QUestion

1/55

M4mahs questions

20. My fight takes o at 2am rom a place at 18N 10E and landed 10 rs later at a place!ith coordinates "#N$0%. %hat is the local time !hen my plane landed&

a' 12 noon

(' #) 40 *M

c' +) 20 ,M

d' #)+0 *M

-emem(er !hile mo/ing rom east to !est countries lag in time. -emem(er !hen estcricket starts in England& ". "0 in aternoon. -ight& ie. %e are in ater noon meansthey are in morning.

the coordinates change rom 10 E to $0% the plane has mo/ed a total o 80 degrees.%e kno! that !ith each degree time increases (y 4 minutes !hile going rom east to!est. o!& 24 3 #0 min "#0 degrees 5o 1 degree 6 4 min'

5o total time change 6 4 3 80 6 "20 min 6 + hrs 7 20 minutes.

*ter 10 hours local time is 2 am 7 10 +.20 hrs' 6 #.40 *M.

1. 9ne day Eesha started "0 min late rom home and reached her o:ce +0 min late!hile dri/ing 2+; slo!er than her usual speed. o! much time in min does eeshausually take to reach her o:ce rom home&

*ns) %e kno! that 5peed is in/ersely proportional to time

%hile she dri/es 2+; slo!er means she dro/e at "45'

%e kno! that < 6 5 3

%hen speed (ecame "45' then ime taken should (e 4"'

i.e 5he has taken 4"' e3tra to co/er the distance.

E3tra ime 6 " 6 20 min as 20 min late due to slo! dri/ing'

*ctual time 6 #0 Minutes

2. n 200" there are 28 days in =e(ruary and "#+ days in a year in 2004 there are 2>days in =e(ruary and "## days in the year. the date march 11 200" is uesday then!hich one o the ollo!ing !ould the date march 11 2004 !ould (e&


2/55

*ns) 11"200" is uesday hen 11" 2004 is hursday

he num(er o odd days (et!een the t!o dates are ?"##$@-em6 2.

"' o! many positi/e integers less than +00 can (e ormed using the num(ers12"and + or digits each digit (eing used only once.

*ns) 5ingle digit num(ers 6 4


3/55

18$

#$40 rom the chocolates alone the ne! price !as not lessthan hal the original price quoted o! many chocolates !ere sold&

5ol) 1#4>0 6 2 I + I 1$ I >$

No! no! chocolate price should (e greater than 1 and less than 2. 5o 2 3 + 3 1$ 6 1$0

5o otal chocolates sold 6 >$ and Ne! chocolate price 6 -s.1.$

>' Eesha (ought t!o /arities o rice costing +0-s per kg and #0 -s per kg and mi3edthem in some ratio.hen she sold that mi3ture at $0 -s per kg making a proGt o 20 ;%hat !as the ratio o the mic3ture&

5ol) 5elling price o the mi3ture 6 $0 and proGt 6 20;

Fost price o the mi3ture 6 $0I1001206$0I+#


4/55

y applying alligation rule)

so ratio 6 #0C1$+")1$""C+0 6 1 ) +

10. 5tar question)

1'64 and 37y'63'7y'7$3y74then 2'7+'6&

5ol) Aet 3 61 and y 6 1

1 7 1' 6 1' 7 1' 7 $ 3 1 3 1 7 4 J 2' 6 1>

Aet 3 62 and y 6 2

2 7 2' 6 1> 7 1> 7 $ 3 2 3 2 7 4 J 4' 6 $0

Aet 3 6 1 and y 6 4

1 7 4' 6 4 7 $0 7 28 7 4 6 10#

2' 7 +' 6 12+

1. *dam sat !ith his riends in the Fhinnas!amy stadium at Madurai to !atch the 100metres running race organiHed (y the *sian athletics *ssociation. =i/e rounds !ere run.*ter e/ery round hal the teams !ere eliminated. =inally one team !ins the game. o!many teams participated in the race&

*ns) otal G/e rounds !ere run. 5o in the Gnal round 2 teams must ha/e participated. nthe penultimate round 4 teams and "rd round 8 2nd round 1# and in the Grst round "2

teams must ha/e participated as in each round hal o the teams got eliminated.

2. =rom the top o a > metres high (uilding * the angle o ele/ation o the top o ato!er F< is "0K and the angle o depression o the oot o the to!er is #0K. %hat is theheight o the to!er&

*ns)*ns) %e ha/e to Gnd the /alue o F"L

n triangle F


5/55

". Aetters o alpha(ets no rom 1 to 2# are consecuti/ely !ith 1 assigned to * and 2# to. y 2$th letter !e mean * 28th . n general 2#m7n m and n negati/e inteHers issame as the letters num(ered n.

Aet , 6 # strange country military general sends this secret message according ot the

ollo!ing codiGcation scheme. n codiying a sentence the 1st time a letter occurs it isreplaced (y the pth letter rom it. 2nd time i occurred it is replaced (y ,2 letter romit. "rd time it occurred it is replaced (y p" letter rom it. %hat is the code !ord or***A

a' DNN99-

(' DOP9-

c' DD9D-

d' DAO9-

*ns) apples

U or real num(er 3int3' denotes integer part o 3.int3' is the largest integer less thanor equal to 3.int12'61int24'6".Gnd the /alue oint12'7int127100'7int1272100'7....7int127>>100'

int12'60

int127100'6100

int1272100'60

int127"100'60

int127+0100'6int100100'61

int127>>100'6int1.4>'61

(y adding all those /alues

!e !ill get 1+0

U.+000 /oted in an election (et!een t!o candidates.14; o the /otes !ere in/alid.he!inner !on (y a margin appro3imately closer to 1+;.=ind the num(er o /otes secured(y the person


8/55

14; o +000 6 $00

so /alid /otes 6+000$0064"00

let loser get 3 /otes so !inner gets 37"320'62"320 /otes

so 372"32064"00

4"32064"00

362000

2"320 6 2"00

so !inner get 2"00 /otes

U.there are 100 !ine glasses. oVered my ser/ant to " paise or e/ery (roken glass to

(e deli/ered saely and oreit > paisa or e/ery glass (roken.at the end o day.herecei/ed rs 2.40 .ho! many glass did he (reak.

a' 20 (' $" c' + d' 8

100 !ine glasses so"W1006"00.i a glass is (roken then >paisa is deducted 7 he !illalso not get the "paisa he !as getting or sae deli/ery so in total he !ill loss>7"612paisa or 1glass (roken. he gets 240paisa i.e. #0 paisa loss sototal no. o glass6 #012 6 +.ans'

U * (oy is cycling such that the !heel o his cycle is undergoing 420 re/olutions perminute. he diameter o the !heel is +0cm. =ind his speed in kmph.

*ns

1 min6 420 re/olutionsdiameter o !heel 6 +0 so radius !ill (e 2+or 0.2+ m.distance co/ered in 1min6 420W2WpieW2+6##0n! in #0 s 6 ##01 s 6 11ms

U 4 lines are parallel to the (ase o the triangle i the lines di/ide the triangle into +equal spaces . the area o the largest space is 2$sqcm !hat is the total area otriangle&


9/55

U * and Gnished a piece o !ork in + days. * had !orked at t!ice the speed and at hal the speed they !ould ha/e Gnished the !ork in our days. o! many days !ouldit ha/e taken * to Gnish the !ork alone&

ans

10 days+37y'64237y2' thus 36yso a !ill take t!ice the time taken (y a7( thus ans!er is 10


10/55

U* (ag has 1"+$>11 and 1" cm sticks .Gnd the pro(a(lity that they they !ill orm atriangle i " sticks are dra!n&

sol*ns is 1""+

otal !ay o selecting6$F"6"+No! selections that are in e/er6"+$'"$>'">11'"111"'+$>'+$11'+>11'+>1"'+111"'$>11'$>1"'$111"'>111"'6total 1".9thers are reXected (ecause to orm a triangle it is neccessary that the sum o 2 smallsides must (e greater than the third greatest side

U the equation k2 +k 7 #'32 7 k2 $k 7 12'3 7 k2 > 6 0 satisy more thant!o /alues o 3 then the /alue o k isoptiona' "

(' "c' 2d' 4

5olas more t!o /alues o 3dn !e can !rt it k2+k7#60'Y k6"2k2$k71260' Y k64"k2>60'Y k67""the common /alue o k is "and or this /alue"' cn get more dn t!o /alue o 3.ans is "

U i the no.s mn is di/ided (y # then 2 and " are the remainders respecti/ely. andmYnthen !hat !ill ( the remainder !hen mn is di/ided (y #&

5ol6*ns is +m6#a7266Ym6#a#7#7266Ym6#a1'78n6#(7"mn6#a1'78#(7"'66Y#a1('7+5othe remainder !hen mn is di/ided (y # is +

U i 4444 is di/ided (y 8n then !hat the ma3 /alue o n can (e&

5ol62> is the ans!er.2 8Ss can perectly di/ide 44W44W445oto perectly di/ide 42 44Ss !e require 28 8Ss at ma3No!the remaining 2 44Ss are perectly di/ided at ma3 (y one 8.5othe ma3 /alue o n is 2>


