TCS Pool Campus Drive: Aptitude Test-2
1. What are are the total total number number of divisors divisors of of 600(includ 600(including ing 1 and 600)? a.16 b. 40 c. 24 d. 2 0 2. What is the the sum of of the squares squares of of the first first 20 natural natural number numberss (1 to 20)? 20)? a. 44100 b. 2000 c. 5650 d. 2!0 ". #ind the number of $ermutations $ermutations that can be made from the letters of the %ord &'*. & and * occu$+ing the end $laces. a. 12 b. 14 c. 20 d. 1 4. #ind the number of combinations that can be formed %ith 5 oranges, 4 mangoes and " bananas, bananas, then one fruit of each -ind is ta-en. a. 120 b. 110 c. !5 d. 60 5. * call center center agent has a list of "05 $hone numbers of $eo$le in al$habetic al$habetic order of names (but she does not have an+ of the names). he needs to quic-l+ contact /ee$a- harma to conve+ a message to him. f each call ta-es 2 minutes to com$lete, and ever+ call is ans%ered, %hat is the minimum amount of time in %hich she can guarantee to deliver the message to 'r.harma? 'r.harma? a. 1 minutes b. 610 minutes c. 206 minutes d. "4 minutes 6. he times ta-en ta-en b+ a $hone o$erator o$erator to com$lete com$lete a call are 2,,",1, 2,,",1,55 minutesres$ minutesres$ectiv ectivel+ el+.. What What is the average time $er call? a. 1 minutes b. ! minutes c. 4 minutes d. 5 minutes !. he times ta-en b+ a $hone o$erator to com$lete a call are 2, ,",1,5 minutes res$ectivel+. res$ectivel+. What is the median time $er call? a. 5 minutes b. ! minutes c. 1 minutes d. " minutes 8 .ric thro%s t%o dice, and his score is the sum of the values sho%n. andra thro%s one die, and her score is the square of the value sho%n. What is the $robabilit+ that andra3s score %ill be strictl+ higher than ric3s score? a. 1"!216 b. 1!"6 c. 1!"216 d. 56 . What is the largest integer that divides all three numbers numbers 2"400,2!2" 2"400,2!2"04,20 04,20524 524 %ithout %ithout leaving leaving a remainder? a. 4 b. 24 c. 6 d. ! 2 10. &f the " $eo$le $eo$le in m+ office office,, 10 li-e to drin- chocola chocolate, te, 15 are cric-e cric-ett fans, fans, and 20 neithe neitherr li-e li-e chocolate nor li-e cric-et. o% man+ $eo$le li-e both cric-et and chocolate? a.1 b. 10 c. 15 d. ! 11. 11. f f() 7 282 282 %hat is f(f(")) f(f("))?? a. 1 b. c. 64 d. 1 6 91 12. f f() 7 ! 812, %hat %hat is f () (the inverse function)? a. !812 b. (912)! c. 1(!812) d. :o :o inverse eists 1". * is thrice as good good as ; and ; is t%ice as good as <. *ll *ll together com$lete a %or- in 12 da+s, then < alone can do the %or- in ho% man+ da+s? (a) (b) (c) 10 (d) 11 14. What is the maimum maimum value of "+" 8 " =+ %hen 8+ 7 ? a. 4144 bb.. 256 c. 12 d. 102 15. %o %o circles circles of radii 5 cm and " cm touch touch each other other at * and also also touch a line line at ; and<. and<. he distance ;< in cms is? a.>60 b. >62 c. >6 d. >6 4 16. n oa beach, there are three small $icnic tables. ables ables 1 and 2 each seat three $eo$le. able able " seats onl+ one $erson, since t%o of its seats are bro-en. *-ash, ;abu,
1!. here are a number of chocolates chocolates in a bag. f the+ %ere to be equall+ divided divided among 14 children, children, there are 10 chocolates left. f the+ %ere to be equall+ divided among 15 children, there are chocolates left. &bviousl+, this can be satisfied if an+ multi$le of 210 chocolates are added to the bag. What is the remainder %hen the minimum feasible number of chocolates in the bag is divided b+ ? a. 2 b. 5 c. 4 d. 6 1. @et f(m,n) f(m,n) 745=m 745=m 8 "6=n, "6=n, %here %here mand n are intege integers rs ($osit ($ositive ive or negati negative) ve) What What is themin theminimu imum m $ositive value for f(m,n) forall values of m,n m,n (this ma+beachievedforvarious values of m and n)? a.5 b. 6 c. d. 1 1. What is the largest number number that %ill divide 020!, 2"255 2"255 and 12!6 %ithout leaving a remainder? a. 25! b. 05 c. "51 d. 4 2 0 . We have an equal arms t%o $an balance and need to %eigh obAects %ith integral %eights in the range 1 to 40 -ilo grams. We have a set of standard %eights and can $lace the %eights in an+ $an. . (i.e.) some %eights can be in a $an %ith obAects and some %eights can be in the other $an. he minimum number of standard %eights required is a. 6 b. 10 c. 5 d. 4 21. * %hite %hite cube (%ith si faces) faces) is $ainted $ainted red on t%o different different faces. faces. o% man+ different different %a+s can this be done (t%o $aintings are considered same if on a suitable rotation of the cube one $ainting can be carried to the other)? a. 2 b. 15 c. 4 d. "0 22. o% man+ divisors (including 1, but ecluding 1000) 1000) are there for the number number 1000? a. "1 b. 16 c. 15 d. 10 4 2 2". n the $ol+nom $ol+nomial ial f() 72= 72= 9 4= 854, %hat is the $roduct $roduct of the roots,and roots,and %hatis the sum of the roots (:ote that denotes the raised to the $o%er n, or multi$liedb+ itself n times)? a. 2!, 0 b. 5 4, 2 c. 42, 54 d. 4, 2! 5 " 4 24. n the $ol+n $ol+nomi omial al f() f() 7 8 a= 8 b= 8c= 8 d, all coefficients a, b, c, d are integers. f " 8 sqrt(!) is a root, %hich of the follo%ing must be also a root? (:ote that sqrt(u) denotes the square root of u, or the number %hich %hen multi$lied b+ itself, gives the t he number u)? a. "9sqrt(!) b. "8sqrt(21) c. 5 d. sqrt(!) 8 sqrt(") 25. f "+ 8 B 2 and 8 2+C", 2+C", %hat can be said about the value of +? *. + 7 91 ;. + B91 <. + C91 /. + 7 1 26. f the $rice of an item is decreased decreased b+ 10D and then increased b+ 10D, the net effect effect on the $rice of the item is *. * decrease of D ;. :o change <. * decrease of 1D /. *n increase of 1D 2!. f m is an odd integer and n an even integer, %hich of the follo%ing is definitel+ odd? *. (2m8n)(m9n) <. m28mn8n2 ;. (m8n2) 8 (m9n2) /. m 8n
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2. What is the sum of all even integers bet%een and "01? 2 . *. 40000 ;. 20000 <. 40400 /. 20200 "0. here are 20 balls %hich %hich are red, blue or green. green. f ! balls are green and the sum of red balls balls and green balls is less than 1", at most ho% man+ red balls are there? " 1. *. 4 ;. 5 <. 6 /. ! "2. f n is the sum of t%o consecutive consecutive odd integers and less than 100, %hat is greatest $ossibilit+ $ossibilit+ of n? " ". *. ;. 4 <. 6 /. "4. "5. 3 6 .