Latest TCS Aptitude Question SOLUTION: :TCS LATEST PATTERN2012-2013: 1. P(x)=(x^2012+x^2011+x^2010+.....+x+1)^2-x^2012 Q(x)=x^2011+x^2010+.......+x+1 The remainder when P(x) is divided by Q(x) is ? 2. In a str

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(#M40011242) TCS Logical Reasoning question Keep an EYE

:TCS LATEST PATTERN2012-2013:

1. P(x)=(x^2012+x^2011+x^2010+.....+x+1)^2-x^2012
Q(x)=x^2011+x^2010+.......+x+1
The remainder when P(x) is divided by Q(x) is ?

2. In a stream running at 2 kmph, a motorboat goes 6 km upstream and back again to the starting point in 33 minutes. Find the speed of the motorboat in still water ?

3. Directions for Q. 1 to Q. 5: Refer the data:
J, K, L, M and N collected stamps. They collected a total of 100 stamps. None of them collected less than 10.
No two among them collected the same number.
(i) 3 collected the same number as K and M together.
(ii) L collected 3 more than the cube of an integer
(iii) The no. Collected by J was the square of an integer.
(iv) Total no. Collected by K was either the square or cube of an integer.
1. The no. Collected by J was:
(1) 27 (2) 49 (3) 36 (4) 64
2. The no. Collected by K was:
(1) 16 (2) 27 (3) 25 (4) 36
3. The difference of numbers collected by L & M was:
(1) 3 (2) 2 (3) 5 (4) 9
L=12, N=11, J=27, M=14, K=36

4. A man can row 6 km/hr. in still water. If the speed of stream is 2km/hr., it takes him 3 hours to row to a place and back. How far is the place?

5. F(n) is a function...where f(f(n))+f(n)=2n+3.
F(n)=0;find f(2012) ?

6. How many vehicle registration plate numbers can be formed with digits 1,2,3,4,5(no digits being repeated)if it is given that registration number can have 1 to 5 digits ?
Options: 205 100 325 105

7. You can have registration plates of 5,4,3,2 or 1 digits
So, it's 5*4*3*2*1 + 5*4*3*2 + 5*4*3 +5*4 + 5
=120 + 120 + 60 + 20 +5
=> 325

8. A merchant buys 20kg of wheat at rs.30.00 per kg and 40kg wheat at rs.25.00 per kg.He mixes them and sell one third of the mixture at rs.26.00 per kg. The price at which the merchant should sell the remaining mixture so that he may earn a profit of 25% on his whole outlay is
Total cp = 20 * 30 + 40*25= 1600
Sp = 125/100 * 1600= 2000
Sp for 20kg mix = 26*20 =520
Rem sp = 2000-520 = 1480
As this sp is for 40 kg = 1480 / 40 = Rs37

9. Four friends namely Rahul, Ravi, Rajesh and Rohan contested for a dairy milk chocolate. To decide which friend will get the chocolate they decided to throw two dice. Every friend was asked to choose a number and if the sum of the numbers on two dice equals that number, the concerned person will get the chocolate. Rahul's choice was7, Ravi's choice was 9, Rajesh's choice was 10 and Rohan's choice was 11. Who has the maximum probability of winning the amount?
A) Rahul b) Ravi c) Rajesh d) Rohan

10. Messrs. Siva Constructions, leading agents in Chennai prepared models of their lands in the shape of a rectangle and triangle. They made models having same area. The length and width of rectangle model are 24 inches and 8 inches respectively. The base of the triangle model is 16 inches. What is the altitude of triangle model from the base to the top?
A) 24 inches b) 8 inches c) 20 inches d) 32 inches
If h is the height of triangle model, then 24*8 = 16*h/2 h= 24 inches

11. In month of jan 4 thursday and 4 sunday then on 1st jan of that month which willbe the day?
1. Monday
2. Friday
3.saturday
4. Wednesday

12. There is a 12*6 grid...grid contains 1*1 squares. What is d total number of squares..(consider 1*1,2*2,3*3,4*4,5*5,6*6 size squares as well).

13. 7,5,9,12,18,36,47,72,?

14. 5, 9, 12, 18, 26, 36, 47, 72, _?
It is 5 ...... 12....... 26......... 47
12= 5+7
26= 12+2×7
47=26+3×7
Next is 47+4×7=75
And 9, 18, 36, 72 hence next 144
Therefore 5, 9, 12, 18, 26, 36, 47, 72, 75, 144

15. F(x)=f(f(x))=f(x^2)....how many such functions with degree >2 exist

16. The length and breadth of a field is 300x400ft, if there are 3 ants on average per square inch of field, find the approximate number of ants in field
As 300 ft=3600 inch and 400 ft=4800 inch.then area in sqr inch=17280000
1 sqr inch need 3 ant hence 17280000 sqr inch need 3*17280000 ants

17. The diagonal of a square is twice the side of equilateral triangle the ratio of Area of the Triangle to the Area of Square is?
A) 3:8
B) 2:5
C) 3:6
D) 2:4
Ratio = sqrt3*a^2/8a^2....i.e sqrt3/8

18. A, B COMMON TO ALL THREE. THEN ATLEAST 1 ELEMNT COMMON TO 2 IE X1,X2,X2,X3,X3,X1. FINDMINIMUM ELEMENTS IN EACH GROUP.
ANSWER IS 4.

