TCS new Placement Paper 2014 (14)

This new set of placement paper is collected from on-campus recruitment for the session (2013-14).

1.There are 18 horses in a race. The winning probability of  the 1st horse is 1/6, 2nd=1/6 and 3rd is 1/7.There is no possibility of tie.Find the chances that one of these will win the race?

Ans. 85/252

Explanation: Losing probability of 1st horse = 1 - 1/6 =5/6
Losing probability of 2nd horse = 1 - 1/6 = 5/6
Losing probability of 3rd horse = 1-1/7=6/7
   
The probability that any one horse out of three will win = (1/6*5/6*6/7)+(5/6*1/6*6/7)+(5/6*5/6*1/7)=85/252

*In the above case we only consider the probability of three horses as they are mentioned. 


2.  There are 10 points in a straight line AB and 8 points in another line AC. How many triangle can be formed joining this line ?

Ans. ¹⁰C₂ *8 + ⁸C₂*10

Explanation: First we have to select two points  from AB and join  it with 1 point  in AC. We can do this  ¹⁰C₂ * 8 ways .Now, we have to select two points  from AC and join it with 1 point  in AB. We can do this in ⁸C₂*10 ways. Add the total you will get the answer.

3. Five different color balls are in straight line. Find the probability that 1st ball is RED and 2nd ball is YELLOW ?

Ans. 3!/5!

Explanation: Total no possible outcome = 5!
Total no of favorable outcome = 3! (as RED and YELLOW will be fixed at 1st and 2nd position, so rest 3 will only change position)

4. A closed cylindrical tank  contains 36 pie cubic feet of water and it’s filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of water in the tank is 4 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?

Ans. 3

Explanation: When the tank is placed on its side, it would still be half filled and the height of the water would equal half the diameter, which is radius.
 r² * 4 = 36 , Therefore r = 3.

5. 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 are mixed to obtain a new mixture in vessel C containing half milk and half water? 

Ans. 7:5

Explanation:Let x quantity of mixture from A will be added to C
Milk in vessels A=4/7. Water in  vessel A=3/7
Let y quantity of mixture from B be added to C
Milk in vessel B=2/5. Water in vessel B=3/5
Therefore,(4x/7+2y/5)/(3x/7+3y/5)=1
x:y=7:5

6. Summation from i=0 to 6409 of ai = ?
where ai= 29(if ai is divided by 13 & 17)
ai= 17(if ai is divided by 13 & 29)
ai= 13(if ai is divided by 17 & 29)
ai=0 (else)

Ans. 1299

Explanation:Case 1: if ai is divided by 13 & 17 then. Now 13*17 = 221
221(1,2,3,.............,29)
Therefore, we get total 29 numbers that are divisible by 13 &17 . So,29*29=841
Case 2: if ai is divided by 13 & 17 then. Now 13* 29 =327
377(1,2,3,..............,17)
Therefore, we get total 17 numbers that are divisible by 13 & 29 . So,17*17=289 
Case 3: if ai is divided by 17 & 29 then. Now 17* 29 = 493
493(1,2,3,..............,13)
Therefore, we get total 13 numbers that are divisible by 17 & 29 . So,13*13=169 Therefore , total sum=841+289+169=1299

7. If m+n is divided by 12 then the remainder is 8. If m-n is divided by 12 then the remainder is 6. Find out the remainder when m*n is divided by 6?

Ans. 1

Explanation: m+n is divided by 12 gives remainder 8. We can write 12x+8 = m + n ----(1)
m-n is divided by 12 gives remainder 6. We can write 12y+6 = m - n ------(2)
Now Solving equation (1) and (2) ,we get m=6(x-y)+1 and n=6(x+y)+7
Now,m*n will give u (36(x+y)(x-y))+42(x-y)+6(x+y) +7).  Except 7 ,we will able to divide it by 6.
Now 7 divide by 6 will give remainder 1. So, the answer will be 1.

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