TCS 30 Question set

1. Find X^y+y^x=46. Find X and Y values?

ANS:  x=45 and y=1
(or) y=45 and x=1... Only hit and try

2. 3 white chips, 7 blue chips, 16 green chips, 2 chips drawn from the box in succession what is the probability that one is blue and other is white?
a) 7/50 b) 8/30 c) 7/25 d) 20/26

ANS: (7*3)/(13*25)          21/13*25

o of ways that 2 chips selected from total of 26 is 26C2=26*25/2=13*25
no of ways that 1 white and 1 blue is selected is 3C1*7C1=21
total probability=21/13*25

3. If a person has to work 8 continuous day & he gets a rest on the 9th day. If a person starts on Monday. What is the day of 12th rest day?

ANS Wednesday

4. How many liters of a 90% of concentrated acid needs to be mixed with a 75% solution of concentrated acid to get a 30 liter solution of 78% concentrated acid?

a) 8 b)9 c) 7 d)6

the concentration is given which is wrt 100, hence we can take x lt of 90% and (30-x)of 75%
x*90 + (30-x)*75 = 30*78 hence the ans is 6 ltr...

5. 3 cars A, B & C are in the race. A is twice as likely to win as B and B is thrice as likely to win as C. what is probability that B will win, if only one can win the race ?
a) ½ b) 2/5 c) 3/10 d) 1/10

ANS:  NS= 3/10 LET C=X
B=3X
A=6X
THEN B'S PROBABILITY= 3X/(X+3X+6X)
B'S = 3/10

6. A cow & Horse brought for Rs.2000. The cow is sold at a profit of 20% and the Horse is sold at a loss of 10%. Of The overall gain is Rs.40. The cost price of the cow is :

ANS 800
a) 700 b) 800 c) 1200 d) 1300

7. The sum of 3 consecutive numbers of the four numbers A, B, C, D are 4613,4961,5010,5099 then what is the largest number among A,B,C,D ?
a) 1948 b) 1463 c) 1601 d) 1550

ANS:  Let, S1,S2,S3,S4 be the sums of A,B,C,D taking 3 of them at a time.
So, by the given data in the problem,it follows that :
S1+S2+S3+S4 = 4613+4961+5010+5099
=>S1+S2+S3+S4 = 19683....[eqn 1]
Now, Without the loss of generality we can assume
S1= A+B+C
S2= B+C+D
S3= C+D+A
S4= D+A+B
-------------------------------------------------------
adding the above terms we get,
S1+S2+S3+S4 = 3(A+B+C+D)
=>19683 = 3(A+B+C+D); [From [eqn 1] ]
=>(A+B+C+D)=(19683/3)
=>(A+B+C+D)=6561

So,the greatest term among them =sum of all four - sum of lowest three terms
So,the greatest term among them=6561-4613 = 1948.

So,the greatest term among them = 1948

So, the correct answer is : OPTION a)1948

8. George printing press can print an edition of newspapers in 12 hours while Paul’s press can print the same edition in 18 hours. What is the total no. of hours the press working together but independent of one another to print the same edition?
a) 15 b) 17.4 c) 7 d) 7.2

ANS 7.2

9. 87th number in the series 2, 10, 26, 50…….

Observing the given we can write the following :


2nd term - 1st term = 1*8;
3rd term - 2nd term = 2*8;
4th term - 3rd term = 3*8;
5th term - 4th term = 4*8;
.
­­.
.
(n-1)th term - (n-2)th term =(n-2)*8
(n)th term - (n-1)th term =(n-1)*8;
---------------------------------------------
Summing up all the above terms we get ,
(n)th term - 1st term = {1+2+......+(n-1)}*8
=>(n)th term = 8*{n*(n-1)}/2 + 1st term
=>(n)th term = 8*{n*(n-1)}/2 +2;
So, Clearly 87th term of the sequence will be :
8*{n*(n-1)}/2 +2 = 8*{87*86}/2 +2 = 4*86*87 +2 = 29930

Hence, 87th term will be : 29930

answer is =29930
series is 2,10,26,50
like 1st term is 2 = 1^2+1
2nd term is 10= 3^2+1
3rd term is 26= 5^2+1
similarly 87 term is = 173^2+1=29930......
as we seen above that in 1st ,2nd,& 3rd term it is squire of corresponding odd numbers+1
since 1st odd no is 1(1*2-1),,,,,2nd odd no is 3 (2*2-1),,,,3rd odd no is 5(2*3-1).....similarly 87 odd no is (2*87-1)= 173.....