19. There are three dice, threw 3 times probability of getting 10 is ?
Possible event.......(1,3,6)(1,4,5)(1,5,4)(1,6,3)(2,2,6)(2,3,5)(2,4,4)(2,5,3)(2,6,2)(3,1,6)(3,2,5)(3,3,4)(3,4,3)(3,5,2)(3,6,1)(4,1,5)(4,2,4)(4,3,3)(4,4,2)(4,5,1)(5,1,4)(5,2,3)(5,3,2)(5,4,1)(6,1,3)(6,2,2)(6,3,1)
Total 27 possible events
Given dice is thrown 3 times
So probability is ..........3*27/216

20. What is the probability of throwing 3 dices to get a sum of 10?

21. Raj tossed 3 dices and there results are noted down then what is the probability that raj gets 10?
A) 1/72
B) 1/9
C) 25/216
D)1/8
27/216 than ans is 1/8

22. From 52 cards 3 cards drawn randomly prob of getting 1 spade , 1 red queen and 1 black king??
13C1*2C1*2C1/52C3 = 0.00235

23. A) in how many ways can 3 postcards can be posted in 5 postboxes?
B) in how many ways can 5 postboxes hold 3 post cards?
A)5^3
B)3^5

24. The climb from foot to top of a hill 800 meters, Jack can climb at 16 meters per minute and rests for two minutes or 20meters per 2 minutes and rest for one minute. Paul can climb at 10 meters per one minute and rest for one minute or16 meters per minute and rest for 2 minutes. If take has to reach the top in exactly two hours. What is the maximum number of rests that he can take?
A) 41 b) 42 c) 40 d) 43
Total=800m
16m per min means for 1m=800/16 =50min to climb
10m per min means for 1m=800/10=80min to climb for paul.....The total time is 2hours==120min....so, time taken for rest by paul is 120-80=40min

25. Two cyclist begin training on oval racecourse at same time the professional cyclist complete each lap in 4 sec noves take 6 minute how many minute after start will both cyclist pass at exactly same spot where they begin to cycle(a)10(b)8(C)14(D)12

26. Two points r there two person from A running to same direction with speed 20 km/hr. & 15/hr. respectively and from other end another person running to opposite direction with 30 km/hr.? Distance between them 100 km??At what time they will meet?

27. Tim and Elan are 90km away from each other .they are starting to move towards eachother simultaneously ,tim at speed 10kmph and elect at 5kmph ,,if every hr. they double the speed ,what is distance that tim will pass until he meets elan? (60)

28. There are 10 stepping stones numbered 1 to 10.a fly jumps from 1st stone as follows: every minute it jumps to the 4th stone from where it started -that is from 1st it would go to 5th, from 5th it would go to 9th, from 9th it would go to 3rd, etc .where would the fly be at 60th minute if it starts at 1?
Answer 1
1minute=1+4=5
1 minute=1+4=5step
2 minute=5+4=9step
3 minute=9+4=3step
4 minute=3+4=7step
5 minute=7+4=1step the same process is repeated 12*5 times hence at 60th minute fly would be at 1st step

29. Given the following information who is youngest?
C is younger than a; a is taller than b;
C is younger than d;
C is older than b;
B is taller than c;
A is older than d
(1)d (2)b (3)a (4)c

30. 1!+2!+3!...+50! Divided by 5! Remainder will be ? (0 or 33)

31. If there are Six periods in each working day of a school, In how many ways can one arrange 5 subjects such that each subject is allowed at least one period?

32. We have 5 sub and 6 periods so their arrangement is 6P5 and now we have 1 period which we can fill with any of the 5 subjects so 5C1
6P5*5C1=3600

33. An article manufactured by a company consists of two parts X and Y. In the process of manufacturing of part X, 9 out 100 parts many be defective. Similarly , 5 out of 100 are likely to be defective in the manufacturer of Y. Calculate the probability that the assembled product will not be defective?
A)0.6485 b)0.6565 c)0.8645 d)none of these
Ans=c (0.8645)
Probability of no defective of x= 91/100=.91
Probability of non-defective of y= 95/100=.95
So, probability of no defective product=.91*.95=0.8645

34. There are six multiple choice questions in the examination. How many sequences of answers are possible, if the first two questions have 3 choices each, the next two have 4 choices each and last two have 5 choices each?
3c1*3c1*4c1*4c1*5c1*5c1=3600

35. The ratio of perimeter of an equilateral triangle having an altitude equal to the radius of the circle, to the perimeter of an equilateral triangle inscribed in that circle is ?

36. Arun was all bent on building a new house. He carefully got the blue print of his house designed by his friend Ashwin, a civil engineer. He wanted to build a room of dimension 27 by 48 ft and lay tiles in this room. Each tile was of dimension 2 by 3 ft. How many tiles should Arun buy?
27*48/2*3=216

37. Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age? A.2 b.5/2 c.3/2 d.1
F=3R.
After 8 yrs.
F+8=5/2(R+8)
2F+16=5R+16
2(3R) +16=5R+40
R=24 ROHIT
Aft further 8
Rohit == 24+8=32
Father == 24*3+8=80
80/32====5/2

38. Roy is now 4 year older than Erik and half of that amount than Lewis. If in two years Roy will be twice as old as Erick, then in two year what would be Roy age multiplied by Lewis age??
Ans is 48
Firstly two equations from 1st sentence...
Suppose Roy=x, Erik=y, Lewis=z
So x=y+4.... (1)
2nd is x=z+2... (2) (Roy is now 4 year older than Erik and half of that amount than Lewis so 4/2=2)
Also after 2 years Erik and Roy relation will b
X+2=2(y+2)... (3)
So put this into 1st equation. U will get y=2...
And then x=6, z=4(by substituting other)
Now asking multiplication after two years of Roy n Lewis is (6+2)*(4+2) =48...

