TCS Placement Paper

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                                                        TCS Placement Paper

An exam was conducted and the following was analyzed. 4 men were able to check some exam papers in 8 days working 5 hours regularly. What is the total number of hours taken by 2 men in 20 days to check double the number of exam papers?

Answer: 8 hours

Solution:

Assuming that 1 unit of work is done in 1 hour
Let’s calculate the total number of working hours:
=> 4 * 8 * 5 = 160 units
Now the work is doubled:
=> 160 * 2 = 320 units
Let ‘x’ be the number of hours taken by 2 men to complete the work in 20 days.
Therefore,
=> 2 * 20 * x = 320
=> x = 8 hours (Answer).

If the alphabets are written in the sequence of a, bb, ccc, dddd, eeeee, ffffff, …. What will be the 120th letter?

Answer: O

Solution:

It can be seen that the letter are in AP sequence, So applying the formula we get,

We find that n = 15 fits the equation
The 15th letter in the English alphabet = O

So 15th term contains O.

There is a tank whose 1/7 th part is filled with fuel. If 22 liters of fuel is poured into the tank, the indicator rises to 1/5 th mark of the tank. So what is the total capacity of the tank?

Answer: 385

Solution:

Let the total capacity of the tank be ‘x’ liters.
According to the question,
=> x/7 + 22 = x/5
=> x/5 – x/7 = 22

=> x = 385 litres(Answer)

There is a fairy island where lives a Knight, a Knave, and a Spy. You go there and meet three people suppose A, B, and C, one of whom is a knight, one a knave, and one a spy. It is known that the knight always tells the truth, the knave always lies, and the spy can either lie or tell the truth.

• A says: “C is a knave.”
• B says: “A is a knight.”
• C says: “I am the spy.”

So who is the knight, who the knave, and who the spy?

Answer: A = Knight, B = Spy, C = Knave

Solution:

Let us say A is the Knight, then he speaks the truth and C is Knave who lied and finally B is Knave, who speaks the truth regarding A. So this condition holds.
Let us say B is the knight. then it contradicts the answer since a knight always speaks the truth and there cannot be two knights.

Same goes with C.

Find the number of perfect squares in the given series 2013, 2020, 2027, ……………., 2300? (Hint 44^2=1936)
a) 2
b) 1
c) 3
d) None of the above

Answer: b) 1

Solution:

We can see that the series is in the form of AP with common difference of 7.
So the series is in the form of 2013 + 7d
The hint is actually a shortcut:
44^2 = 1936
45^2 = 2025
46^2 = 2116
47^2 = 2209
48^2 = 2304
Therefore among these numbers, we need to find which of them are in the form of 2013 + 7d
Only one number 2209 can be written in the form 2013 + 7*28.

Therefore the answer is 1.

In the series of 7^1+7^2+7^3+7^4…….+7^204+7^205, how many numbers are there with the unit place as 3?

Answer: 51

Solution: According to the cyclicity of 7, the unit digit follows the pattern of 7, 9, 3, 1 and this repeats. So in every 4 numbers, we get one 3 in the unit place. Dividing 205 by 4 we get 51 which is the answer to the following question.

Find the number of divisors of 1728(including 1 and the number itself).

Answer: 28

Solution:

There is a direct formula for this:
Number = 
where p, q and r are prime numbers. Simply we need to prime factorize the Number.
Then, (a+1).(b+1).(c+1) is the number of divisors.
For 1728 = 

Therfore, (6+1).(3+1) = 28

 

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