10. 70, 54, 45, 41……. What is the next number in the given series?

it is very simple question of series
ans=40
70-40=16=square of 4
54-45=9=square of 3
45-41=4=square of 2
so next no will be square of 1
41-1=40

11. If the sum of the numbers in each row column, diagonal are same then find the value of (Y+Z)

-16
W
-2
X
Y
5
Z
-9

12. If the sum of the numbers in each row column, diagonal are same then find the value of (Y+Z)

Ans: answer is - 66
values are
V=33 -2 5
-16 X=12 Z=40
W=19 Y=26 -9


so y+Z=26+40 = 66

13. In the simple subtraction problem Below , sum single digits (not necessarily distinct) are replace by letters , find the value of 7*A + 7*B +6*C*D
A 7  C   2
-   4  B  6   8
————–
5  4   3   D
a) 77 b) 95 c) 84 d) 70

77 ANS A=9,C=4,B=2,C=0

14. How many polynomial functions f of degree >=1 satisfy f(X2) = (f(X)) 2 =f (f(X)).
a) 1 b) 0 c) 2 d) more than 2

15. What is the remainder when 50! (50 factorial ) is divided by 16 ^ 15 (1615)
Answer is: 1

16. 1,5,6 ,25, 26,30,31, 125,126,130,131,150,151,155,156,…………………
What is the value of 30th term in the given series?
a) 781 b) 3125 c) 776 d) 780

17. 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 or

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

40 ANS

18. If the 20th term of an AP=560 and 30th term of AP=840 then what is the sum of 5th term and 40th term of the series.
a) 1450 b) 1560 c) 1260 d) 1340

ANS 1260

19. 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: d=1/8

20. 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

ANS: a) √3:8

21. 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

ANS 3.60

22. 1,2,2,3,3,3,4,4,4,4,1,1,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,…………………………………..
Then what is the 2532 position of the number in the sequence?
a) 2 b) 1c) 3 d) 4

23.1,2,2,3,3,3,4,4,4,4,1,1,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,…………………………………..
Then what is the 2320 position of the number in the sequence?
b) 2 b) 1c) 3 d) 4

24. How many 7’s are there between 0 to 400?

ANS : 80

25. 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

26. The letters in the word TALION are permuted in all possible ways and arranged in alphabetical order then find the word at position 33 in the permuted alphabetical order?

27. The letters in the word SHOVEL are permuted in all possible ways and arranged in alphabetical order then find the word at position 31 in the permuted alphabetical order?

28. 15 students join a summer course. Every day 3 students are on duty after school to clean the class rooms. After the course, it was found that every pair of students has been on duty exactly once. How many days does the course last for?

a) 35 b) 45 c) 105 d)none of these

29. Consider all permutations (i.e., arrangements) of digits 1, 2&3. We will say that a hit has been scored if at least one digit occurs in its proper position in the permutation. If 1 (one) occurs in the first position or 2 in the second position or 3(three) in the 3rd position in how many ways of these permutations is a hit scored?
a) 4 b) 1 c) 2 d) 3

1 can be arrange in 123, 132
2 can be arrange in 321
3 can be arrange in 213

4 ANS

30. If the word MONOS is permuted then the probability that O’s never come together?

Total permutations by MONOS = 5!/2!=120/2=60
If O's comes together then with M,N,OO,S we can form 4!=24 words
So the words with O's never come together are =total- O's comes together
=60-24=36
so probability of O's never come together=36/60=3/5...

ANS : 3/5

31. Next number in the given series 1, 7, 8, 49, 50, 56, 57, 343,

344 because
1*7=7
7+1-8
7*7=49
49+1=50
8*7=56
56+1=57
49*7=343
343+1=344
ans= 344