39. My name is PREET. But my son accidentally types the by interchanging a pair of letters in my name. What is the probability that despite this interchange, the name remains unchanged? A.5% b.20% c.25% d.12.5%
10% there are 10 possible pairs. Out of which 1 will not change my name.
So probability that name remains unchanged = 1/10 = 10%

40. In how many ways can 20 identical pencils be distributed among three girls so
That each gets at least 1 pencil?
Consider 3 girls as A, B, C THEN A+B+C=20, but each one should get at least 1 pencil so giving 1 pencil to each student, the remaining pencils are 20-3=17 now A'+B'+C''=17,
Number of non-negative integers of A', B’, C’ are (17+3-1) C (3-1)
So total Combinations are 19c2=19*9 = 171

41. A sequence {An}is defined A(1)=0&A(n+1)=A(n)+2(n)WHAT IS VALUE OF A(100)(a)9902(B)9900(C)10100(D)9904
Last will be A (1) +2*99*98*.....1
Now put the value 1+2(1+2+......+99)
2+ 2*99(99+1)/2
=9902

42. The sequence {A (n)} is defined by A (1) =2 and A (n+1) =A (n) +2n. What is the value of a (100)
Let a=2, d=2, a.p formula find nth term i.e... TN=a+ (n-1) d
Where TN=100...
100=2+ (n-1)2 gives n=50.
Now sum of n terms n/2(a+l) =2550(ans).

43. In a sequence of integers, A(n)=A(n-1)-A(n-2),where A(n) is the nth term in the sequence, n is an integer and n>=3, A(1)=1,A(2)=1. Calculate S (1000), where S (1000) is the sum of first 1000 terms.
Ans: 3

44. In base 7, number is written only using digit0, 1, 6.a number 135in base 7 is 1*7^2+3*7+5=75in base10.what is sum of base7 numbers1234&6543in base 7? (A) 11101(B) 11110(C) 10111(D) 11011
Ans: b) 11110
Explanation:
Convert the number from base 7 to base 10
Base 7(1234) = base 10(466)
Base 7(6543) = base 10(2334)
Sum of 466 + 2334 = 2800
Convert to base 7
Base 10 (2800) ===> 11110

45. M,N,O,P ARE DIFFERENT INDIVIDUAL M IS DAUGHTER OF N; MIS SON OF P;WHICH FOLOWING TRUE (a)M IS DAUGHTER OF P (B)IF B IS DAUGHTER OF N THEN M AND B ARE SISTER (b)IF C IS GRANDDAUGHTER OF O ,C AND M ARE SISTERS(d)P AND N ARE BROTHER

46. Which of following true: A occur only B or C occur B occur D&E occur if C not occur g occur if A and F occur option A occur whenever F occur2) F never occur3) G not occur if D not occur (3584) 4) none of these

47. House1 is older than H2, H3 is taller than H4, and H4 is older than H1... (I)H1 is older than H3 (ii) H2 is taller than H4 (a) only 1 (b) both (c) neither (d) only2

48. Apple costs L rupees per kilogram for first 30kgs and Q rupees per kilogram for each additional kilogram. If the price of 33 kilograms is 11.67and for 36kgs of Apples is 12.48 then the cost of first 10 kegs of Apples is
A) 3.50 b) 10.53 c) 1.17 d) 2.8
30L+3Q=11.67
30L+6Q=12.48
------------
3Q=.81 Q= .27
From that L=0.362 cost of 10 kg apple is 10*.362=3.6

49. The letters in the word ABUSER are permuted in all possible ways and arranged in alphabetical order then find the word at position 49 in the permuted alphabetical order?
A) ARBSEU
B) ARBESU
C) ARBSUE
D) ARBEUS
AB**** =4! = 24 ways
AE****=4! =24 ways next word is 49th so
AR**** in alphabetical order **** will be BESU
Ans is B

50. X,Y,W,Z ARE INTEGER THE EXPRESSION X-Y-Z IS EVEN&Y-W-Z ODD IF X IS EVEN THEN WHICH OF FOLLOWING IS TRUE(a)Y MUST BE ODD(b)Y-Z MUST BE ODD(c)W MUST BE ODD(d)Z MUST BE ODD
Ans. (c) W must be ODD
X-Y-Z=even and X even no.
Hence (y-z) must be even because (even -even = even)
And y-w-z=y-z-w=odd and (y-z) is even so W must be odd because (even - odd=odd)
Hence option (c) is correct

51. The milk and water in two vessels A and B are in the ratio 4 : 3 and 2: 3 respectively. In what ratio, the liquids in both the vessels are mixed to obtain a new mixture in vessel C containing half milk and half water?
Mr and Mrs smith had invited 9 of their friend and their spouses for party at wiki beachresort.the stand for group photograph if Mr smith never stand next to Mrs smith then how many way group arrange in row
(A) 20!
(B) 19! +18!
(C) 18*19!
(D) 2*19!

52. A father purchases dress for his three daughters. The dresses are of same colour but of different size .the dress is kept in dark room .What is the probability that all the three will not choose their own dress...

53. An empty tank is filled with an inlet pipe 'A' in 42 minutes. After 12 minutes an outlet pipe 'B' is opened which can empty the tank in 30 minutes. After 6 minutes another inlet pipe 'C' opened into the same tank, which can fill the tank in 35 minutes and the tank is filled find the time taken to fill the tank?

54. There are three buckets. Of 8, 5 n 3 litres...out of which only 8 ltr buckets is fully filled...u have to fill exact 4-4 ltr liquid in 8 and 5 litre bucket by using only these buckets in minimum number of steps.

55. 16 meters per minute and rest for 2 minutes. If take has to reach the top in exactly two hours. What is the maximum number of rests that he can take?
A) 41 b) 42 c) 40 d) 43

56. There are 4 boxes colored red, yellow, green and blue. If 2 boxes are selected, how many combinations are there for at least one green box or one red box to be selected?
A) 1 b) 6 c) 9 d) 5

57. N! Have 13 zeros than what is the highest and lowest value of n??
65! Will have 13 +2= 15 zeros.55! , 56! .59! Will have 13 zeros. Lowest value of n=55 highest value of n =59

58. N is an integers and N>2 at most how many integers among N+2,N+4,N+5,N+6 and N+7 are prime integers?
A) 1, b) 3, c) 2, d) 4
If n=3 than 5 7 8 9 10 so prime no. 2

Asked In TCS (11 years ago)

Unsolved Read Solution (127)

Is this Puzzle helpful?   (182)   (24) Submit Your Solution Blood Relations

Read Solution (127) :

nisar sami  (11 years ago)

friends today i attended the tcs written test..in my experience what i say to u is.... at the last day of ur preparation plz spend an hour to remember the answers 4 the questions(blindly remember the options of the present year tcs papers) becoz same questions with exact values will be given,,these questions will be repeated..so try to remember the answer directly....I got the same questions..i got about 10 questions in the above tcs paper...Remember the direct answer/option..u will b getting the same questions and exact values..bt do this only at ur last day of ur preparation..ALL THE BEST.