11/55

U last t!o digit o 12"'12"Z..e3plain

5ol6

U our parallel lines are dra!n parallel to one side o an equilateral triangle such that itcuts the other t!o sides at equal inter/als.the area o the largest segment thus ormedis 2$msqr.Gnd the area o the triangle&

5ol6

*rea o rapeHoid6 a7('Wh''2!here a and ( are length o parallel sides'No! 5ince side is di/ided in + parts thereorelength o one inter/al6a+No! use 5in#0 and to calculate the height o trapeHoid ie. a root "10'. and cos#0 tocalculate the (ase o the triangle !hose hypotenuse is a+..i.e. !ill (e a10'[%e get (6 aa107a10'(6 4a+no! equate the area o trapeHoid !ith 2$..ence area o equilateral triangle is $+ sqm

U ho! many lattice points are there (et!een 20' and 1#20"'

5ol

U */erage salary o 1$ teachers is 4+000." teachers let and the a/erage salarydropped (y 2+00.%hat is the sum o salaries o " teachers !ho let&

5ol6otal nitial 5alary ) 1$W4+000 6 $#+000*/erage 5alary *ter remo/al o " eachers 6 4+0002+00 6 42+00

otal =inal 5alary ) 14W42+00 6 +>+0005um o 5alaries o " teachers !ho let ) $#+000 +>+000 6 1$0000

U there is a circle !hich circumscri(es three unit circle !hich are tangential to eachother.!hat is the circumerence o (igger circle.&

5ol6Pust dra! according to questionno! Xoin the center o the smaller circles.radius o (igger circle6 17 radius o circle circumscri(ing the equilateral triangle.ence radius o (igger circle 6 2root " 7 1ence circumerance 6 2W pie W -


12/55

ie. pi472sqrt"'sqrt"

U in ho! many !ays can 2"10 (e e3pressed as a product o three actors

21"062W+W$W11W"W1

# prime actors...to e3press this as a product o " !e take n1'cr1'+c2610

U the mean o three no.s is 10 more than the least o the no.s and 1+ less than thegreatest o the three.i the median o three nos is + then the sum o three is

5ol6"0 is the ans!erlet " num(s (e \] !ith /alues in ascending ordermedian is the middle term !hich is gi/en as + i.e ]6+mean6\7]7'"6107\ 66Y"07"\6\7+7 66Y2\62+

107\61+ 66Y\62+ rom the 2 equations\6062+hereoresum o num(ers607+72+6"0

U pro(a(ility that a leap year is chosen at random !ill ha/e +" sundays

5ol6* Aeap ]ear has "##


13/55

5ol612'W2W4 6 4height !ill (e radius o circle(ase !ill (e diam

orarea o circle 6 4 pi

rom ,ythagoras. 2.32642'61#so 3 6 sqrt8'so triangle area 6 .+ Wsqrt8'Wsqrt8'64

U * !oman goes to a shop to (uy a product !orth -s.200. 5he (uys the product andgi/es a thousand rupee note. he shopkeeper goes to the other shop to get the change.

hen he returns (ack and gi/es the change (ack to the !oman and then she departs.*ter sometime the second shopkeeper comes and reports that 1000 rupee note is akeso the Grst shopkeeper gi/es him 1000rs.%hat is the net loss incurred (y Grstshopkeeper in the transaction&

5ol6ans))1000 rupees lossnitiallyhe gets 1000rupees rom second shopkeeper and repays him 1000 rupees.5othere is no loss and no gain till no!.=urthurhe gi/es 800 rupees to the !oman andalso looses the 200rupees product.5othe o/er all loss is 1000 rupees.

Uhe radii o top and (ottom o a (ucket are 2+cms and 20cms respecti/ely. the/olume o the (ucket is #$100 cu(ic cms Gnd the height o the (ucket.

5ol6

_olume o the =rustrum is cone6 ".14Wh-2 7 r27 -r'",utting the /alues_6#$100 -62+ r620eight o the rustrum is 4#2cms

U Deorge !orks + times aster than his son and hence completes a Xo( 40 days earlierthan his son. =ind the time they !ould take to Gnish the Xo( !orking together.

5ol6 george63

son6+3so +336403610so 11071+06#+0ans 8.""


14/55

U122"""4444112222""""""4....... !hat is the 2888th num(er in thissequence&&&

5ol6let consider 1st sequence 1122""446 total 10 termslet consider 2nd sequence 1224"#486 total 20 termslet consider "rd sequence 1"2#">4126 total "0 terms

let consider 4th sequence 1428"1241#6 total 40 terms and so on...so the series is in *.,1020"040+0#0......101727"747+7#7....n'63 !here 3 is the near /alue to the gi/en 2888th num(er!.k.t sum o n terms 6nn71'210`nn71'263nearer to 2888'(y trail and error method !e get n62"and !e get 362$#0no.o more terms628882$#06128as 2" is completed !e ha/e start !ith 24 digit i.e241482$2">#4as !e add no.o 1Ss and 2Ss !e get $2

as !e add no.o 1Ss and 2Ss and "Ss !e get 144so the required num(er T128T is in (et!een $21Ss72Ss' and 1441Ss72Ss7"Ss'so the 128th num(er is T"T.Gnally the 2888th num(er is T"T

U Gnd the last t!o digits o +8"+12&

#1..considering last t!o digits8"168"8"268>

8""68$.....8"126#1.....8"1>64$8"206018"2168"..thereore !e see po!er repeats itsel ater 20.. so di/iding +12 (y 20 !e getremainder612 so 8"126#1 last t!o digits.

U n an airorce o a country there are "32+32' Gghter planes and 3232' cargoplanes. oth types o planes are put in diVerent group in such a !ay that e/ery groupconsists o equal num(er o planes. *n o:cial is appointed to take care o each ande/ery group. =ind out the least num(er o o:cials to (e appointed so that there isatleast one o:cial or e/ery group.

5ol6 the a(o/e quadratic equations can (e sol/e !hich !ill gi/e the groups made andhence the o:cials required ...hence the ans is 2.


15/55

do /alue putting... put 361 or 2 or "... !e get a 7/e solution or 36"..... !hich gi/esGghter 610 and cargo64...thus 2 groups !ill (e ormed o + Gghter and 2 cargo each.....)'

U n (ase $a num(er is !ritten only using the digits 12...#. he num(er 21 in (ase $is equal to 2W$7161+ in (ase 10.5imilarly the num(er 1"+ in (ase $ is 13$27"3$7+ in(ase 10. %hat is the sum o (ase $ num(ers 12"4 and #+4" in (ase $.&

5ol612"4 in (ase $6 4## in (ase 10.4W$07"W$172W$271W$"'#+4" in (ase $ 62""4 in (ase 10.adding 4##72""462800 in (ase 10.con/ert it into (ase $ (y di/iding !ith $.2800 in (ase 10 6 11110 in (ase $.

U %rite an email to the manager o a company called E\ Fomplaining a(out adeli/ery ser/ice

(ought a productdidnbt !orkcalled customer careput me through automatedteleser/iceson hold or 1> minutesgot disconnected!rote an emailreply sorted out2 days pro(lem still unresol/ed

he ManagerE\

!ant to say that (eing a customer o your company (ought a product.ut !ithin 2days it stopped !orking and no! its is not !orking and in a non !orking

condition.5e/eral times called the customer care (ut e/ery time they used to put methrough automated teleser/ices .%hen called them they put me on hold or 1>minutes Xust (y saying that !e are checking and !ithout saying anythingthe call Xustgot disconnected.hey !rote anmail in reply and said that the pro(lem !ill (e sortedout .ut t!o days passedthe pro(lem is still unresol/ed.so request you to takenecessary steps regarding this as soon as possi(le.

5%*

U he letter in the !ord *


16/55

U Deorge ,aul and ari started a (usiness (y contri(uting -s "0000 -s 40000 -s+0000 respecti/ely. *ter 12 year Deorge !ithdra!s hal his contri(ution. *t the end othe year the (usiness sho!ed a proGt o -s >0000 !hich is di/ided amongst the " menproportionate to amount and duration o their in/estment in enterprise. ,aul got&

"0000W#71+000W#)40000W127+0000W1262$)48)#06>)1#)20thereore paul got61#4+'W>00006"2000

U*l/in en and Flinton run a race !ith *l/in Gnishing 48 meters ahead o enand$2 meters ahead o Flinton !hile runner en Gnishes "2 meters ahead o runnerFlinton. Each runner tra/els the entire distance at constant speed. %hat is the length o

the race&optiona. 480(. >#c. 1>2d. None o these

5olans!er is 1>2...let !hole distance is SdS and speed o *l/in en and Flinton is *Fthen*Wt6d .... 1

Wt6d48'.....2FWt6d$2'....."sorom eqt 12 ^ "*))F))d)d48')d$2'.....4no! second condition is..)F))d)d"2'....+ro eqtn 4 and +..d48'd$2'6dd"2'...on sol/ingor (y option' d6 1>2...

U a and ( run 1k.m race i a gi/es ( start o +0m a !in (y 14sec...i ( gi/es a start o22sec ( !in (y 20m...Gnd timen (y a to complete the race

5ol6


17/55

%rite an email to your (oss using the (elo! stated lines)

Aearnt that (oss is taking up a ne! proXect planned or in/estment o millions o dollarsin it unortunately plan !ill not !ork competitor has similar proXect this proXect !as aailure no demand in the market hence should stop this idea immediately.

