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# Placement Questions & Answers :: TCS

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Not Attempted

241. In 4 years, Raj's father age twice as raj, Two years ago, Raj's mother's age twice as raj. If Raj is 32yrs old in eight yrs from now, what is the age of Raj's mother and father?

Explanation:

Raj present age = 32 - 8 = 24.
After 4 years Raj's age is 28. and Raj's fathers age is 28 x 2 = 56, and his present age is 52.
Two years ago, Raj's age is 22. and his mother's age is 22 x 2 = 44. His mother's present age = 46

Tags: TCS

Not Attempted

242. The sum of two numbers is 45. Sum of their quotient and reciprocal is 2.05, Find the product of the numbers.

Explanation:

a + b = 45
a/b+b/a = 2.05
=>(a^2+b^2)/ab = 2.05
=>((a+b)^2?2ab)/ab=2.05
=>(a+b)^2 = 2.05ab + 2ab = 4.05ab
=> ab = 45^2 / 4.05 = 500

Tags: TCS

Not Attempted

243. Two vertical ladders length of 6 m and 11 m are kept vertically at a distance of 12 m. Find the top distance of both ladders?

Explanation:

So distance between the top points = AD = sqrt(12^2+5^2) = 13

Tags: TCS

Not Attempted

244.

Here are 15 dots. If you select 3 dots randomly, what is the probability that 3 dots make a triangle?

Explanation:

total possibilities=4c3=455

now we have to find the number of dots that do not make a triangle;

3 dots from each row are collinear.So they will not form a triangle.thus total dots from each row possible=3*5c3=30

Each column is collinear.So 5 straight lines formed.

now consider the dots [ { (1,1),(2,2),(3,3)} , {(1,2),(2,3),(3,4)} ,{ (1,3),(2,4).(3,5)}  ] each set here does not make a triangle as they are collinear.Same goes for other three points {(1,3),(2,2),(3,1)} {(1,4),(2,3),(3,2)},{(1,5),(2,4),(3,3)}.So 3+3=6 straight lines that does not make a triangle.Also each dots from diagonals are collinear and thus does not make a triangle.So again 2 straight lines formed.

So total dots that does not make a triangle are=30+5+6+2=43

So no of triangles formed are=455-43=412

probability=412/455

Tags: TCS

Not Attempted

245. In a series of numbers , the next number is formed by adding 1 to the sum of the previous numbers, and the 10th number is 1280. Then what is the first number in the series? (series will be like this x , x+1, (x+(x+1))+1,....... )

Explanation:

The given series is x, x + 1, 2x + 2, 4x + 4 ......
If you observe the pattern here, the coefficient of x + 1 is in the powers of 2. So 4th term has a power of 2, 5th term has a power of 3... 10th term has a power of 8. So tenth term would be 2^8(x + 1)
= 256(x+1).
Given 256(x+1) = 1280
x = 4.

Tags: TCS

Not Attempted

246. The number of multiples of 10 which are less than 1000, which can be written as a sum of four consecutive integers is

Explanation:

We can write 10 = 1 + 2 + 3 + 4. So we have to find how many multiples of 10 can be written in this manner.
Let the first of the four numbers be n. So
n + (n+1) + (n+2) + (n+3) = 10k
4n + 6 = 10k
2n + 3 = 5k
n = (5k-3)/2
=2k-1+(k-1)/2
So n is integer for k = an odd number. So for k = 1, 3, 5, .... 99 we can write a number as a sum of four consecutive intezers.
So there are 50 numbers.

Tags: TCS

Not Attempted

247. Mr. Bean chooses a number and he keeps on doubling the number followed by subtracting one from it, if he chooses 3 as initial number and he repeats the operation for 30 times then what is the final result?

Explanation:

Step 1: (3 * 2) - 1 = 5 ( 2^2 + 1)

Step 2: (5 * 2) - 1 = 9 (2^3 + 1)

Step 3: (9 * 2) - 1 = 17 (2^4 + 1)

Step 4: (17 * 2) - 1 = 33 (2^5 + 1)

So After 30 steps we have 2^31 + 1

Tags: TCS

Not Attempted

248. Tony alone can paint a wall in 7 days and his friend Roy alone can paint the same wall in 9 days. In how many days they can paint the wall working together? Round off the answer to the nearest integer.

Explanation:

use formula (xy / x+y)
So nearest value for 3.93 = 4

Tags: TCS

Not Attempted

249. In this question, A^B means A raised to the power B. Let f(X)=1+X+X^2+....X^6. The remainder when f(X^7) is divided by f(X) is

Explanation:

f(x)=1+x+x^2+x^3+.........+x^6
When we, put x = 0 in the given functions, then we will have remainder as 1.
f(0) = 1.
1/1 remainder = 0.
For x =1, remainder also will be 0.
But for x >1 (x = 2,3,4.......)
Remainder would be 7.

You can find remainder for x > 1 through this formula,
f(x) = 1+x+x^2+.....+x^(n).
for x > 1,
then the remainder when f(x^(n+1)) is divided by f(x) is (n+1).
n = maximum power of the f(x).

Tags: TCS

Not Attempted

250. A number is divided by 406 leaves remainder 115 , What will be the reminder when it will be divided by 29?