Is this solution Helpfull? Yes (203) | No (8)  

PARAG KAMRA  (11 years ago)

ans no:2
Let the speed of the motorboat in still water be x kmph.
Then, speed downstream = (x + 2) kmph.
Speed upstream = (x - 2) kmph.
:. 6/(x + 2) + 6/(x - 2) = 33/60 0r 11X^2 – 240x – 44=0
11X^2 – 242X + 2X –44 =0 or 11x(x – 22) + 2(x – 22) = 0
or (x-22)(11x+2)=0 or x=22.
:. Speed of motorboat in still water = 22 kmph.

Is this solution Helpfull? Yes (46) | No (11)  

Kabirul Islam  (11 years ago)

Q.9. rahul(answer)
rahul choose 7 as a sum of two digit
it can be (6,1),(1,6),(3,4),(4,3),(5,2),(2,5)
probability= 6/36(max)
so rahul has more chance to get the chocolet

Is this solution Helpfull? Yes (28) | No (9)  

maahi sharma  (11 years ago)

hi .... can someone send me the total answer key of this placement paper..... its too urgent..
my mail id luvmaahisharma@gmail.com

Is this solution Helpfull? Yes (25) | No (7)  

Rashmi Chouhary  (11 years ago)

1)let us multiply x with g(x)
xg(x)=x+x^2+.....+x^2012
1+xg(x)=1+x+x^2+.....+x^2012
therfor f(x) can be written as:
f(x)=(1+xg(x))^2-X^2012
=(xg(x))^2+2xg(x)+1-x^2012
when we divide f(x) by g(x) first 2 terms leaves no rem so last 2 terms can be written as:
1-x^2012=(1-x)(1+x+x^2+.....+x^2011)
therefore, remainder=(1-x)

Is this solution Helpfull? Yes (18) | No (11)  

prateek dixit  (11 years ago)

ques. P(x)=(x^2012+x^2011+x^2010+...+x+1)^2-x^2012
Q(x)=x^2011+x^2010+....+x+1

sol. since it is a polynomial it must be true for every value of x.
put x=1, then
p(1)= (2013)^2 - 1
= (2013+1)(2013-1) = 2014*2012

q(1) = 2012,
now p(x)/q(x)=p(1)/q(1)=2012*2014/2012 = 2014.
therefore remainder is zero

Is this solution Helpfull? Yes (18) | No (5)  

Ankita Paunikar   (11 years ago)

Can u plz give he solution of other questions too?
Thankyou

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kashi  (11 years ago)

Q4.ans is 8 km

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Kabirul Islam  (11 years ago)

1)remainder 1
2)22 kmph
3)L=12, N=11, J=36, M=14, K=27
4)0.82
5)2n+3
6)325
8)37
next answer uploaderd soon.........

Is this solution Helpfull? Yes (13) | No (47)  

Kabirul Islam  (11 years ago)

Q14.5, 9, 12, 18, 26, 36, 47, 72, _?
it is 5 ...... 12....... 26......... 47
12= 5+7
26= 12+2×7
47=26+3×7
Next is 47+4×7=75
and 9, 18, 36, 72 hence next 144
Therefore 5, 9, 12, 18, 26, 36, 47, 72, 75, 144...

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Pranita Sharma  (11 years ago)

ARE THESE QUESTIONS ASKED RECENTLY IN PLACEMENT PROCESS?? HOW MANY OF THEM HAVE REALLY APPEARED IN THE PAPERS?

Is this solution Helpfull? Yes (11) | No (1)  

seetha  (11 years ago)

answer for questn 3).
L=12, N=11, J=27, M=14, K=36 may not b correct as it doesnot follow the given constraints.j=36,l=11,

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surajit  (11 years ago)

remainder is 0

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sanjana  (11 years ago)

@nisar :from dese which ques r cuming...??can u tel..plzz...

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Mayur Somvanshi  (11 years ago)

guys plz help/....

tcs this week end solutins plz asap

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dinesh gupta  (11 years ago)

can any one send me the solution of these tcs questions it will coming soon in my clg my id is dineshgupta592@hotmail.com thnx...

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gourhari ghosh  (11 years ago)

if anybody have question of TCS apt of any college please mail me mandalarijit040@gmail.com because i have apt exam of TCS on 16th oct........sSo frnds plz mail me plzzzzzzzzzzzzzzzzzzzzzzzzz..........................

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saiyam gambhir  (11 years ago)

please if anyone can send me the answers of above question my aptitude is on 16 oct please help thanks
mail me at saiyamgambhir@gmail.com

Is this solution Helpfull? Yes (4) | No (1)  

Rashmi Chouhary  (11 years ago)

11) the ans will be monday

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Mayur Somvanshi  (11 years ago)

yeah exactly :) there is no change in options....

