TCS Online Test Papers with Solutions

TCS Online Test Placement Papers

what is the remainder when 50! is divided by 529 ?
answer is zero because 529 is square of 23 and 23  is factor of 50!.


0,4,18,48,100,?
1^3-1^2=0
2^3-2^2=4
3^3-3^2=18
4^3-4^2=48
5^3-5^2=100
6^3-6^2=180
ans 180


Find the number of (1/2) of a number is 3 more than the (1/6) of the same number?
a) 6
b) 7
c) 8
d) 9
(x/2)=(x/6)+3
6x = 2x+36
4x=36
x=9


Find the next number in the series.
2,6,12,19,...?
a) 30
b) 27
c) 29
d) none of the above
yes if it is 20 then answer explained by Karthik is right.
or we can do 2+4=6,
6+6=12,
12+8=20,
20+10=30
+4,+6,+8,+10


f(1)=0 and f(m+n)=f(m)+f(n)+4(9mn-1) for natural numbers m and n. What is the value of f(17)?







f(1) = 0
f(2) = f(1+1) = f(1)+f(1)+4(9×1×1 – 1) = 0+0+4×8 = 32
f(4) = f(2+2) = f(2)+f(2)+4(9×2×2 – 1) = 32+32+4×35 = 204
f(8) = f(4+4) = f(4)+f(4)+4(9×4×4 – 1) = 204+204+4×143 = 980
f(16) = f(8+8) = f(8)+f(8)+4(9×8×8 – 1) = 980+980+4×575 = 4260
f(17) = f(1+16) = f(16)+f(1)+4(9×16×1 –1) = 4260+0+ 4×143 = 4832

A series of books were published at an interval of seven years. When the seventh book was published, the total sum of publication years was 13,524. The first book was published in 
Let the first year of publication be x,
 7*x + 7*(1+2+3+4+5+6) = 13,524
7*x = 13377
x = 1911

When the sum of the numbers from 9 to 33 is divided by 9 the remainder is 
Sm=(33*34)/2-(8*9)/2=525
525/9=58+(3/9) where 3 is the remainder


x,y,z are positive integers. If x(y+z)=63, y(z+x)=40, z(y+x)=33, what is the value of x+y+z? 
As we look at the third equations,
 z = 11 or 3
 but, z=11 does not satisfies the other two equations
 therefore, z=3
 => y = 11-x
Now, as we see in the second equation, i.e.,
 y(z+x)=40
=> (11-x)(3+x)=40
=> x=1; y=10
Therefore, x+y+z = 14 

A series 1234123441234441234444 and what is the value on 200th position? 
1234 => 4 times
12344 => 5 times
123444 => 6 times
.
.
.
4 + 5 + 6 + ...n < 200
n(n+1)/2 - 6 = 200
Solving  n = 19
i.e. 4+5+6+...19 = 184
After the 184th term,the sequence has 20 terms
12344444444444444444 = 20 terms
=> 200th term = 4

7+7*7+(7/7)-7 = ?
50

Sixty-five percent of a number is 21 less than fourth-fifth of that number. What is the number?
1.120
2.140
3.160
4.130
140
(4/5)x-21=0.65x
(0.8-0.65)x=21
x=140

The hen can lay 5 whole eggs and what is the probability that the first egg is male and the second is female?



Children go to school at 8:00 A.M. Child 1 runs for 1 minute and sits for next 1 minute continuosly. Child 2 runs for 2 minutes and sits for next 1 minute and this goes on as child n runs for n minutes and sits for 1 minute. All the children sit at once. At what time the school will ring home bell?
A.9:30AM   B.11:30AM    C.2:00PM   D.3:00PM

In how many ways a team of 11 must be selected a team 5 men and 11 women such that the team must comprise of not more than 3 men.
a) 1565          
b) 2256             
c) 2456            
d) 1243

University of Vikramsila has enrolled nine PhD candidates. Babu, Chitra, Dheeraj , Eesha, Farooq,Gowri , Hameed, Iqbal, Jacob.
- Farooq and Iqbal were enrolled on the same day as each other, and no one else was enrolled that day.
- Chitra and gowri were enrolled on the same day as each other, and no one else was enrolled that day.
- On each of the other days of hiring , exactly one candidate was enrolled.
- Eesha was enrolled before Babu.
- Hameed was enrolled before Dheeraj
- Dheeraj was enrolled after Iqbal but before Eesha
- Gowri was enrolled after both Jacob and Babu
- Babu was enrolled before Jacob
Who were the last two candidates to be enrolled?
a. Babu and Gowri
b. Eesha and Jacob
c. Babu and Chitra
d. Gowri and Chitra

George and Mark can paint 720 boxes in 20 days, Mark and Harry in 24 days and Harry and George in 15 days. George works for 4 days, Mark for 8 days and Harry for 8 days. The total number of boxes painted by them is
a. 252
b. 516
c. 348
d. 492


How many of the numbers x (x being integer) with 10 <= x <= 99 are 18 more than the sum of their digits?
a. 9
b. 12
c. 18
d. 10
let the integer at ten's place be x & at unit place be y
therefore, num=10x+y
acc to the condition:-
       10x+y=18+x+y
        9x=18
        x=2
now with ten's place as 2 there can be 10 possible values of y from 0-9
total number of num= 10
ans:-10 

Three containers A, B and C are having mixtures of milk and water in the ratio of 1:5, 3:5, 5:7 respectively.  If the capacities of the containers are in the ratio 5:4:5, find the ratio of milk to water, if all the three containers are mixed together.
a. 53:115
b. 53:113
c. 54:115
d. 54:113


