TCS PREPARATORY PAPER 1
1 
What is the total number of divisors of 600(including 1 and 600)? 



(a) 24 
(b) 40 
(c) 16 
(d) 20 
2 
What is the sum of the squares of the first 20 natural numbers (1 to 20)? 


(a) 2870 
(b) 2000 
(c) 5650 
(d) 44100 
3A call center agent has a list of 305 phone numbers of people in alphabetic order of names (but she does not have any of the names). She needs to quickly contact Deepak Sharma to convey a message to him. If each call takes 2 minutes to complete, and every call is answered, what is the minimum amount of time in which she can guarantee to deliver the message to Mr. Sharma?
(a) 18 minutes 
(b) 610 minutes 
(c) 206 minutes 
(d) 34 minutes 
4The times taken by a phone operator to complete a call are 2, 9, 3, 1, 5 minutes respectively. What is the average time per call?
(a) 4 minutes 
(b) 7 minutes 
(c) 1 minute 
(d) 5 minutes 
5The times taken by a phone operator to complete a call are 2, 9, 3, 1, 5 minutes respectively. What is the median time per call?
(a) 5 minutes 
(b) 3 minutes 
(c) 1 minute 
(d) 4 minutes 
6Eric throws two dice, and his score is the sum of the values shown. Sandra throws one die, and her score is the square of the value shown. What is the probability that
Sandraâ€™s score will be strictly higher than Ericâ€™s score?
(a) 137/216 
(b) 17/36 
(c) 173/216 
(d) 5/6 
7What is the largest integer that divides all three numbers 23400,272304,205248 without leaving a remainder?
(a) 48 
(b) 24 
(c) 96 
(d) 72 
8Of 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? 




(a) 7 
(b) 10 
(c) 15 
(d) 20 
9 
If f(x) = 2x+2 what is f(f(3))? 




(a) 18 
(b) 8 
(c) 64 
(d) 16 
10 
If f(x) = 7 x +12, what is 



(a) 
(b) 7x+12 
(c) 1/(7x+12) 
(d) None of these 
11 
If we consider the permutation of 7 numbers then what is order of (1457)(236) 


(a) 12 
(b) 7 
(c) 7! 
(d) 14 
12 
What is the maximum value of x3y3 + 3 x*y when x+y = 8? 



(a) 4144 
(b) 256 
(c) 8192 
(d) 104 
TCS PREPARATORY PAPER 1
13Two circles of radii 5 cm and 3 cm touch each other at A and also touch a line at B and C. The distance BC in cms is?
(a) âˆš60 
(b) âˆš62 
(c) âˆš68 
(d) âˆš64 
14In Goa beach, there are three small picnic tables. Tables 1 and 2 each seat three people. Table 3 seats only one person, since two of its seats are broken. Akash, Babu, Chitra, David, Eesha, Farooq, and Govind all sit at seats at these picnic tables. Who sits with whom and at which table are determined by the following constraints:
i.Chitra does not sit at the same table as Govind.
ii.Eesha does not sit at the same table as David.
iii.Farooq does not sit at the same table as Chitra.
iv.Akash does not sit at the same table as Babu.
v.Govind does not sit at the same table as Farooq.
Which of the following is a list of people who could sit together at table 2?
(a) Govind, Eesha, 
(b) Babu, Farooq, 
(c) Chitra, Govind, 
(d) Farooq, David, 
Akash 
Chitra 
David. 
Eesha. 
15There are a number of chocolates in a bag. If they were to be equally divided among 14 children, there are 10 chocolates left. If they were to be equally divided among 15 children, there are 8 chocolates left. Obviously, this can be satisfied if any multiple of 210 chocolates are added to the bag. What is the remainder when the minimum
feasible number of chocolates in the bag is divided by 9? 


(a) 2 
(b) 5 
(c) 4 
(d) 6 
16 Let f(m,n) =45*m + 36*n, where m and n are integers (positive or negative) What is the minimum positive value for f(m,n) for all values of m,n (this may be achieved for
various values of m and n)? 



(a) 9 
(b) 6 
(c) 5 
(d) 18 
17What is the largest number that will divide 90207, 232585 and 127986 without leaving a remainder?
(a) 257 
(b) 905 
(c) 351 
(d) 498 
18We have an equal arms two pan balance and need to weigh objects with integral weights in the range 1 to 40 kilo grams. We have a set of standard weights and can place the weights in any pan. . (i.e) some weights can be in a pan with objects and some weights can be in the other pan. The minimum number of standard weights required is:
(a) 4 
(b) 10 
(c) 5 
(d) 6 
19A white cube (with six faces) is painted red on two different faces. How many different ways can this be done (two paintings are considered same if on a suitable rotation of the cube one painting can be carried to the other)?
TCS PREPARATORY PAPER 1
(a) 2 (b) 15 (c) 4 (d) 30
20 How many divisors (including 1, but excluding 1000) are there for the number 1000?
(a) 15 (b) 16 (c) 31 (d) 10
21In the polynomial f(x) =2*x^4  49*x^2 +54, what is the product of the roots, and what is the sum of the roots (Note that x^n denotes the x raised to the power n, or x
multiplied by itself n times)? 



(a) 27,0 
(b) 54,2 
(c) 49/2,54 
(d) 49,27 
22In the polynomial f(x) = x^5 + a*x^3 + b*x^4 +c*x + d, all coefficients a, b, c, d are integers. If 3 + sqrt(7) is a root, which of the following must be also a root?(Note that x^n denotes the x raised to the power n, or x multiplied by itself n times. Also sqrt(u) denotes the square root of u, or the number which when multiplied by itself, gives the number u)?

(a) 
(b) 3+sqrt(21) 
(c) 5 
(d) sqrt(7)+sqrt(3) 
23 
If 3*y+x >2 and x+2y <3, what can be said about the value of y? 



(a) y> 
(b) y< 
(c) y= 
(d) y=1 
24 
If m is an odd integer and n an even integer, which of the following is definitely even? 


(a) 
(b) m+n 
(c)(m+n^2)+(mn^2) 
(d) m^2+mn+n^2 
25 
If the price of an item is increased by 10% and then decreased by 10%, the net effect 


on the price of the item is? 




(a) an increase of 
(b) No change 
(c) a decrease of 1% 
(d) an increase of 

99% 


1% 
26 
What is the sum of all even integers between 99 and 301? 



(a) 20000 
(b) 40400 
(c) 20200 
(d) 40000 
27 
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) 5 
(b) 7 
(c) 4 
(d) 6 
28 
If â€˜nâ€™ is the sum of two consecutive odd integers and less than 100, what is the 


maximum possible value of â€˜nâ€™? 




(a) 96 
(b) 94 
(c) 98 
(d) 99 
29 
If x^2 < (1/100) and x<0, what is the highest range in which x can lie? 


(a) 
(b) 
(c) 
(d) 
30 
There are 4 boxes colored red, yellow, blue and green. 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) 9 
(c) 5 
(d) 6 