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TousfiAhamed  (11 years ago)

35)Altitude of a triangle is equal to the radius of the circle,
so the side of tri is 2a ( if 'a' is the radius )
so the perimeter of equi tri is = 3 * 2a
and that of circle is = 2 * pi * a
Ratio = (3 * 2a) / (2 * pi * a)
= 3 / pi
= 21 / 22

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prabakar  (11 years ago)

please if anyone can send me the answers of above questions my aptitude is on 31 oct please help thanks
mail me at praba1992kar@gmail.com

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divya trivedi  (11 years ago)

plz anyone plzzzz send ans. of the above ques ppr bcz tcs z cumming @ my clg soon....plz send me ans on divyatrivedi61@yahoo.com

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Manikumar R  (10 years ago)

ans for q4: 8km
vel in still water 6
down stream 6-2=4
up stream 6+2=8
time=vel/dis
dis=3 so,
3=d/4+d/8
then d=8

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saima kidwai  (10 years ago)

Q) 12
squares with area 1*1 = 12*6 = 72
2*2 = 11*5 = 55
3*3 = 10*4 = 40
4*4 = 9*3 = 27
5*5 = 8*2 = 16
6*6 = 7*1 = 7

Total possible squares = 72+55+40+27+16+7 = 217

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nazma  (11 years ago)

hey can you give ans to the first question please...!!!

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kushi  (11 years ago)

hey KABIRUL ISLAM plz send me solutions for the tcs pattern questin paper to dis mail kushikumari50@gmail.com if u don't mind

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Ashutosh verma  (11 years ago)

pls send me present year tcs papers
ashutosh_08@ymail.com
admin if you have present year tcs papers pls snd me

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MATADEEN SINGH  (11 years ago)

plz send me the answer key as soon as possible......thanks

Is this solution Helpfull? Yes (2) | No   

Aashish Khiste  (11 years ago)

if anybody have question of TCS aptitude of new pattern. plz mail me questions with solution. aashishkhiste@gmail.com

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kaushal jaiswal  (10 years ago)

Q.n 1) in question there is polynomial equation. so it will satisfied all the values. let us try to hit and trial method.
put the value as x=1 the we have
p(x)=2013^2-1
it can be written as (2013+1)(2013-1)=2014*2012
and q(x)=2012
and p(x)/q(x)=(2014*2012)/2012=2014 and gives the remainder 0

Is this solution Helpfull? Yes (2) | No   

Preety Soni  (10 years ago)

56) 2(1C1*3C1)/4C2
=2*3/6
=1 ans...

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Palash   (10 years ago)

12) Let we have m x n grid .
If we want to form squares 0f r x r then
There are (m-r+1) position of length r by length m to from a square .
There are (n-r+1) position of length r by length n to from a square .
So no of squares are = (m-r+1).(n-r+1).

In case of 12x6 grid
No. of squares of 1*1 =(12-1+1).(6-1+1)=72
No. of squares of 2*2 =(12-2+1).(6-2+1)=55
No. of squares of 1*1 =(12-3+1).(6-3+1)=40
No. of squares of 1*1 =(12-4+1).(6-4+1)=27
No. of squares of 1*1 =(12-5+1).(6-5+1)=16
No. of squares of 1*1 =(12-6+1).(6-6+1)=72

The ans is =(72+55+40+27+16+7)=217

Is this solution Helpfull? Yes (2) | No   

dola  (11 years ago)

@kabirul how 1?? what is the answer of 1st Q??

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Mayur Somvanshi  (11 years ago)

yeah exactly :) there is no change in options....

Is this solution Helpfull? Yes (1) | No (1)  

vivek kumar  (11 years ago)

9. 6/36>4/36>3/36>1/36 so.a

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aman  (11 years ago)

heyy.. any one plz tell mei d ratio of puzzels nd sudoku in tcs xams??

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arushi tyagi  (11 years ago)

please mail me the solutions of these questions as i have my aptitude exam on 16th oct. plsssssssssssssssss mail me plssssssss...
my id is arushi_nesy@yahoo.co.in

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OWAIS AHMAD  (11 years ago)

if anyone have answers please post or mail me at er.owaisahmad@gmail.com

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TousfiAhamed  (11 years ago)

35)the ratio is 7:27

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TousfiAhamed  (11 years ago)

35)sry itz 7:22

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Ashutosh verma  (11 years ago)

@nisar sami : pls send me the present year tcs papers...will be thankfull to you

Is this solution Helpfull? Yes (1) | No   

ankita   (11 years ago)

please if anyone can send me the answers of above questions my aptitude is on 29 oct please help thanks
mail me at ankitatiwari2013@gmail.com

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sampath  (11 years ago)

plz anyone send me the solutions of above questions.plzzzz.My id is
sampathms89@gmail.com

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Nancy Thakral  (11 years ago)

please someone send me the solution to all TCS latest paper pattern questions my id is nancythkrl88@gmail.com

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Nancy Thakral  (11 years ago)

please someone send me the solution to all TCS latest paper pattern questions my id is nancythkrl88@gmail.com

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Nancy Thakral  (11 years ago)

please someone send me the solution to all TCS latest paper pattern questions my id is nancythkrl88@gmail.com

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alpesh rawal  (11 years ago)

rawal.alpesh@gmail.com pls mail me the solutions ... tcs is coming on 1st of nov :) thanks in advance

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Sayed Maruf  (11 years ago)

Plz some1 send me the total answer wid solutn of d abv qus, Its too urgent, Apti is on 19th Nov, My ID is marksayed123@gmail.com. Plz help me plzzzzz...

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Hossainara Begum  (11 years ago)

some1 plz send me the total answers (wid solutns) of the above questions. My Apti is on 19th Nov, Email Id- hossainara786@gmail.com, Plz help me plzzzzzzz........

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Shruti Mendiratta  (11 years ago)

47 ques-(c)neither

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arpit jain  (11 years ago)

put x=0 in qun no. 1 and u will get the ans zero instantly.

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sreenu  (11 years ago)

for q1:
Let us multiply g(x) with x on the both sides
x.g(x) = x+x2+x3+.......x2012
add 1 on both sides
x. g(x) + 1 = 1+x+x2+x3+.......x2012
Substitute this value in f(x)
then f(x) = (x.g(x)+1)2−x2012
f(x) = x2.g(x)2+2.g(x)+1−x2012
Now f(x) is divisible by g(x) first two terms are exactly divisible by g(x) and we get 1 - x2012
But 1 - x2012 = (1 - x)(1+x+x2+x3+.......x2011)
if this expression is divisible by g(x) we get (1 -x) as remainder.