-espected sir

]esterday came to kno! that you are taking up a ne! proXect !hich is planned or thein/estment o millions o dollars in it.5ince it is a huge amountone important thing that !ant to inorm you that unortunatelythe plan !ill not !ork.he reason (ehind this isthat our competitor has also the similar proXect and their proXect !as a (ig ailure(ecause it has no demand in the market.ence request you to stop this ideaimmediately.t !ould sa/e us rom a (ig loss.

thanking youyours aithully5%*D**

U* hut is in the shape o a hemisphere surmounted on a cylinder. he diameter o the(ase is 24m. %hat is the area o the can/as required to co/er the hut i the ma3imumheight o the hut is 20m &a'4$2 sq.m('4+# sq.mc'480 sq.md'"42 sq.m

5ol6 hut area6cur/ed surace o hemispere7 cur/ed area o cylindere3clude t!o

circles'62WpiWr2'72WpiWrWh'6480pi sq.m

U1+ people sit round a circular ta(le !hat are the odds against t!o particular peoplesitting together.a'$)1('#)1c'+)1d'1)+

5ol6ans is #)1odds agianst an e/ent6possi(ilities o e/ent not happenning'possi(ilities o e/ent happening'6possi(ilities that 2 people are not togeatherpossi that they are togeather6 14Z2W1"Z'2W1"Z'6 #)1


18/55

U 2"#2"20" is di/isi(le (y !hich o the ollo!ing .a' 1" ^ #$(' 41 ^ "1c' 1$ ^ $d' > ^ $

U he interior angle o a regular polygon is 1+# . o! many diagonals does the polygonha/e &a'#0('>0c'$+d'120

5olans is >0interior angle ormula6180Wn2'nherein1+#6180Wn2'n

!e get n61+num(er o diagnols6nWn"'261+W12'26>0

UPake is aster than ,aul. Pake and ,aul each !alk 40 km. he sum o their speeds is 1"kmh and the sum o time taken (y them is 1" hours. hen Pakebs speed in OM, isequal toa'>('$c'8d'1"

5ols17s261"[40s1'740s2'61"[sol/ing these eqn u get s168 or +.

U 9 a set o "0 num(ers a/erage o Grst 10 num(ers 6 a/erage o last 20 num(ers.hen the sum o the last 20 num(ers is &a'2 \ sum o Grst ten num(ers('2 \ sum o last ten num(ersc'5um o Grst ten num(ers

d'Fannot (e determined !ith gi/en data

5olsince a/erage6sum o n no.s'total no'thereore sum o Grst 10 no.s'10 66sum o last 20 no'20hence. sum o last 20 no.s' 6 2Wsum o Grst 10 no.s'


19/55

U a( are t!o perect square digits and a( is a t!o digit perect square num(ersuchthat a3('7a7('6a( then the /alue o ?(a(7a'@ isa'2$('81c'1#d'None o these

5ol81 is the solution.the num(er is 4>...so a64(6> !hich satisGes the relation4W>'747>64>so the /alue >4>74''681

U5peed o a train is 20kmhr . he strength o the steam !as increased t!oold (utdue tocertain other actors the riction also increased 1 times. in the (eginning the ratioo the strength o steam and riction !as ")1 . =ind the present speed o the train.

a'40kmhr('"0kmhrc'4+ kmhrd'None o these

5olne! ratio steam)riction is #)1.+ as steam dou(le and riction is "2 times so #)1.+64)1 no! as gi/en ")1620 means "336203610s0 4)1 is 4336"0 ans is "0

U %hat should (e su(tracted rom 41+ so that the remaining is di/isi(le (y "1a'0

('1c'2d'"

5ol 4"'+"1 6#4'+"1 62+"1 6 "2"11 is the remainder so 1 is to (e su(tracted

U=ind the 5um ^ ,roduct o the roots in the polynomial 4347"3"72327360

5olas it is an e/en polynomial so sum o roots is (a and here (6"a64 so sum6"4

and product is equal to const terma and here constant term is 0 so product is 0

U he addition 4+$ 7 >82 7 8># 6 2"4+ is incorrect. %hat is the least digit that can (echanged to make the addition correct&

5ol6++ in 4+$ changed to #...so ne! num( is 4#$ satisying the sum


20/55

U + coVee and 4 tea costs -s.># + (adam milk and # coVee costs -s. "2 and $ tea and# (adam milk costs -s."$. %hat is the com(ined price o 1tea 1 coVee and 1 (adammilk&

5ol+c74t6># ........1'+(7#c6"2 ........2'$t7#(6"$ ........."'no! 1'72'7"'11c711t711(61#+11c7t7('61#+c7t7(61+

U * 5amsung duo and a Dala3y are (ought or -s.40000. he ># 7 "">4"7""n.

5ol"1# ' "7"1>>#7"">4"7"n'"5o it is equi/alent to a"7"a2(7"a(27("5o"W"1#'2W"n6"1>>#"""7n'6"1>>#

n61>#"

U *ish!arya !ant to cele(rate her (irthday !ith her riends. 5he had $4 choco sticks!ith her she !ants one choco stick or her and also !ant to distri(ute to her riends.o! many !ays she can do this&a' 4(' 2c' "$d' $4

5oldummie

U !o 5 alumni decide to meet at Fa Ainger 9n (et!een >)"0 am and 10)"0 am.hey agree that the person !ho arri/es Grst at the cae !ould !ait or e3actly 1+minutes or the other. each o them arri/es at a random time (et!een >)"0 *M and


21/55

10)"0 *M. %hat is the pro(a(ility that the meeting takes place&$18 >1# $1# 1118

5ol$1# is the ans!er....the pro(a(ility that they meet61pro( that they donSt meetpro( that they donSt meet6"4'W"4'6>1#

hence pro( that they meet61>1#6$1#

U o! many polynomial unctions o degree Y6 1 satisy 3 2' 6 ?3' @2 6 3' ' &a'More than 2('2c'0d'1

3'632 is the only equation that satisGes the ruleans) 1

U he letters o the !ord -*NDAE are permuted in all possi(le !ays then !hat is thepro(a(ility o choosing a !ord rom this list in !hich the relati/e positions o /o!els andconsonants remain unaltered isa'1+#('2+c'"8d'+#

5olans)1+#

" /o!el can (e placed in "Z !ays.+ consonant can (e placed in +Z !ays.so pro(a(ility is "ZW+Z'8Z61+#

U n a +00m race U starts 1+m ahead o ,. ut , !ins the race !hile U is still 10m(ehind. he ratio o their speeds ,)U' assuming that (oth start at the same time isa'20)1>('4)+c'+)#d'4)$

5ol!hen p complete the race q lag o 10 and also it starts 1+m ahed so !hen pcomletethe race q lag o 2+m so ration is +00)4$+ ie 20)1>

/1)/2 6d1t1')d2t2't1 6 t2so /1)/2 6 d1)d2 6 +00)+00101+' 6 +00)4$+ 6 20)1>


22/55

U * group o t!el/e persons is to (e seated around a circular ta(le. here are only t!o!omen in the group Gnd the pro(a(ility that there is atleast three men (et!een the t!o!omen.a'+11

('$12c'1"d'2>

5ol

U%hat is the pro(a(ility that a > digit num(er ormed using 12"4+#$8> is di/isi(le(y "#.!ithout repetition'

5olans) 2>

here the >digit num(er ormed should (e di/isi(le (y "#"#6>W4ie the num(er should (e di/isi(le (y (oth > nd 41727"7...7> 6 4+so e/ery num(er ormed !ith these digits can (e di/isi(le (y >no! the last t!o digits o the num(er should (e di/isi(le (y 4so last 2 digits can (e 121#2428"2"#48+2+##4#8$2$#84>2>8total 1# possi(ilitiesso starting $ digits can (e arranged in $Z !aysso pro(a(ility 6 1# W $Z'>Z

U 1. n ho! many !ays a team o 11 can (e must (e selected rom +men and 11!omen such that the team must not comprise o more than " men&2. the perimeter o a square is equal to t!ice the perimeter o rectangle o length 8cmand (readth $cm. !hat is the circumerence o a semicircle !hose diameter is equal toside o the square&". area o a quadrilateral !hose /ertices are 11'22'21'22'4. speed o the train is 20kmhr. he strenght o steam !as incrsed t!o old (ut due tocertain other actors the riction also increase "2 times. in the (eginning the ratio ostrength o steam and riction !as ")1.=ind present speed o the train.+. *nubs ages !as " times older to the age o (anu bs age 10 years ago.%hat !ill(e the age o anu ne3t yeari their present age ratio is 2)11. *nXu started to mo/e in the direction o east and turn to his let ater mo/ing 2+m.

hen he turned to his let ater mo/in 10 m and ater this he mo/ed "+ m. hen heturned to his let and mo/ed 20 m. No! ho! ar is he rom his starting point&

5ol


23/55

U!rite email .

thank you keep it up client !eekend night appreciating the !ork done hard!ork Fustomer (illing proXect (eyond call o duty e3tra !orking hours

days appro/e the e3tension shortage o money

email to your parents descri(ing the e3perience related to your Grst campus inter/ie!.

