Fresher Station: TCS Questions New Pattern 2013 Set 1

1. An empty tank be 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? Ans

2. A boy wants to make cuboids of dimension 5m,6m & 7m from small cubes of .03m^3.Later he realized that he can make some cuboids by making it hollow.Then it takes some cubes less.What is the number of cubes to be removed

a)2000 b)5000 c)3000 d)7000 Ans

3. Leena cuts small cubes of 3 cubic cm each.She joined it to make a cuboid of length 10 cm,width 3cm, and depth 3 cm.How many more cubes does she need to make a perfect cube?

a)910 b)250 c)750 d)650 Ans

4. What is the distance between the z-intercept from x-intercept in the eqn ax+by+cz+d=0 Ans

5. 10 men and 10 women are there.They dance with each other.Is there possibility that two men are dance with same girl and vice versa?

a)22 b)20 c)10 d)none of these

6. 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…

2/3 b) 1/3 c) 1/6 d) 1/9

7. 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! Ans

8. Tim and Elan are 90 km from each other, they start to move each other simultaneously, Tim at speed 10 and Elan 5kmph, 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 Ans

9. MOTHER +DAUGHTER+INFANT AGE IS 74. MOTHER AGE IS 46 MORE THEN DAUGHTER AND INFANT.

AND INFANT AGE IS 0.4 OF DAUGHTER. FIND DAUGHTERS AGE. Ans

10. The age of two people is in the ratio 6:8. the sum of their ages is 77. after 2 years the ratio of their ages becomes 5:7. wat is their present age? Ans

11. A Grocer bought 24 kg coffee beans at price X per kg. After a while one third of stock got spoiled so he sold the rest for $200 per kg and made a total profit of twice the cost. What must be the price of X?

$33 1/3 B. 66 2/3 C.44 4/9 D.50 1/3 Ans

12. Let exp(m,n) = m to the power n. If exp(10, m) = n exp(2, 2) where to and n are integers then n = â€¦â€¦â€¦â€¦â€¦â€¦? Ans

13. Bhanu spends 30% of his income on petrol on scooter. ? of the remaining on house rent and the balance on food. If he spends Rs.300 on petrol then what is the expenditure on house rent? Ans

14. 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.

3 collected the same number as K and M together.

L collected 3 more than the cube of an integer

The no. collected by J was the square of an integer.

Total no. collected by K was either the square or cube of an integer.

The no. collected by J was:

27 (2) 49 (3) 36 (4) 64

The no. collected by K was:

16 (2) 27 (3) 25 (4) 36

The difference of numbers collected by L & M was:

(1) 3 (2) 2 (3) 5 (4) 9 Ans

15. A,B COMMON TO ALL THREE. THEN AT LEAST 1 ELEMENT COMMON TO 2 IE X1,X2,X2,X3,X3,X1.

FIND MINIMUM ELEMENTS IN EACH GROUP. Ans

16. How many kgs. of wheat costing Rs. 8 per kg must be mixed with 86 kg of rice costing Rs. 6.40 per kg so that 20% gain may be obtained by Belling the mixture at Rs. 7.20 per kg ? Ans

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) âˆš3:8 b) âˆš2:5 c) âˆš3:6 d) âˆš2:4 Ans

18. 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 Ans

19. 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 Ans

20. length of minute hand is 5.4 cm, area covered by this in 10 min is ?

a)50.97 b)57.23 c)55.45 d)59.14 Ans

21. 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 Ans

22. there r three buckets..of 8,5 n 3 litres…out of which only 8 ltr bucket is fully filled…u hv to fill exact 4-4 ltr liquid in 8 and 5 litre bucket by using only these buckets in minimm num of steps….. Ans

23. A number has exactly 3 prime factors, 125 factors of this number are perfect squares and 27 factors of this number are perfect cubes. overall how many factors does the number have??? Ans

24. there are two boxes,one containing 39 red balls & the other containing 26 green balls.you are allowed to move the balls b/w the boxes so that when you choose a box random & a ball at random from the chosen box,the probability of getting a red ball is maximized.this maximum probability is

a)60 b)50 c)80 d)30 Ans

25. A dog taken four leaps for every five leaps of hare but three leaps of the dog is equal to four leaps of the hare. Compare speed? Ans

26. 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 be mixed to obtain a new mixture in vessel C containing half milk and half water? Ans

27. In what ratio must water be mixed with milk to gain 20 % by selling the mixture at cost price? Ans

28. x=(sin nx/n)=? Ans

29. How much water must be added to 60 litres of mixture of milk? 1 ½ litres of milk for Rs. 20. So as to have a mixture worth Rs.10⅔ a litre ? Ans

30. Find the no of zeros in the product of 1^1*2^2*3^3*…..*49^49? Ans

31. 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 Ans

32. The sequence {A(n)} is defined by A(1)=2 and A(n+1)=A(n)+2n. What is the value of A(100). Ans

33. n! has 13 zeros than what is the highest and lowest value of n?? Ans

solutions

Rate at which A fill is 1/42 per min

A filled for 12 min so tank filled by A will be 12/42

Similarly B empty the tank for 6 min

now the volume will be (18/42) -(6/30) = 8/35 because at the 6 min A has also filled.