Is this solution Helpfull? Yes (1) | No (1)  

anjul meid  (11 years ago)

5) it will be MONDAY on 1st of january

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vinay kumar  (10 years ago)

1)1st of jan will be monday
since thu on 4th of month and sunday on 7th of month

Is this solution Helpfull? Yes (1) | No   

KADIYALA JANAKI RAM  (10 years ago)

2).. Let the speed of the boat be x kmph. By the formula, time=(distance/speed),, we have Total Time=33min. i.e., ( (6/x-2)+(6/x+2) )=(33/60)hours.
By solving ,we get x=22,i.e., speed of the boat.
(x-2) and (x+2) are speed of the boat in upstream and downstream respectively.

Is this solution Helpfull? Yes (1) | No   

Preety Soni  (10 years ago)

40) in identicl case
(n-1)C(r-1)
(20-1)C(4-1)=171 ans..

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Benjamin  (10 years ago)

hi .... can someone send me the total answer key of this placement paper..... its too urgent..
my mail id saifmd19196@gmail.com

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S SHAFI  (10 years ago)

plz send me solutions of this paper, tcs drive is there in our clz
mail id: skshafi.iiitk@gmail.com

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Anik  (10 years ago)

Answer for question number 1: Zero
Solution
(1-x)(x^2011+x^2010+..1)=(1-x)Q(x)=(1-x^2012)
xQ(x)=x+x^2+.....+x^2012
1+xQ(x)=1+x+x^2+.....+x^2012
So (1+xQ(x))^2=form of (a+b)^2
So P(x)=(xQ(x))^2+2.xQ(x)+(1-x^2012)
=> P(x)=(xQ(x))^2+2.xQ(x)+(1-x)Q(x)=Q(x)[x^2.Q(x)+2x+1-x]
So P(x) is completely divisible by Q(x)

Is this solution Helpfull? Yes (1) | No   

Rajashik Paul  (8 years ago)

3) k=16, M=34, L=11,J=25,N=14

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Shruti Mendiratta  (11 years ago)

29 ques--(2)b

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Shruti Mendiratta  (11 years ago)

52ques-- (2/3)*(2/3)*(2/3)=8/27

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Shruti Mendiratta  (11 years ago)

45 ques--(B)

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mekala naresh  (11 years ago)

sbgudhws,dnkj

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mekala naresh  (11 years ago)

sbgudhws,dnkj

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praveen kumar  (11 years ago)

plz send me solutions of this paper tcs drive is there in our clz
mail id: konda2praveen@gmail.com

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sree surekha k  (11 years ago)

can sum1 plz give solution for Q3??

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sree surekha k  (11 years ago)

can sum1 plz give solution for Q3??

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sree surekha k  (11 years ago)

can sum1 plz give solution for Q3??

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sree surekha k  (11 years ago)

can sum1 plz give solution for Q3??

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PANKAJ  (11 years ago)

WHAT IS THIS IN FIRST QUESTION (…)????

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gauthami  (11 years ago)

A secret message is divided into Θ parts and each part is shared with a different
person. People communicate with each other using two-way phone calls and, in each
communication, share all the information they know until that point. What is the minimum
number of communications required for all Θ of them to know the secret? Find a
sequence of communications that achieves this minimum.

Is this solution Helpfull? Yes | No   

Mukesh Kushwah  (11 years ago)

N:320/7=45
45*7+5=5th day Thursday. i.e, starting day of weak is Sunday

N+1: 206/7=29*7 + 3 => 3rd day is Thursday . i.e, starting day is Tuesday

here we get 2 odd days,,,so it is a leap year....
as (N+1)th Year is leap year, Nth, (N-1)th ,(N-2)th Can't be leap Years and so we will get 1 odd day for (N-1) th year.
Starting Day in weak for (N-1) year is Saturday....
N-1: 168/7=28*7 => last day of the weak => Friday

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SHOBIT PATNI  (10 years ago)

q11.
ans-monday

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sameer  (10 years ago)

let x km be the distance of one side.
then,
x/(6-2) + x/(6+2) =3

x=8km.....

Is this solution Helpfull? Yes | No (1)  

Anilkumar  (10 years ago)

Q1.answer 8km
Speed upstream=6-2=4
Down stream speed=6=2=8
Time for down stream=1
Time for upstream=
So the place is 8kms away

Is this solution Helpfull? Yes | No (1)  

navin   (10 years ago)

in ques-11, how it is monday can anyone explain it to me.....

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Sanjeev R  (10 years ago)

Solution for Puzzle 9 is Rahul.
Each dice has numbers from 1 to 6. This is 6 possibilities in each dice. Two dice have a total combinations of 36.
The question is simply how many of these possibilities exist for Rahul, etc.
7 = 4+3, 5+2, 6+1 which can be represented through 2 dice i.e. 3*2= 6 possibilities (each dice can take either number)
9 = 6+3, 5+4 which is 4 possibilities
10 = 6+4, 5+5 again 4 possibilities
11 = 6+5 only 2 possibilities (poor choice).
Hence, Rahul's pick 7 is most probably with probability 6/36 = 1/6.