80 minutes tensed ormal shirt negati/e marking polish !rite a program early inthe morning !ritten test our mem(er panel e3plain oVer /ery happy

Un a mi3ture o a ( ^ c i a and ( are mi3ed in ")+ ratio and ( and c are mi3ed in 8)+-atio and i the Gnal mi3ture is "+ liters Gnd the amount o (&

5ol")+ 8)+24)40 40)2+so a)()c))24)40)2+so (6"+W408>61+.$" ans

U * telegraph has + arms and each arm is capa(le o our distinct positions includingthe positions including the position o rest. %hat is the total num(er o signals that can(e made&

5oloption ()102".each arm has 4 chances i.e. 4 positions.thereore 4+.(ut in thatthere is a position !here all the arms are in rest position so that there !ill (e nosignal.so !e ha/e to e3clude it.sothe ans!er is 4+16102".

U * and tra/elling rom 3 to y .* starts at 12pm at a speed o #"mh . at 1)"0 pm ata speed o 84 mh .at !hat time !ill (e "4m ahead o *


24/55

5olat 12pm * is at 3...*t 1)"0pm he reaches #"W1.+m a!ay rom 3soat 1)"0pm dist (! * and is >4.+m.. has to co/er the >4.+m and also "4m ahead.time taken6>4.+7"4'84#"'6#.11>hrs6#hrs $min 10 secthe time then is $)"$)10pm

U m7n gi/es remainder 8 ^ mn gi/es remainder # !hen di/ided (y 12 !hat isremainder !hen mn di/ided (y #&&

5ol12a786m7n[12(7#6mn[thereore mn6?#a7(71'71@W?#a('71@[so theremainder is 1 !hen di/ided (y #

m7n612378mn612y7#

sol/e or m ^ nm6#37y'7$

n6#3y'71

mn#61

U3y 7y3 64#. =ind 3 and y.

5ol364+y61trail and error is the pnly !ay to get the ans

U =ind last three digits o 2>88#8$

5ol

Ua pack o +2 cards.." cards are dra!n at random.Gnd the pro(a(ility. 9 dra!ingkinga queen and Xack.

sol4c1W4c1W4c1'+2c"

U *ish!arya !ant to cele(rate her (irthday !ith her riends. 5he had $4 choco sticks!ith her she !ants one choco stick or her and also !ant to distri(ute to her riends.o! many !ays she can do this&a' 4(' 2c' "$d' $4


25/55

5ol think dummy questionZZn the question didnSt mentioned num(er o riends5o $4 chocosticks or n num(er o riends&&

U!o 5 alumni decide to meet at Fa Ainger 9n (et!een >)"0 am and 10)"0 am.hey agree that the person !ho arri/es Grst at the cae !ould !ait or e3actly 1+minutes or the other. each o them arri/es at a random time (et!een >)"0 *M and10)"0 *M. %hat is the pro(a(ility that the meeting takes place&$18 >1# $1# 1118

5ol

$1# is the ans!er....the pro(a(ility that they meet61pro( that they donSt meetpro( that they donSt meet6"4'W"4'6>1#hence pro( that they meet61>1#6$1#

Uhe letters o the !ord -*NDAE are permuted in all possi(le !ays then !hat is thepro(a(ility o choosing a !ord rom this list in !hich the relati/e positions o /o!els andconsonants remain unaltered isa'1+#('2+c'"8d'+#

5olans)1+#

" /o!el can (e placed in "Z !ays.+ consonant can (e placed in +Z !ays.so pro(a(ility is "ZW+Z'8Z61+#

Un a +00m race U starts 1+m ahead o ,. ut , !ins the race !hile U is still 10m(ehind. he ratio o their speeds ,)U' assuming that (oth start at the same time isa'20)1>('4)+c'+)#d'4)$

5ol!hen p complete the race q lag o 10 and also it starts 1+m ahed so !hen pcomletethe race q lag o 2+m so ration is +00)4$+ ie 20)1>

Uemail to to the customer Mr. Dill -oy e3plain.una(le to deli/er product on time issues (eneGts $ days late time e3tra money reasons.


26/55

U!rite email .thank you keep it up client !eekend night appreciating the !ork done hard!ork Fustomer (illing proXect (eyond call o duty e3tra !orking hours

Uemail to your Gnal year proXect guide e3plaining the delay in the proXect su(mission.

su(mission date oreign edition (ooks 5chedule 10th Pune laptop crash delay inprinting o/erall status > days appro/e the e3tension shortage o money

Q-email to a company requesting them to sponsor your college culturalfestival.

pdf le - reputed institute - 10 days - 200 college - sparkling performance -

extravaganza - sponsor the event - request appointment - rochure attached

Uemail to your parents descri(ing the e3perience related to your Grst campusinter/ie!.

80 minutes tensed ormal shirt negati/e marking polish !rite a program early inthe morning !ritten test our mem(er panel e3plain oVer /ery happy

U the price o petrol increases "0; and (a(u intends spend only an additional 10;

on petrol(y ho! much percentage should he reduce the consumption

5ol6 1+."8;

Q-! "#" grid is coloured using red and lue colours$such that if %e rotate thegrid aout its centre plane y 1&0 degrees$the grid looks the same.'henumer of %ays to colour the grid this %ay is(a)2*+ )+, c)1+ d)"2ans9,9N


27/55

U >. i there are 10 people standing in a queue and * is standing (eore is standing(eore Fand F (eore 5 $.

U and ( run a 1000m race. * gi/es a start o +0m * !ins (y 14sec. gi/es *start o 22sec !ins (y 20m.=ind timen (y * to complete the race

sol

Q-n ho% many %ays " oys can e placed in > seats in a single ro%$such thatno t%o oys are ad@acent to each other.

5ol

Q-the sum of anitha and sunitha age is ,".hence 11 years anitha age %ill eAB+ times of sunitha age.nd the present sunitha age?

5ollet age o sunitha (e y yearsn anitha (e 3 yearsthen

37y64"ater 11 years37116$#y711'!e get#3$y611 and 37y64"ater sol/ing !e get y61> and 3624therore age o sunitha is 1> years

U ere a( means a raised to the po!er o (.Gnd the highest possi(le /alue o n suchthat 8n is e3actly di/isi(le (y 4444

5olans62>444462W2W11'44622W11'446288 W 1144no! 8n can (e !ritten as 2"n886"nn62> hence 2> is the ans

8. ho! many no.s are orm rom num(er 12"4+.include all digit no.s'ans is "2+


28/55

5ol

U a person co/ers hal his Xourney (y train at #0 kmph the remainder hal (y (us at "0kmph and the rest (y cycle at 10 kmph. Gnd his a/erage speed during his entire

Xourney&&

5ol24kmphlet the total distance (e 3 km32 km is tra/elled (y train at a speed o #0kmph34 km is tra/elled (y (us at a speed o "0kmphand 34 is tra/elled (y cycle at a speed o 10kmphso a/g speed 6 total distancetotal time6Y 332W#0 7 34W"0 7 34W10'6Ysol/ing this a/g speed6 24kmph

U'here is a pie to e divided among 20 people. a man eats " pizzas and%omen eats t%o pieces and a child eats a half of pie. nd the numer ofmen $%omen and children so that they are 20 people in total and every onegets some pie .there are 20 pieces of pie in all ?optiona) A %omen 1 men and 12 children) *% 1m and 1,cc) +% 2m and 12cd) ,% 2m 1,c!ns-m 7! 7c620

1W"7+W2714W12620so ans is (

U* piece o paper is in the shape o rt angld tringl. this paper is cut to its hypotenuselea/ing a smaller triangle !ith "+; smaller hypotenuse............i the initial area !as+4sq units !hat is the area o E NE% smaller triangle....

ol-as (oth triangles are similar so)hyp1hyp26sqrtarea1'sqrtarea2'5olet (igger hyp63 unitsmall hyp61"+100'36#+3100.3#+3100'6sqrt+4'sqrtarea2'.so area2622.81+ sq units.

U m7n gi/es remainder 8 and mn gi/es remainder # !hen di/ided (y 12 !hat is theremainder !hen mn is di/ided (y # &

ol-m7n612378mn612y7#m61237y'7142n61237y'722


29/55

$W1#1 remainder

Udetermine the distance (! 3intercept and H intercept o equation is 237>y"H618.

optiona' #."2(' 10.82c' "d' +

5olto Gnd 3 intercept put y60 and H60. !e get 36>. his can (e !ritten as >00'to Gnd H intercept put 360 and y60. !e get H6#. his can (e !ritten as 00#'n! Gnd d distance (t!n these 2 points.. i.e sqrt3231'2 7 y2y1'2 7 H2H1'2'...sqrt? >2 7 0 7 #'2 @6sqrt 11$ 6 10.81## 10.82

Ua group o riends tomtimdickdianaharry and harriet go out to a air three hundredmeters rom the me mdonald !hich is G/e kms a!ay.the y see !eighing machine anddecided to ha/e some un.ho!e/er the girl reuse to step on the !eighing machine.sotomdick and harry !eigh themsel/es in a particular order.Grst tom and dick and harry!eigh themsel/es indi/idually.and then tomdick and harry tom and harry and then tomand dick and harry together.the recorded !eight or the last measure is 1+8kgsthen thea/g total o the $ measure isoptiona' 111.8#(' +2.#$c' >0.2>

d' #$.$1

5ol6Y`'70m.6Y!hen mo/es 1m F mo/es .>m.6Y!hen mo/es 8+m F mo/es .>W8+m6$#.+m. * (eats F (y + sec6Yc takes +sec to mo/es 2".+m.