In 2003, there are 28 days in February and there are 365 days in the year. In 2004, there are 29 days in February and there are 366 days in the year. If the date March 11, 2003 is Tuesday, then which one of the following days would the date March 11, 2004 be?
A. Monday
B. Tuesday
C. Thursday
D. Wednesday


X takes 4 days to complete one-third of a work, Y takes 3 days to complete one-sixth of the same work and Z takes 5 days to complete half the work. If all of them work together for 3 days and X and Z quit, how long will it take for Y to complete the remaining work?
a. 6 days
b. 5.1 days
c. 7 days
d. 8.1 days

The average marks of student A,B and C is 60. When another student D joins the group, the new Average becomes 56 marks. if another student E, who has 3 marks more then D, joins the group, the average of the 4 students B,C,D and E becomes 55 marks. how many marks did A get in Exam?
a. 51
b. 52
c. 53
d. 54


Babla alone can do a piece of work in 10 days. Ashu also can do it in 15 days. The total wages for the work is Rs.5000. how much should be babla be paid if they work togather for an entire duration of work.







a. 3000
b. 2000
c. 1000
d. 4000

find the sum of all 5 digit number formed by 1,2,3,5,7,9 and the number should not be repeted?
note: options are not remembered and data may be changed but the question was same.



of a set of 30 numbers,average of first 10 numbers is equal to average of last 20 numbers. then the sum of last 20 numbers is?
a. 2 x sum of last 10 numbers
b. sum of first 10 numbers
c. cannot be deyermined
d. 2 x first 10 numbers


The maximum power of 143 in 87! is?
Expressing as product of primes ,<br>143 = 11*13 <br>As 13 is the largest, highest power of 143 is same as the highest power of 13&nbsp; in 87! = 87/13 + 87/(13^2) + ...<br>= 6 + 0 + 0 + ...<br>= 6<br><br>


Average salary of 17 teachers is 45000. 3 teachers went out and the average dropped by 2500. What is the sum of salaries of 3 teachers who left?
salary of 17 teacher=765000
after left the three teacher avg sal is=45000-2500
    =42500
then sal of 14 teacher is=14*42500
  =595000
after that sal of three teacher is=765000-595000
170000


8+88+888+.....+8888......8888. there are 21 "8" digits in the last term of the series. Find the last three digit of the sum.

In how many ways can the letters of the English alphabet be arranged so that there are seven letters between the letters A and B (no letter is repeated)?


P, Q, R, S are distinct integers numbered from 1 to 12. What is the smallest possible value for (P/Q) + (R/S) ?


Find the number of ways in which 7^11 can be expressed as the product of three factors (excluding 1)


Mr. X, is a good programmer. He coded a program to calculate the sum of consecutive numbers. Later he found a mistake that a number was added twice in the sum totals to 1710 . Find the number that was added twice ? (Asked in an Off Campus Hiring event on 08-Mar-2014)


From a pack of 52 playing cards all cards whose numbers are multiples of 3 are removed. A card is now drawn randomly. What is the probability that the card drawn is an even numbered red card ? (Asked in an Off Campus Hiring event on 08-Mar-2014)


Of the 38 people in my office, 10 like to drink chocolate, 15 are cricket fans, and 20 neither like chocolate nor like cricket. How many people like both cricket and chocolate?


What is the remainder when 135^77 is divided by 7 ?  (Asked in an Off Campus Hiring event on 08-Mar-2014)
Remainder when 135 is divided by 7 is 2.
So using remainder thm, the remainder will be 2^77 mod 7.
Now 2^77 = 2^75 * 2^2
= 8^25 * 2^2
Remainder when 8^25 is divided by 7 is 1^25 = 1
So the final remainder is 1*2^2 mod 7 = 4 mod 7 = 4


There were 18 runners in a 400 metre race. The probability of three candidates winning were 1/8 1/8 1/7 respectively. Find the probability that atleast one of them will win the race.

What is the remainder when 6^17+17^6+169^235 is divided by 7 ?  


Tiger and Deer are 900 meter apart. After seeing Tiger, Deer started running away at the rate of 60 Km/hr and Tiger started chasing at the rate of 80 Km/hr. After how much time Tiger will catch deer ?  (Asked in an Off Campus Hiring event on 08-Mar-2014)
Relative Speed = 80-60 = 20 kmph = 20 * 5/18 = 50/9 m/sec
Time reqd = 900/(50/9) = 162 seconds

2,5,9,1,5,10,3,8,? 
Ans: 14

In how many ways can 2310 be expressed as product of 3 factors?


set A {1,3,10,17,19} and set B {9,12,15,18,21} and set C {4,7,10,13,16,19}. What is the probabilty of 'a num from A + a num from B > a num from C? 
Ans: 133/150
Let us consider one by one from set C.
For 4: All 25 combos will be greater than 4. Hence probability =1
For 7: All 25 combos will be greater than 7. Hence probability =1
For 10: Out of all 25 combos, 1,9 alone is not greater. Hence probability = 24/25
For 13: 1,9 and 1,12, 3,9 are not greater. Hence probability = 22/25
For 16: 1,9 and 1,12 and 1,15 and 3,9 and 3,12 are not greater. Hence probability = 20/25
For 19: 1,9 1,12 1,15 1,18 3,9 and 3,12 3,15, 10,9 are not greater. Hence probability = 17/25
Net required probability = 1/6 *1 + 1/6*1 + 1/6*24/25 + 1/6*22/25 + 1/6*20/25 + 1/6 * 17/25
= 2/6 + 4/25 + 11/75 + 10/75 + 17/150
= 1/3 + 33/75 + 17/150
= (50+66+17)/150
= 133/150


A women says her age is 25 excluding saturdays and sundays.Now what is her current age? 
Excluding Saturday and Sunday we have 5 days in a week. 
So actual age = 25 * 7/5 = 35