TCS Placement paper 2014 (10)

This set of placement paper is collected from on-campus recruitment for the session (2013-2014). TCS will follow the same pattern and same set of questions for its off-campus recruitment 2014. If you go through all the sets of TCS placement papers posted in interviewtime.in, you will surely get some common questions in your online aptitude Test.

Here are some questions collected form NIT, Jamshedpur

1. How many seven digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6, 7 and 8 , if repetition of digits is not allowed and the second last digit is even?

Ans. 8640

Explanation: Total no of digits =8  (1,2,3,4,5,6.7,8)
No. of even number = 4 (2,4,6,8)
As we have to find the seven digit even numbers. So the numbers must end with even digit. No of ways this can be done is 4.   
Now, the second last digit should also be even.This can be done in 3 ways.
Now we can fill the remaining digit in the numbers with any of the remaining digits from the digit list. No of remaining digit = 6.
Therfore,
Place                         1   2   3  4  5   6   7     
No. of ways               2   3  4  5   6   3   4  
Therefore, total no of 7 digit even number possible = 2*3*4*5*6*3*4=8460


2. What is the probability that a particular selected leap year has 53 sundays?

Ans. 2/7

Explanation: No. of days in a leap year = 366 Days.
366 Days = 52 Weeks and 2 Days
Thus, a Leap Year has 52 Sundays.
The Remaining 2 Days can be :
1. Sunday & Monday
2. Monday & Tuesday
3. Tuesday & Wednesday
4. Wednesday & Thursday
5. Thursday & Friday
6. Friday & Saturday
7. Saturday & Sunday.
Therefore, no of event =7

Favourable Outcomes = 2
Required Probability = 2/7.

3.  Which of the following  value of “n” is the number 2⁷⁴ + 2²⁰⁵⁸ + 2²ⁿ is a perfect square?

Ans. 2020

Explanation: 2⁷⁴+2²⁰⁵⁸+2²ⁿ= (2³⁷)²+ (2ⁿ)²+ 2²⁰⁵⁸
It is in the formula as (a+b)²=a²+b²+2*a*b
Therefore, 2*(2³⁷)*(2ⁿ)=2⁽³⁸⁺ⁿ⁾=2²⁰⁵⁸
38+n=2058
n=2020

4. In a 3 x 3 grid, comprising 9 tiles can be painted in red or blue. When tile is rotated by 180 degrees, there is no difference which can be spotted. How many such possibilities are there?

Ans. 32

Explanation: Let assign number to grids,
1     2     3
4     5     6
7     8     9
We can fill position 5 in 2 ways. 
We can fill position 1 in 2 ways, so position 9 should  be fill 1ways
We can fill position 2 in 2 ways,so position 8 should  be fill 1ways
Similarly, we can fill position 3 in 2 ways,so position 7 should  be fill 1 ways
We can fill position 4 in 2 ways, so position 6 should  be fill 1 ways.
Total no. of possibility = 2⁵=32

7. A tree of height 36 m at the edge of a road broke at certain height and it fell in such a way that its top touched the other edge of the road.If the breadth of the road is 12m, then find the height at which tree broke?

Ans. 16 m

Explanation: By applying Pythagoras theorem
(36-x)² = 12² + x²
1296 + x² - 72x = 144 + x²
72x = 1152
x = 1152/72
x = 16


7.  1(1!)+2(2!)+.............+2012(2012!)=?

Ans. 2013!-1

Explanation: 1(1!) = (2-1)*1!= 2!-1!
2(2)! = (3-1)(2!)=3!-2!
Therefore, the equation = 2!-1!+3!-2!+4!-3!........2013!-2012! = 2013!-1

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