30/55

6Yc takes 1sec to mo/es 4.$m.6Yspeed64.$msec.

Q-ll dirt or ll soil is usually the su soil removed from an excavation side

and is used to level a place or used to create a artical mounds .if the averagedensity of su soil is removed form as ite is " gmBcu cm and its %eight is ,00kgs. ho% many hemispherical pits each of volume 2,0 cu cm$can this su soilll?optiona) ***) 2AAc) **+d) **,ol-*ns)++#Y 400W1000"61"""""."""Y1""""".""""240

Y++#

U" (oys (o( pete .and oli/er and t!o girls samantha and kristie are to (e seated in aro!.samantha al!ays sits to the let od (o(.no gril sits at hte e3treme positions andmiddle positions .pete al!ays sits at e3treme positions .!ho sits to the right o kriste&optiomsa' pete or oli/er(' petec' oli/erd' (o(e' none

ol-pete or oli/er

Uthe great mathamatican names (haskaracharya ormulated this pro(lem t!elthcentury or his teenaged prime num(er aged lila/ati.he also authoredd the eponymouslila/ati a compendeum mathamtican puHHels in !hich no o pro(lems that use thisormula is sum o t!o prime num(ers .the product o t!o prime num(ers is smaller thanthe total o pro(lems in lila/ati .no!the diVerence o t!o num(ers is 4 and theirproduct is 18 .!hat is the sum o their squares&optionsa' "4(' 40c' +2

d' 42e' none

5ol a27(26a('272a(61#72W186+2*ns. +2


31/55

Q-n a room there are A persons.'he chance that 2 of them %ere orn on same day of the %eek

5olhe ans!er is 1$.he Grst person can ha/e the (irthday in any o the days o the !eek !hich gi/es thepro(a(ility as 1 ie $$'.

he second person should ha/e the (irthday on the same day as the 1st ones !hichdecreases the sample spaces to 1dayhe (irthday o the 1st person' making thepro(a(ility 1$. hence total pro(a(ility 6 1W1$61$.9-%e can the (irthday pro(lemSs solution N9 2 ,E-59N5 F*N *_E E 5*ME -10'l and >10'( contri(utes to 81100'_. so the (readth is decreased (y 110'(ie 10; o original (. so ne! (64.+

Un is a natural num(er and n" has 1# actors. hen ho! many actors can n4ha/e&

5olsay no is 46 21 W 21then n"6 4" 62" W 2" then no o actors 6 "71' W"71' 61#thereore or n4 6 446 24 W 24then no o actors 6 471'W471'6 2+ ..thus ans!er is 2+.

U ho! many three digit num(ers !hen di/ided (y +# and $ lea/e a remainder o 2"and + respecti/ely&

5olans6+

Q-! tradesman marks his good "0D aove the cost price.if he allo%s a dicountof + 1B,D. then his gain percent is(let cp 6100mp61"0sp612+400'1"06121.8$+p;621.8$+


32/55

Ua t!o digit no is 18 less than square o the sum o its digit.ho! many such no arethere..&&

5olonly 1

ans is #"(coH #27"264+#"4+618

U here are 100 !ine glasses. oVered my ser/ant to " paise or e/ery (roken glass to(e deli/ered saely and oreit > paisa or e/ery glass (roken at the end o day. erecie/ed -s.2.40 .ho! many glass did he (reak

ol-1003'W">W3'6240#0612W3'\6+

U * person (uys a (rand ne! onda (icycle or -s.800. e uses it or a year and thensells it. e makes a proGt o 10; in this transaction. hen again he (uys a ne! cycle(ut Gnds that the price has gone up (y 20;. e uses the ne! cycle or a year and thensells it or a proGt o "0;. =ind the a/erage annual proGt o the person through thesetransactions.

ol-cp o Grst (icycle 800sp o Grst (icycle 880cp o second (icycle >#0sp o second (icycle >#0 7 0."0W>#06 1248total proGt in 2 years 6 8807 1248800>#0 6 "#8

proGt in 1 year 6 184Q-tarting from 1 if you are asked to %rite rst 1A2 digits of the naturalnumers $ %hich digit you stop atoption1) ,2) A") &,) >sol-12"4+#$8>10611digits1120620digits21>06140 digitstotal 1$1digits are completedne3t num(er is >1 >is 1$2th digit ^ 1 is 1$"rd digitso ans!er is >or> is the ans. he natural no are 12"4+#$8>1011......think to it as digits so rom 1> !eha/e > digits ^ rom 10>> !e ha/e >0 natural no thereore digits rom 10>> are 180total digits rom 1>>618> no! !e !ant 1$2th digit !hich is 1$ less rom 18>


33/55

U#. _inay dropped a (all rom his terrace !hose height is +0 meters i the height othe (all reduces to hal ater e/ery contact !ith the ground. %hat is the total distancetra/elled (y the (all&a' $+(' 100c' 1+0

d' 200

5ol s6+072W+02172W+022772W+02"7....72W+02inGnites6+0?17171217122712".......@s6+07+0?171217122712".......@s6a1r YinGnte D,'s6+07+0?1112'@s61+0

U +. _ictor takes an escalator in the metro station. %hen he runs 10 steps on the

escalators it takes him 40 seconds to reach the top[ !hereas !hen the runs 20 steps ittakes him 2+ seconds. %hat is the total num(er o steps in the escalator&a' "#(' "8c' 40d' "2

5ollet total num(er o steps (e 3!hen _ictor takes 10 steps)distancesteps remaining 6 310' time 6 40 sec speed 6 310'40!hen _ictor takes 20 steps)distancesteps remaining 6 320' time 6 2+ sec speed 6 320'2+

(ut speed o escalator !onSt change so)310'40 6 320'2+6Y 3 6 "#.##$ 6 "# steps

U 5um o the digits in the equation 1#100'W12+1"+' is

ol-it can (e also !ritten as2400'W+40+''2400'W+400'W++''2W+'400'W++''10400'W++''as !e kno! that 10n6 10000......so 1000....'W"12+''!e get "12+00000.....ans6"71727+707070..... 611

U5e/en speakers *1 *2 *".... *$ !ere scheduled to speak at a unction. n ho!many !ays their speech can (e arranged such that)


34/55

*1 speaks (eore *" and *" speaks (eore *+ .optiona' 840(' 8#0c' 420d' 410

5ol" people can (e selected rom $ in $c" !aysarranging those " people is only in one !ay.remaining 4 can (e arranged in 4Z !ays.so $c"W1W4Z6840short cut) $Z"Z

U %hat is the remainder !hen 121212.."00 digits' is di/ided (y >>&optiona' 18(' "#c' $2d' 0

5ol1' >> can (e e3pressed as >W11

2' di/isi(ility rule or >) sum o digits must (e di/isi(le (y >sopair 2 digits. 1+0 total pairs and sum o digits o each pair is 1726" toal sum is"W1+0'64+0.4+0 is completely di/isi(le (y >. rem60

"' di/isi(ility rule or 11) sum o e/n places sum o odd places must (e 0 0r 11

multiple.consider 1st 2 digits 2161similarly 1+0 pairsW16 1+01+0116 rem is $

4' !e can e3press it as >*6117$gi/e *60!e !ill get > $gi/e *61!e !ill get 18 18

!e should gi/e same /alues or * and untill !e get equal /alues and that !ill (eans!er. so ans!er to this is 18

U!hat is the last t!o digits o 12"12"Z

ol-12"Z !ill ha/e more than 2 Hero at the end so it is a multiple o 4.

No! 12"4'...00'622888##41'...00'No! po!ers o 41 repeat the last t!o digits.ie 411641 41#6..414126..81 41$6..81


35/55

41"6..21 4186..214146..#1 41>6..#141+6..01 41106..01

*s 12"Z !ill still (e ha/ing some Heroes let at the end so it /alue is a multiple o 10 andso the last 2 digits are 01.

Uhree runners * and F run a race!ith runner * Gnishing 24 meters ahead o and"#meters ahead o F!hile runner Gnishes 1# meters ahead o run F.Each runnertra/els the entire distance at a constant distance.!hat !as the length o race &

a'$2m('>#mc'120md'144m

ol-let race is o6 3 meters

!hen * completed the race distance co/ered (y 6 324'and (y F6 3"#'!hen completed the race 63' distance co/ered (y F6 31#'6Y 324'3 6 3"#'31#'6Y 3 6 >#m

U!hat !ill (e da unit digit o 11221122Z&

ol-1122Z !ill end !ith a lot o Heros!hich is di/isi(le (y 4'and 11221112221122"112241122+ends !ith 248#2 up to so on.

so the actorial /alue di/ided (y 4. and the ans!er !ill (e #

UGnd the last t!o digits o 1021">21'7"081">21'

ol-!hen a no ends !ith 1 the last digit is 1.or last 2nd digit the short cut is1021tenths place digitWunit place digit o the po!er621'62similarly or the second no "081 it is 81'68so the last t!o digits are 217816102.so ans!er is 02

U9ranges can (e packed in sets o 10 oranges in a (o3 type * or 2+ oranges in (o3type .* carton comprising o 1000 oranges o type * and type is packed. o! manydiVerent com(inations possi(le in the num(er o type * and type (o3es !hileorganiHing the oranges&a'21 ('20 c'1> d'18

ol-or gi/en data the e3pression !ill (e 10372+y61000the a(o/e e3p !ill (e satisGed only !ith multiples o 2 up to "8.


