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Tcs Placement Papers Question

TCS New Pattern Placement paper Question And Answers

1.If 3y + x > 2 and x + 2y ≤ 3, What can be said about the value of y?

A. y = -1
B. y >-1
C. y <-1
D. y = 1

Answer: B
Multiply the second equation with -1 then it will become – x – 2y ≥ – 3. Add the equations. You will get y > -1.

2.If m is an odd integer and n an even integer, which of the following is definitely odd?

A. (2m+n)(m-n)
B. (m + n2) + (m – n2)
C. m2 + mn + n2
D. m +n

Answer: C and D (Original Answer given as D)
You just remember the following odd ± odd = even; even ± even = even; even ± odd = odd
Also odd × odd = odd; even × even = even; even × odd = even.

3. There are 20 balls which are red, blue or green. If 7 balls are green and the sum of red balls and green balls is less than 13, at most how many red balls are there?

A. 4
B. 5
C. 6
D. 7

Answer: B
Given R + B + G = 17; G = 7; and R + G < 13. Substituting G = 7 in the last equation, We get R < 6. So maximum value of R = 6

4. x2 < 1/100, and x < 0 what is the highest range in which x can lie?

A. -1/10 < x < 0
B. -1 < x < 0
C. -1/10 < x < 1/10
D. -1/10 < x

Answer: A
(x – a)(x – b) < 0 then value of x lies in between a and b.
(x – a)(x – b) > 0 then value of x does not lie inbetween a and b. or ( −∞, a) and (b, −∞) if a < b
x2 < 1/100 
(x2−1/100)<0  (x2−(1/10)2)<0  (x−1/10)(x+1/10)<0
So x should lie in between – 1/10 and 1/10.  But it was given that x is -ve. So x lies in -1/10 to 0

5.All faces of a cube with an eight – meter edge are painted red.  If the cube is cut into smaller cubes with a two – meter edge, how many of the two meter cubes have paint on exactly one face?

A. 24
B. 36
C. 60
D. 48

Answer : A
If there are n cubes lie on an edge, then total number of cubes with one side painting is given by 6×(n−2)2.  Here side of the bigger cube is 8, and small cube is 2.  So there are 4 cubes lie on an edge. Hence answer = 24

6.M, N, O and P are all different individuals; M is the daughter of N; N is the son of O; O is the father of P; Among the following statements, which one is true?

A. M is the daughter of P
B. If B is the daughter of N, then M and B are sisters
C. If C is the granddaughter of O, then C and M are sisters
D. P and N are bothers.
Answer: B

From the diagram it is clear that If B is the daughter of N, then M and B are sisters.  Rectangle indicates Male, and Oval indicates Female.

7.There are 10 stepping stones numbered 1 to 10 as shown at the side.  A fly jumps from the first stone as follows; Every minute it jumps to the 4th stone from where it started – that is from 1st it would go to 5th and from 5th it would go to 9th and from 9th it would go to 3rd etc.  Where would the fly be at the 60th minute if it starts at 1?

A. 1
B. 5
C. 4
D. 9
Answer : A

Assume these steps are in circular fashion.
Then the fly jumps are denoted in the diagram.  It is clear that fly came to the 1st position after 5th minute.  So again it will be at 1st position after 10th 15th …..60th. min.
So the fly will be at 1st stone after 60th min.

8.In base 7, a number is written only using the digits 0, 1, 2, …..6.  The number 135 in base 7 is 1 x 72 + 3 x 7 + 5 = 75 in base 10.  What is the sum of the base 7 numbers 1234 and 6543 in base 7. 

A. 11101
B. 11110
C. 10111
D. 11011

Answer: B

In base 7 there is no 7.  So to write 7 we use 10.  for 8 we use 11…… for 13 we use 16, for 14 we use 20 and so on.
So from the column d, 4 + 3 = 7 = 10, we write 0 and 1 carried over.  now 1 + 3 + 4 = 8 = 11, then we write 1 and 1 carried over.  again 1 + 2 + 5 = 8 = 11 and so on

9.Find the number of rectangles from the adjoining figure (A square is also considered a rectangle)

A. 864
B. 3276
C. 1638
D. None

Answer: C
To form a rectangle we need two horizontal lines and two vertical lines.  Here there are 13 vertical lines and 7 horizontal lines.  The number of ways of selecting 2 lines from 13 vertical lines is 13C2 and the number of ways of selecting 2 lines from 7 horizontals is 7C2. So total rectangles = 7C2×13C2

10.Roy is now 4 years older than Erik and half of that amount older than Iris.  If in 2 years, roy will be twice as old as Erik, then in 2 years what would be Roy’s age multiplied by Iris’s age?

A. 28
B. 48
C. 50
D. 52

Answer: 48

11.Mr and Mrs Smith have invited 9 of their friends and their spouses for a party at the Waikiki Beach resort.  They stand for a group photograph.  If Mr Smith never stands next to Mrs Smith (as he says they are always together otherwise). How many ways the group can be arranged in a row for the photograph?

A. 20!
B. 19! + 18!
C. 18 x 19!
D. 2 x 19!

Answer: C

12.A drawer holds 4 red hats and 4 blue hats.  What is the probability of getting exactly three red hats or exactly three blue hats when taking out 4 hats randomly out of the drawer and immediately returning every hat to the drawer before taking out the next?

A. 1/2
B. 1/8
C. 1/4
D. 3/8

Answer: B

13.The prime factorization of integer N is A x A x B x C, where A, B and C are all distinct prime integers.  How many factors does N have?

A. 12
B. 24
C. 4
D. 6

Answer: A

14.A father purchases dress for his three daughter. The dresses are of same color 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.

A.  2/3
B.  1/3
C.  1/6
D.  1/9

Answer: B

15. A turtle is crossing a field.  What is the total distance (in meters) passed by turtle? Consider the following two statements
(X) The average speed of the turtle is 2 meters per minute
(Y) Had the turtle walked 1 meter per minute faster than his average speed it would have finished 40 minutes earlier

A. Statement X alone is enough to get the answer
B. Both statements X and Y are needed to get the answer
C. Statement Y alone is enough to get the answer
D. Data inadequate

Answer: B

16.If P(x) = ax4+bx3+cx2+dx+e has roots at x = 1, 2, 3, 4 and P(0) = 48, what is P(5)

A. 48
B. 24
C. 0
D. 50

Answer: A

17.Given the following information, who is youngest?

C is younger than A; A is taller than B
C is older than B; C is younger than D
B is taller than C; A is older than D

A. D
B. B
C. C
D. A

Answer: B

18. N is an integer and N>2, at most how many integers among N + 2, N + 3, N + 4, N + 5, N + 6,  and N + 7 are prime integers?

A. 1
B. 3
C. 2
D. 4

Answer: C

19. Tim and Elan are 90 km from each other.they start to move each other simultaneously Tim at speed 10 and elan 5 kmph. If every hour they double their speed what is the distance that Tim will pass until he meet Elan 

A. 45
B. 60
C. 20
D. 80

Answer: B

20. In how many ways can we distribute 10 identical looking pencils to 4 students so that each student gets at least one pencil?

A. 5040
B. 210
C. 84
D. None of these

Answer: C

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