Now the amount left to be filled is (1-8/35) = 27/35

Now C comes it fills 1/35 per minute.

So from now the amount will be filled is (1/42+1/35-1/30) = 2/105 per minute

So to fill the required amount it will take 105/2 * 27/35 = 40.5 min

So total time is 12+6+40.5 = 58.5 min

Total no of cubes = 5*6*7/0.03=7000

for making it hollow we have to remove (5-2)*(6-2)*(7-2)/0.03=2000.

To make cube we need 10*10*10=1000.

Now we have only 10*3*3=90.

So the more cube we need are 1000-90=910.

square root of (d/a)^2 + (d/c)^2

none of these

Proper Selections:

A B C

A C B

C B A

B A C (i.e. total 4)

Improper selection:

B C A

C A B (i.e. total 2)

Probability for improper selection= 2/6 = 1/3

Mr and Mrs smith never be together so out of 20 (with both them) 19 can b any place so total = 19!

20 because their invitees are with their spouses.

Also 1 of them can stand with other so 18 places

So total is 18*19!

m+d+i=74 (1)

m=46+(d+i) (2)

i=0.4d (3)

solving we get d = 10

11.

Cost price= 24*X,
spoiled= 24*1/3=8 kg, now total amount= (24-8)=16 kg
selling price= 16*200 =3200
profit= (3200-24*X)
profit=2* cost , (3200-24*X)= 2*24*X, x=400/9 =44 4/9

12.

exp(10, m) = n * exp(2, 2) = n*(2^2) = 4*n

10^m=4*n ; where m,n integers

m=2, n=25 satisfies for the least value

13.

Let the income x, so in petrol he spends 3x/10 rs,remaining x-3x/10=7x/10 on house rent and balance on.now 3x/10=300,so x=1000,

on house rent he spends rs 700-balance.

14.

L=12,N=11,J=27,M=14,K=36

Given,

K+M+J+L+N=100 ———(i)

K,M,J,L,N>10 ———(ii)

K≠M≠N≠J≠L ———(iii)

K+M=J+L+N ———(iv)

L=3 + X^3 , where X is an integer ———(v)

J= Y^3, where Y is an integer (Modify the question here it should be like that) ———(vi)

K=Z^2 or Z^3, where Z is an integer ———(vii)

Now from the ques value of J can be 27 or 64

but if we take 64 then eqn iv would not satisfy so J=27

Again considering eqn ii, iv & ii we can say that L+N = 23 & K+M=50

Now from eqn v the value of L must be 11, thus L=11

That conclude N = 12

Now from the questio part 3,

The difference of numbers collected by L & M was:

3 (2) 2 (3) 5 (4) 9

Considering the fact M-L=any of those values

Now M=L+any of those values

M=11+any of those values

Now considering each values, M= 14, value =3; K=50-14 =36 which is a square of integer, thus satisfies

again M=13, value = 2; K=37 which is neither square or cube of any integer

M=16, value = 5; K=34 which is neither square or cube of any integer

M=20, value = 9; K=30 which is neither square or cube of any integer

Thus M = 14 & K = 36.

15.

16. Modified:

1. How many kgs. of wheat costing Rs. 8 per kg must be mixed with 86 kg of rice costing Rs. 5.40 per kg so that 20% gain may be obtained by Belling the mixture at Rs. 7.20 per kg ?

Ans : 25.8

17.

Given diagonal of square (a)= 2* side of triangle;

Area of square =1/2 a^2 where a = length of diagonal

Area of triangle = √3/4 * a^2/4

Ratio of triangle to square: √3/8

18.

Possible events

(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 no. of possible event = 27

So probability = 27/216 = 1/8

answer (1/8)

19.

20.

(3.14*5.4*5.4)*10/60 = 15.26 cm2

21.

22.

Number of step must be 2^n where n= no. of buckets

8ltr 5ltr 3ltr

5 0 3

5 3 0

2 3 3

2 5 1

7 0 1

7 1 0

4 1 3

4 4 0

Total 8 steps are required.

24.

Well Keep a single red ball in 1 box and move 38 red balls to the other

1st box = 1R

2nd box = 38R + 26G

p(red) = 1/2 * 1 + 1/2 * 38/64 ≈ 0.8

25.

16:15

26.

7:5

27.

1:5

28.

x=0

29. Modified:

1. How much water must be added to 60 litres of mixture of milk? 1 ½ litres of milk for Rs. 20. So as to have a mixture worth Rs.10⅔ a litre ?

Ratio of water and milk =8 : 32 = 8 : 32 = 1 : 4

∴

Quantity of water to be added to 60 lts of milk =

[1/5 X 60]

litres =12 litre.

30.

Total zeros at the end of product 5^5 x 10^10 x 15^15 x 20^20 x 25^25 x 30^30 x 35^35 x 40^40 x 45^45 will be 5+10+15+20+50+30+35+40+45 = 250 zeros

31.

for odd = 2

for even =1

32.

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).

33.

55!