36/55

so no. o com(inations are 1>.i oranges are packed in type * (o3es only6 1 !ayi oranges are packed in type (o3es only6 1 !ayso tatal 6 1>7171621

U %EN E NjME-5 *-E %-EN N *5E ( %E *_EE 1+W2+6414 EN E_*AjE 9= (is

ol-!rite 1+W2+6414 as

1W(17+W(0'72W(17+W(0'64W(271W(174W(0'666Y(7+'2(7+'64(27(74666Y 2(214(2160on sol/ing !e get roots as 8.2#>$ and 1.2#>$hence (68.2# or 8

U ]%j5U is 2+ 2" 21 1> 1$ then MOD= isoption*'> 8 $ # +'1 2 " + $F'$ 8 4 + "


37/55

aY2410>(Y++412cY10+12dYnone o these

5oltotal num(er o choices6+W+W+W+W+6++

a/oura(le cases6+W4W"W2W16+Zpro(a(ility6+Z++

U24 random points. $ are collinear. *ny " points are not collinear.Gnd the num(er otriangles ormed.

oltotal 6 24 pointscolinear points6$num(er o traingles can (e ormed6? 24c"$c" 6 1>"2"+ 61>8> @.

Un a room o length 24mts (readth 18mts height 1# mts. !hat is the length olongest rod that can (e placed in the room&

ol--oot242718271#2'6 "4

Ua; o a'7 (; o('62; o a( then !hat percentage o a is (& options a'+0; ('$+;c'100; d' cant (e determined

5ola21007(210062WaW(100...so a(60 ...a6( so 100;

Un an e3am students !ere asked to Gnd the perimeter o a square !hich containsthree circles such that their enters on the diagonal o the square the middle circletouches t!o e3treme circles on either side and t!o e3treme circles touch t!o sides othe square and the radius o the three are equal . *nd ate !hat times the radius equalsthe perimeter&

ol-Aet the radius o circle (e rlet the side o square (e athen diagonal o square6 aWsqrt2'

his diagonal length 6 4Wr 7 2r W sqrt2'(ecause the e3treme circleSs radius is perpendicular to side o square.'

hus !e get

4Wr72rWsqrt2'6aWsqrt2'

r2Wsqrt2'72'6a

ra612Wsqrt2'72'

hus ratio) r)4a 6 1)42Wsqrt2'72'


38/55

Un the reading room o a li(rary there are 10 reading spots. Each reading spotconsists o a round ta(le !ith4 chairs placed around it. here are some readers suchthat in each occupied reading spot there are diVerent num(ers o readers. in all thereare 10 readers ho! many reading spots do not ha/e e/en a single reader& F52011'

optiona. "(. 4c. #d. +

5olor diVerent no o reader612"4total 10'in this !ay only 4 reading spot is Glledso # is letans!er6#

U* runs 4." times as ast as . * gi/es a start o 4+ m ho! ar must the !inningpost (e so that * and reach it at the same time.

ol-let distance co/ered (y 6dthen distance co/ered (y *6d74+

and let speed o 63then speed o *64."3

(y equating or time6 d74+'4."36d3sol/ing or d61".#"

so !inning post must (e 1".#"74+6+8.#"m rom *

Uhere are t!o (ottles * and each Glled !ith milk and !ater in the ratio +)" and 1)2respecti/ely. * ne! mi3ture is ormed (y mi3ing the contents o * and in the ratio4)".%hat is the ratio o composition o milk and !ater in the ne! mi3ture&

ol-in Grst mi3ture ) milk 6 +8 [ !ater6"8in second mi3ture ) milk 6 1" [ !ater62"no! in ne! mi3ture )milk 6 +8W4$' 7 1"W"$' 6 12!ater 6 "8W4$' 7 2"W"$' 6 12so in ne! mi3ture milk ) !ater 6 1 ) 1

Uhere are 80 litres o milk in a /essel. 8 litres milk are dra!n oV and equal quantity o!ater is added. he same operation is repeated or a second and a third time. =ind thequantity o milk in the resultant mi3ture.

ol-there is a ormula or sol/ing this pro(lem\W1]\'n


39/55

!here \6initial quantityhere it is 80']6replaced quantityhere it is 8'n6num(er o times it is (eing replacedhere it is "'thereoreresultant680W1880'"'6+8."2

U"4. m 7 n !hen di/ided (y 12 gi/es the remainder 8. 5imilarly !hen m b n isdi/ided (y 12 gi/es the remainder #. %hat should (e the remainder !hen mn is di/ided(y #.

ol-i a is quotient thenm7n612a78mn612a7#on sol/ing i a61then m61> and n61mn61># remainder is 1

Uhree sides o a triangle ,U U- and -, contains + # and " points respecti/ely. %hatis the ma3 num(er o triangles can (e made using these points.

ol-ans!er is """.here there are +7#7" 614 points rom !hich triangle can (e made. there or num(er otriangles made out o it is 14F".(ut as triangle cannot (e made out o collinear points thereore total num(er o triangle!ould (e14F""F"#F"+F"6""".

U5um o the digits o a three digit num(er is 1$ and sum o the squares o the digit is10>. *lso !hen the num(er is su(tracted (y 4>+ the num(er gets re/ersed. =ind thenum(er

ol-let the num(er (e 3yHgi/e that 37y7H61$327y27H2610>1003710y7H4>+6100H710y73on sol/ing !e get 368y6#H6"so 3yH is 8#"

U9n a certain internet polling the reXection rate o ru E3otic production !as 4; orru Flassic production 8; and or (oth the coVee /arities com(ined !as $;. %hat !asthe ratio o ru e3otic to ru classic production

ol-let 3 (e production o (ru e3oticy (e production o (ru classicreXection o 37reXection o y 6reXection o 37y'4W310078Wy1006$W37y'1003y61"


40/55

U* (ook called * romantic e/ening !as printed ater e/ery se/en years. you add allthe years o the (ookSs printed ater $th pu(lication the sum o those years added up1"+24. %hen !as the 1st (ook o the series pu(lished.

5ol3737$737147372173728737"+7374261"+24$361""$$361>11

Q- 9rom the given digit 1$2$"$,$*$+ ho% many three digit numer could emade such that the three digit used must e in !E.ol-he a(o/e digits are arranged in12"1"+2"424#"4+4+##+4+4"#424"2+"1"21so there 12 num(ers

U*run !anted to Gnd the largest num(er o 4 digits such that !hen added to $24>

generated a num(er that ga/e a remainder 0 !hen de/ided (y +4 12 14 21 "". =indthe num(er.

5olthe ans!er is >"8" (coH its the largest 4 digit no..Grst !e ha/e to Gnd the AFM o all the gi/en num(ers !hich is 8"1#no! t!ice the AFM is 1##"2..and thus 1##"2$24> gi/es >"8"...!hich is the ans..hope u undertood...ZZ

U here is a square Geld o side 10m. * man runs !ith diVerent speed 10kmph1+kmph 20kmph 2+kmph on the our sides o the Geld. %hat is the a/erage speed o

man

ol-total distance to (e co/ered6 410m'640m60.04kmtotal time6sum o indi/idual times6Y0.0110'70.011+'70.0120'70.012+'60.$$"00a/g speed 6total distance total time6 0.040.$$"00'61+.+8kmph

U=ind the remainder !hen #+0 is di/ided (y 21+

ol-ans is "##;21+6#

"#;21+6"#21#;21+6112>#;21+6# and hence the pattern gets repeated..thus +0;"62!hich means...the ans!er is "#..

Q-9ind the remainder %hen "2;"";", is devided y 11.ol-!e can use remainder theorem !hen consecuti/e no. are there...so here !ecosider it as "2W""W"4 (ut as "" di/isi(le its not required so "2W"4 so taking /e and


41/55

7/e remainder i.e. 1'W1' 6 1 no! the remainder is111 6 10.(coH !hen the remainder is /e !e su(tract it rom no. di/iding' so ans is 10.

Q-Fate %anted to uy 2 kgs of apples. 'he vendor kept the 2 kg %eights onthe right side and %eighed , apples for that. he douted on the correctnessof alance and placed 2 kg %eight on the left side and she could %eigh 12

apples for 2 kgs. f the alance %as correct ho% many apples she %ould havegotol-Q-/hat %ill e the last t%o digits of :*"0+);21,ol-last t!o digit o#26"##"61##46>##+6$###6+#repeats#$6"#

214;#64so ans is >#

U=ind the sum o num(er (et!een 200 and "00 !hich is multiple o "&

ol-n6""a6201l62>$thereore s6n2?2a7n1'd@6821$

U=ind the last three digits o 2>88#$8&

ol-Q-n a cricket match$t%o atsman scores are >+$>+ respectively.'hey requireonly * runs in " alls$ho% oth the atsman complete their centuries?ol-atsmen in crease hits a (oundary then he completes 100no! equation (e 1run rom 2(allsthen ne3t (all he tries to hit si3 then it !ill (e in airthe other (atsmen crosses themiddle o the pitch.1st (atsmen gets out.no! other (atsmen comes to crease..no!equation (e 1run 1(allthen the other >#runs scorer hits a (oundary..