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Sanjeev R  (10 years ago)

Solution for puzzle 54 in table below in 7 steps
Bucket8 Bucket5 Bucket3
8 0 0 (start)
3 5 0
3 2 3
6 2 0
6 0 2
1 5 2
1 4 3
4 4 0

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mohini gupta  (10 years ago)

answer to question no. 6 - 325 explain..
if number plate can have only one digit, then it can be selected in 5 ways,either 1,2,3,4,or 5.if two digit no. can be taken, then it can be selected in 5*4 ways since digit cant be repeated.then for 3 digit, we have 5*4*3 ways and so on.
hence ans is 5 + 5*4 + 5*4*3 + 5*4*3*2 + 5*4*3*2*1=325

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vinay kumar  (10 years ago)

4) distance be x
x/(6+2)+x/(6-2)=3
solving eq: ans will 8 km

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vinay kumar  (10 years ago)

8)ans will be 30.62

Is this solution Helpfull? Yes | No (1)  

vinay kumar  (10 years ago)

14)75
5-12=-7
12-26=-14
26-47=-21
47-x=-28
x=75

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esther  (10 years ago)

45) ans is option B

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ROHIT KUMAR GUPTA  (10 years ago)

ans4.
let the distance travelled be d
time taken going upstream=d/(6-2)=d/4
time taken going downstream=d/(6+2)=d/8
d/4+d/8=3
d=8

Is this solution Helpfull? Yes | No   

ROHIT KUMAR GUPTA  (10 years ago)

ans9.
probability of rahul winning is highest since he has the maximum no of option that is 6 [(1,6)(2,5)(3,4)(4,3)(5,2)(6,1)]compare to others.

Is this solution Helpfull? Yes | No   

vinay kumar  (10 years ago)

56)2c1*2c1+2c2+2c2=6

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Sudharsan  (10 years ago)

Q9)rahul has the maximum probability (2,5)(5,2)(3,4)(4,3)(1,6)(6,1)
others have only 2 possibility

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ravi  (10 years ago)

soln. to ques no.52:
prob. of individual girl selecting right dress=1/3
prob. of individual girl selecting wrong dress=1-(1/3)=2/3
so,req. prob. of all girls selecting wrong drss=(2/3)^3=8/27

Is this solution Helpfull? Yes | No   

ravi  (10 years ago)

anvs. to ques. no.9:
n(s)=36
firstly for rahul,we have to get a sum of 7
so,n(e)={(1,6),(6,1),(2,5),(5,2),(3,4)(4,3)}
prob. of rahul=6/36=1/6
secondly,for ravi,we have to get a sum of 9
so,n(e)={(4,5),(5,4),(3,6),(6,3)}
prob. of ravi=4/36=1/9
thirdly,for rajesh,we have to get a sum of 10
so,n(e)={(5,5)(6,4)(4,6)}
prob. of rajesh=3/36=1/12
lastly,for rohan,we have to get a sum of 11
so,n(e)={(5,6),(6,5)}
prob. of rohan=2/36=1/18
thus we can say that rahul has the max. prob. of getting the chocolate

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devendra  (10 years ago)

if anybody have question of TCS apt of any college please mail me devendrarathore07@gmail.com because i have apt exam of TCS on 16th oct........sSo frnds plz mail me plzzzzzzzzzzzzzzzzzzzzzzzzz..........................

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ch.jyothsna  (10 years ago)

Q30)(1!+2!+3!+...............+50!)= 5![6+(6*7)+.......+(6*7*.....*50)]+[1+2+6+24]
= 5![6+(6*7)+.......+(6*7*.....*50)]+33
so the remainder will be 33

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mounika  (10 years ago)

please send the solution of all questions to pokalamouni@gmail.com plzzzzzzzz

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MoghanaPriya  (10 years ago)

can anyone please send me tcs question papers with solutions... my mailid is itspriya1293@gmail.com

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ABHISHEK CHANDEL  (10 years ago)

SOLN OF QUES-54:-
minimum seven step as follows:-
1. 8lt to 5lt,now 8lt contain 3lt
2. 5lt to 3lt, now 5lt contain 2 lt nd 3lt contain 3lt
3. 3lt to 8lt, now 8lt contain 6lt nd 3lt is empty
4. 5lt to 3lt, now 5lt empty nd 3lt contain 2lt
5. 8lt to 5lt, now 8lt contain 1lt nd 5lt full
6. 5lt to 3lt, now 3lt is full nd 5 lt contain 4lt
7. 3lt to 8lt, now 8lt also contain4lt. solved

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vinay H M  (10 years ago)

Plz some1 send me the total answer wid solutn of d abv qus, Its too urgent, Apti is on 26 sep, My ID is vinay0727@gmail.com. Plz help me plzzzzz...

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priya  (10 years ago)

1)remainder=0

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Swapnasish Dutta  (10 years ago)

hi .... can someone send me the total answer key of this placement paper..... its too urgent..
my mail id dream.nit@gmail.com

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Arth Gupta  (10 years ago)

Q.4 ans. 8km
Q.11 ans. Monday

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Aarthi  (10 years ago)

assume x=1
p(x)=(1^2012+....+1^1)^2-1^2012 =>2013^2-1^2
q(x)=1^2011+....+1^1 => 2012
p(x)/q(x)=(2013-1)(2013+1)/2012((a^2 - b^2)=(a+b)(a-b))
=> (2012*2014)/2012
this divides exactly
hence remainder=0

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poonam  (10 years ago)

please mail me tcs latest papers . my mail id is ..
preeti.iit10@gmail.com

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sillygrl  (10 years ago)

kindly mail me the solution for d latest paper of tcs...my email id ravishingroohi15@gmail.com

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sillygrl  (10 years ago)

kindly mail me the solution for d latest paper of tcs...my email id ravishingroohi15@gmail.com

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sillygrl  (10 years ago)

kindly mail me the solution for d latest paper of tcs...my email id ravishingroohi15@gmail.com

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sillygrl  (10 years ago)

kindly mail me the solution for d latest paper of tcs...my email id ravishingroohi15@gmail.com

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sillygrl  (10 years ago)

kindly mail me the solution for d latest paper of tcs...my email id ravishingroohi15@gmail.com

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GAYATHRI  (10 years ago)

9.Rahul's choice was7, Ravi's choice was 9, Rajesh's choice was 10 and Rohan's choice was 11

chance for Rahul's choice(7) = 1,6 2,5 3,4 4,3 5,2 6,1 (sum is 7)
chance for Ravi's choice(9) = 3,6 4,5 5,4 6,3 (sum is 9)
chance for Rajesh's choice(10) = 5,5 (sum is 10)
chance for Rohan's choice(11) = 5,6 6,5 (sum is 11)

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mukesh  (10 years ago)

ans.56)
R Y G B.....only 2 boxes will remain if we removed pair of y and b box....
4c2-1(y+b)=5

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Sayanika Dutta  (10 years ago)

51.2nd part:-18*19!