*5 or

Grst (atsman hit 4 then hit or a run (ut gets run out. No! 2nd (atsman !ith ># is onstrike and hit a si3 or our.

U . *62"F' and c612*7' and *77F6"000 then Gnd F.

ol-c6"000a7('!e kno! that c612a7(' Y 2c6a7(


42/55

c6"0002cc61000

q!hen a num(er di/ided (y "+$ gi/es remainder +.!hat !ill (e remainder i the sameno is di/ided (y 1$&

ol-the num(er !hich !hen di/ided (y "+$ and gi/es remainder + !ill (e like "+$3\'7+ or2131$3\'7+....this num(er !hen di/ided (y 1$ !ill also generate remainder equal to+...(coH the Grst part o gi/en num(r ie. 2131$3\' is di/isi(le (y 1$...oruse the simple ormuladi/idend 6di/isorWquotient 7remlet the num(er (e nn6"+$Wq17+similarly orn61$Wq2 7 - `- is the remainder !hich is to (e ounded on equating !e get

1$Wq2 7 - 6 "+$Wq1 7+thereore - 6 1$W21Wq1 7+ 1$ Wq26 1$21Wq1 q2' 7+so -emainder 6 +Q-/hat is the value of G:"xH&=)B:x-2=)IJ if xB2y2?

*ns is 10.......*s gi/en 32y 6 2364y20y2y610

U Mohan (ought a total o $2 apples(ananas ^ oranges and paid 21#.Eachapple(anana and orange costs -s 2-s "-s 4 respecti/ely.=ind the ma3 no o orangeshe could ha/e purchased&*'"4 '"0 F'28


43/55

1W1Z72W2Z7"W"Z62" 4Z1'.so ans!er !ill (e 201"Z1'

U *n escalqtor is mo/ing do!n!ards . \ takes 40 steps to reach (ottom rom top and ]

takes #0 steps to reach top rom (ottom . he speeds o \ and ] are equal . %hat isnum(er o steps on the escalator rom (ottom to the top....&

5ol\ mo/es !ith the escalator and ] mo/es against the escalator....(oth \ and ] speeds are same....let escalator mo/es e steps totally....hence 407e6#0e2e620 ie...e610 steps...total no o steps in escalator are 407e6407106+0steps

U 112"4$8"1"WWW n the gi/en series Gll the star marked.

ol-he gi/en series is like2"116124$2"6248"4$6"#1"18"6481>11"16#02#"1>16$2....so on

U =ind the remainder !hen #+0 is di/ided (y 21+

ol-ans is "##;21+6#"#;21+6"#21#;21+6112>#;21+6# and hence the pattern gets repeated..thus +0;"62!hich means...the ans!er is "#...ZZ

U * and run a 1km race. a gi/es a start o +0m a !ins (y 14 seconds and i *gi/es a start o 22 seconds !ins (y 20 meters. =ind the time taken (y * to run 1km.

a(61000>+0C14('6>801000C22('+0000 1100( 6 4#++0 #8#(5ol/ing !e get ( 6 2+"No! *ssume *Ss speed 6 31000>+0C142+"''632+"'3 6 105o 3 takes 100010 6 100 seconds.


44/55

U 1.2."72.".47".4.+74.+.#7.... 12$.128.12>. Gnd d sum.

Q-@ack started %alking from 10("0am at speed of +kmph and at 1"("0 am paulfollo%s him on a cycle %ith a speed of & kmph at %hat time %ill e @ack "kmehind paul?

5olans!er !ill (etime required #W"'7"'8#'610.+5o ans!er is 24)00

U n ho! many !ays can !e orm # digit num(er rom 12"4+#$ so that last andsecond last digit must (e e/en

5ollast 2 digits should (e e/en24#'6"W"1st 4 digits can (e any12"4+#'6$W$W$W$ans6$4W"2

*nd i -epetations not allo!ed here are " e/en num(ers ) 2 4 #.5o Gll the last place in " !ays. 2nd last in 2 !ays.

+W 4W "W 2W 1W 2W "

ans 6 $20 !ays

U !hat is the remainder o 1#>"$"0'"1 &

ol-1 is the ans1#>"$"0'"161+"0'"1as 1+ is the remainder !hen 1#>"$ is di/ided (y "1'!e can !rite 1+"0'"1 as 22+1+'"1!hich is equal to 81+'"1 as 8 is the remainder !hen !hen 22+ is di/ided (y "1'!e can !rite 81+"1 as #4$W8"1' 6 2$W8"1' as 2 is remainder !hen #4 isdi/ided (y "1!e can !rite 2$W8"1 as "2W22'W8'"1 6"2W"2'"1!hich !hen di/ided (y "1 lea/es remainder 1W1'"1so remainder is 1

U N is a natural num(er and n" has 1# actors. hen ho! many actors can n4ha/e&

5ol"71'"71'61#..this is or n"..or n4 it !ill (e "717""''"717""''6+W+62+9rlets take n as 8then 4"W2"6"71'W"71'61# actorssame as 44W246471'W471'62+ actors!hate/er may (e the /alue o n Xust apply this method


45/55

U Far * lea/es city F at +pm and is dri/en at a speed o 40 kmph. !o hours lateranother car lea/es city F and is dri/en in same direction as car *. n ho! much time car (e > km ahead o car * i the speed o car is #0 kmph.

car * speed 6 40 kmph car speed #0 kmphrelati/e speed6#040620 kmphsame direction'!hen car stated * has already co/ered 40W2680m distancetime required or t!o car to (e at same position 6 802064hradditional distance is > minto additional time6 >20'W#062$ minans!er is 4grs 2$ min

q o! many 2 digits num(er are there !hich !hen su(tracted rom the num(er ormed(y re/ersing its digits as !ell as !hen added to the num(er ormed (y re/ersing itsdigit result is a perect square.

#+ is one such num(er. 3y is num(er then 1137y' and >W3y' should (e perect square.!hich is possi(le !hen37y611 and 3y 6 14>/alue o 3y is /alid only !hen 3y61 then 36#y6+so num(er is #+.

U =ind the ++th !ord o 5j_*NO in dictionary.

*rranging the letters in alpha(etical order !e get ) * O N 5 j _

No! otal !ords start !ith * are #Zotal !ords start !ith * are +Z 6 120No!

otal !ords start !ith *O are 4Z 6 24otal !ords start !ith *N are 4Z 6 24otal !ords start !ith *5O are "Z 6 #No! *5NOj_ !ill (e the last !ord required

U he a/erage o uesday %ednesday and hursday is "$ !here as the a/erage o%ednesday hursday and =riday is "8. =riday is "> Gnd uesday

ans 6 "#tue7!ed7thu6"$W" i.e6111 eq1!ed7thu7ri6"8W" i.e6114 eq2gi/en ri6">!ed7thur7">6114 i.e 114">6$+so !ed7thur6$+ eq"see eq 1put eq " in 1


46/55

u gettue6111$+6"# ans.

U 5ome men are !eird5ome !eird are students

*' *ll men are !eird'5ome men are !eirdF' 5ome men S!ho are !eird are studentsc'12.4d'1$."solsol or 2nd)


47/55

" unit circle 6Y each o radius61constructing the Ggure accordingly!e get to Gnd out the radius o larger circler' i.e.the circle circumscri(ing themi u are amiliar !ith geometry concepts u !ill get cos"061r1'sol/ing this !e !ill get r62.1#$ and hence area appro3 14.>

"'one guy !ent to ruit stall to (uy oranges.he ound that price o one orange is reduced(y "rs and so he (ought "0 instead o 20.ho!much money he had&a'1#0('1+0c'180d'1$0

ol-ans!er 180let price o one orange is 3i price o orange not reduced he could (uy 20.i the price reduced (y rs " then he could (y "0.

thereore 2036"03"'(y sol/ing this 3 is >thereore he has 180 rs.

Qa person starts %riting all , digits numers .ho% many times had he %rittenthe digit 2?a)"A00)"2000c)"200d)"A000ol-ans)"$00at 1Ss place6>00 times

at 10Ss place6>00 timesat 100Ss place6>00 timesat 1000Ss placerom 2000 to 2>>>'61000 timestotal610007>007>007>006"$00

Un a class there are #0; girls and out o them 4+; are poor. * student is selected atrandom Gnd the pro(a(ility that the student is a poor girl.

5ol ans)2$100let there (e 100 studentsno o girls 6 #0

4+; o #0 are poorpoor girls62$pro(a(ility62$100

U-oy !as playing a game !ith n similar coins.he !as in need o arranging all the coinsin a !ay such that atleast one coin must (e in contact !ith all other coins.Gnd ma3 noo coins that he can arrange...