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pankaj bajaj  (10 years ago)

ams 54-
8ltr 5ltr 3ltr
8 0 0
3 5 0
3 2 3
6 2 0
6 0 2
1 5 2
1 4 3
4 4 0

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DHIRENDRA   (10 years ago)

q 20: What is the probability of throwing 3 dices to get a sum of 10?
solution
(2,2,6) (2,3,5) (3,3,4) (4,4,2) (5,4,1) (6,1,3)
(6,2,2) (5,3,2) (4,3,3) (2,4,4) (5,1,4) (3,1,6)
(2,6,2) (2,5,3) (3,4,3) (4,2,4) (1,4,5) (1,3,6)
18/(6*6*6)=1/12
probability is=1/12

Is this solution Helpfull? Yes | No (1)  

shaloo  (10 years ago)

asdhhjhdjj

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Faizulla Khan  (10 years ago)

1.) put x=1, since it is a polynomial then we have
p(x)= 2013^(2-1)^2012=2013^(1)^(2012)=2013.
Q(x)= 2012
therefore p(x)/q(x)= 2013/2012 hence remainder is 1.

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Wasim Akram Khan  (10 years ago)

koi pehle que ka shi ans btao yaaar ???

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Rajat Goyal  (10 years ago)

Ans 1. zero
Explanation: P(x) = (1+x+x^2+x^3....+x^2012)^2 - x^2012
so,according to Geometric Progression= (1(1-x^2013)/(1-x))^2 - x^2012
Similarly, we get Q(x)= 1(1-x^2012)/(1-x)
So, P(x)/Q(x) = (1-x^2014)(1-x^2012)/(1-x)(1-x^2012)
= (1-x^2014)/(1-x)
So, Remainder is 0. We can get this just by simply dividing just above expression and seeing the pattern.

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Rajat Goyal  (10 years ago)

Ans6) 325 is correct
if 1 digit registration, then he has 5 choices.
if 2 digit registration, then he has 5*4 = 20 choices.
if 3 digit registration, then he has 5*4*3 = 60 choices.
if 4 digit registration, then he has 5*4*3*2 = 120 choices.
if 5 digit registration, then he has 5*4*3*2*1 = 120 choices.
So, total choices = 5+20+60+120+120 = 325.

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Rajat Goyal  (10 years ago)

Ans 11) Monday is the correct option.
Since there are 31 days in Jan, and if there are 4 Thursday and 4 Sunday, then it means there are also 4 Friday and 4 saturday. so, left days are 31-16=15. So, Mon,Tue, Wed are 5 each to make it 31.And this is possible only if Mon is the first day of this month.

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D.HARINATH REDDY  (10 years ago)

q.no 30:
1!+2!+3!+....+50!= 1+2+6+24+5!(1+6+7*6+8*7*6+....)
= 33+5!(1+6+6*7+6*7*8+.....)
above number is divisible by 5! then we get 33 as remainder.

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Komala.G  (10 years ago)

Q4. 6 km/hr still water
2 km/hr stream
time taken 3 hours
for an hour he can row 8 km with stream 6+2 = 8
for an hour he can row 4 kn against stream 6-2 =4
So in 3 hours he goes to place and comes back a distance of 8 km

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disha  (10 years ago)

can anyone pls mail me solution for this paper @divyamegh@yahoo.com

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sony  (10 years ago)

can anyone mail me solutions for these urgent...mail id sonyreddy146@gmail.com

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Sneha paliwal  (10 years ago)

ansistgn vsdgufsn fvsgism,fcsuiofvsm, fvgs

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VIMALRAJ V  (10 years ago)

2) In a stream running at 2 kmph, a motorboat goes 6 km upstream and back again to the starting point in 33 minutes. Find the speed of the motorboat in still water ?
Solution:Let the speed of the motorboat in still water be x kmph. Then,
Speed downstream = (x + 2) kmph; Speed upstream = (x - 2) kmph.
∴ 6/x+2 + 6/x-2 = 33/60
⇔ 11x² - 240x - 44 = 0
⇔ 11x² - 242x + 2x - 44 = 0
⇔ (x - 22) (11x + 2) = 0 ⇔ x = 22.
Hence, speed of motorboat in strill water = 22 kmph.

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ROHIT YANAMANDRA  (10 years ago)

6. How many vehicle registration plate numbers can be formed with digits 1,2,3,4,5(no digits being repeated)if it is given that registration number can have 1 to 5 digits ?
Options: 205 100 325 105

Answer : 325.

1 digit number can be filled in 5 ways.
2 digit number can be filled in 5*4=20ways.
3 digit number can be filled in 5*4*3=60ways.
4 digit number can be filled in 5*4*3*2=120ways.
5 digit number can be filled in 5*4*3*2*1=120 ways.
Hence now Total=5+20+60120+120=325 ways.

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sabyasachi dey  (10 years ago)

Q4.
ans 8
still water he can row 6 km/hr
streem speed 2 km/hr and when he start rowing to go a point the steem reduse his speed,
that 6-2= 4 km/hr
and when he re rutun his speed is now 6+2=8 km/hr so
his travel time 3 hr
his last poin distance 8 km
so he need 2 hr to go(4*2=8km)that point and 1 hr for get back

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gagandeep singh  (9 years ago)

q 53 Ans is 32 min!!!

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