48/55

5ol i talking a(out 2


49/55

no! 200 is reduced rom (oth tank37"00623200'36$00in cylindrical tank /637+0061200

U three people can do a piece o !ork in "# days. *nd Grst and second can do t!iceas the third. =irst and third can do thrice the second. hen Gnd hop! many days !ill ctake to do the !ork.

ol-a7(7c61"#a7(62c2c7c61"#"c61"#c61108c takes 108 days

Uhere are 8 people = D P O A M N. 2 groups are to (e ormed. = !ill al!ays go !ithP. D and M !ill ne/er go tohether. !ill al!ays go !ith A. N !ill al!ays go !ith D. Gndout the t!o groups

ol-in these type o questions..check the options..eg =PND *N< AMO=PMO *N< AND

U . n city * +0; people support (rand \. in city there are 100 people and #0;support (rand \. i rom (oth city ++; support (rand \. then Gnd out in total ho! manypeople support (rand \.

ol-Aet the strength o city * (e 3.5o rom question !e ha/e32'7100W#0100'637100'W++100'6Y 361005o the total num(er o people supporting (rand \ !ill (e61007100'W++100'6110

U the diagonal o the square is equal to t!ice o side o a equilateral triangle. =ind outthe ratio o the area o the triangle to the square.

5olarea o equilateral triangle is sqrt"'a24a is side o triangle'

diagonal o square is sqrt2'33 is side o square'they gi/en condition sqrt2'362a6Y36sqrt2'aarea o square is 326Y2a2ratio is sqrt"'a24'2a2sqrt"'8*N5 )sqrt"'8


50/55

Uhe a/erage o *F is "1. *nd a/erage o F and < is "0. a is 22. hen Gnd out.a/erage o a(c is "1 it means a7(7c6>"a/erage o (cd6"0it means (7c7d6>0

gi/en a622227(7c6>"(7c6$1putting /alue o (7c in (7c7d6>0$17d6>0 hence 0$161>[

U a !on 80; o the games and they play + more games and !on " and lost 2.9/erall loss (ecomes 1+;. =ind out the total games played&

5olhis must (e a dummy question (cH/e ans is coming (y sol/ing this....

Falculating the loss

3+72637+'W1+100'36 2+2+ canSt (e an ans!er....

Q-f salary of !$ 3 and c is in the ratio 1(2(" and their expenditure is in theratio "(2(1. 9ind out %ho saves the most and the least

5olsalary o *F in ratio 1)2)"6#their e3penditure are in the ratio ")2)16#hence *6"#612

62#61"F61#F sa/es most* sa/es least

U=ind out 11Z'722Z'7""Z'7201"201"Z'.

5ol*ns!er is 2014Z1reason)11Z'62Z1Z

11Z'722Z'61746+6"Z111Z'722Z'7""Z'617471862"64Z1similarly upto 201"201"Z'6 2014Z1

U m7n is di/ided (y 12 then the remainder is 8. *nd i mn is di/ided (y 12 then theremainder is #. =ind out the remainder !hen mn is di/ided (y #.


51/55

m7n !hen di/ide (y 12 lea/es rem 86Y 123786m7nmn !hen di/ided (y 12 lea/es rem #6Y 12y7#6mn5ol/ing (oth !e get m6#3y'71 and n6#37y'7$mn !ill gi/e u ##37y'3y''7$'# .5o "#Wany thing ' !ould lea/ 0 rem$ !hen di/ide!ould lea/ 1 as rem

U * o!es +0 rs on a . he decides to return the money in 10rs and 20rs note only one/ery alternate day starting on Monday. =ind out the diVerent !ays in !hich he canreturn the money.t!o !ays are said to (e diVerent i diVerent denominations o notesare gi/en '

5ol* can return money to in 8 !ays10 10 10 10 10 1!ay10 10 10 20 4Z"Z6!ays10 20 20 "Z2Z6"!aysso total 8!ays

Un a clock the long hand is o 8cm and the short hand is o $cm. i the clock runs or 4days Gnd out the total distance co/ered (y (oth the hands.

5ol ans +1$4.$2

ans61#48Wpi..e3plaination

42W2WpiW$724W2WpiW8'61#48Wpi6 +1$4.$2

U5eries T +1+"01"+40+121+"#4+. =ind the odd man.

5ol*ns!er)"04+ instead o "0'+W"61+1+W"64+4+W"61"+1"+W"640+40+W"6121+121+W"6"#4+

ere odd is "0.

U* and F are three girls !ho go to a haunted house and get trapped. hey Gnd threedoor !ith theollo!ing things !ritten there...1'!ay to hea/en2'!ay to hell


52/55

"'door 2 is a !ay to hell

at least one thing !ritten is correct and at least one thing is !rong then !hich doorshould they opt i only one door is sae&

5olans optn " or 1

U* !hite cu(e is painted red on t!o diVerent aces. o! many diVerent !ays can this(e donet!o paintings are considered the same i on a suita(le rotation o the cu(e onepainting can (e carried to the other'&

5olans)2paint any one side o cu(e.1'paint on the opposite side.2'paint on any o the 4 adXacent sides.

Usum o digits o a t!o digit num(er is 12.on adding + to the num(er then the ne!num(er orm has units and tenSs digit equal then Gnd the num(er&

5ol"> is the num(er"7>612and ">7+6445o unitSs digit6tenSs digit.Do through the options or this type o questions..

$. a pu(lication occurs e/ery se/en years and the sum o the years is 1"+24. henGnd the Grst year.*ns 1>11

1$. a can do a piece o !ork in 1# days and ( can do in 24 days and * and F can doin 8 days then Gnd out in ho! many days can F do the !ork.*ns48

UAeena cut cu(es o 10cm dimension each.5he Xoined it to make a cu(oid o lngth100cm !idth +0cm and depth +0cm.o! many more cu(es does she need to make aperect cu(e&

sol/olume o large cu(e6 100W100W100/olume o small cu(e 6 10W10W10total cu(es needed or large cu(e6 1000/olume o cu(oid6 100W+0W+0num(er o small cu(es used or (uilding the cu(oid 6 2+0remaining small cu(es needed or the perect cu(e 6 1000 2+0so the ans!er is $+0.


53/55

Uhere are + packers *F#05imilarly or F !e ha/e 8#4 and < 81#. ence contri(utes or more proGt

UFrusoe hatched rom a mysterious egg disco/ered (y *ngus !as gro!ing at a astpace that *ngus had to mo/e it rom home to the lake. Di/en the !eights o Frusoe inits Grst !eeks o (irth as + 1+ "01"+ 40+ 121+ "#4+. =ind the odd !eight out.optiona' "#4+(' 1"+c' "0d' 1+

5ol"0.++W"61+1+W"64+here it is gi/en as "0'4+W"61"+1"+W"640+40+W"6121+121+W"6"#4+


54/55

U9n a certain assem(ly line the reXection rate or yundai i10s production !as 4percent or yundai i20s production 8 percent and or the 2 cars com(ined $ percent.%hat !as the ratio o yundais i10 production&optiona' "1(' 21

c' 11d' 12

let the no o i10 cars (e 3 and i20 (e yno! th reXcted i10 cars are 43100 and i20 cars are 8y100

and it is gi/en that 43100 78y100 6 $37y'100so !e get y 6 "3so the ratio is ")

U-am and 5akil run a race o 2000 meters. =irst -am gi/es 5akil a start o 200 metersand (eats him (y one minute. Ne3t -am gi/es 5akil a start o # minutes and is (eaten(y 1000 meters. =ind the time in minutes in !hich -am and 5akil can run the racesseparately.optiona' 810(' 1018c' 1218d' 1012

ram tra/el 2000m then sakil tra/el 1800/.?/6/elocity o sakil@ram tra/el 1000m then sakil tra/el 2000#/.

i.e.2000100061800/2000#//6200mmintime taken (y sakil62000200610minsimilrly time taken (y ram68min

UFonsider all permutations i.e arrangements ' o the digits 1 2 " !e !ill say that ahit has (een scored i at least one digit occurs in its proper position i.e 1 occurs in theGrst position 2 occurs in the second position and " occurs in the third position '. n ho!many !ays o this permutation can (e scoredoptiona' 4(' 2c' 1d' "

5ol4 !ays ....12"1"221""21


55/55

Uhe sum o the digits o a three digit num(er is 1$ and the sum o the squares o itsdigits is 10>. !e su(tract 4>+ rom that num(er !e shall get a num(er consisting othe same digits !ritten in the re/erse order. =ind the num(er

5olts (etter i !e do option /eriGcation.he ans!er could (e 8#".

coH !e ha/e 37y7H61$1003710y7H4>+6100H710y73 ie 3H6+using this !e can ha/e2H7y612 (y trial and error !e ha/e 8#"

U

1". there are e3actly 4 hursdays and 4 5undays in a month o Panuary then Gnd outPanuary 1st is on !hich day& *ns T Monday

5tar mark question in F5..a(cde are distinct integer /alues in ascending order and 8>a'W8>('W8>c'W8>d'W8>e'64>#1. Gnd a7(7c7d6&int is also gi/en) 4>#1 is di/isi(le (y 11.sorry that i dont remem(er the options.can someone e3plain the procedure.&*ns6 "04

Date post:	16-Feb-2018
Category:	Documents
Upload:	harish
View:	226 times
Download:	0 times

TCs QUestion

Documents