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# Placement Questions & Answers :: TCS

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Not Attempted

241. 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

242. 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

243.

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

244. 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

245. 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

246. 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

247. 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

248. 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

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

Explanation:

Let the number be N.
So N = 406x + 115.
Now divide this number by 29. As 406 is exactly divisible by 29, we have to divide 115 by 29 and find the remainder. So remainder = 28

Tags: TCS

Not Attempted

250. (p/q-q/p)=21/10. Then find 4p/q+4q/p?

Explanation:

let us take p/q=x and q/p=1/x
x-1/x=21/10
then by solving we get a quadratic equation like 10x^2-10-21x=0
10x^2-25x+4x-10=0
then by taking factors we get two values for x,x=-2/5 and x=5/2
by substituting x=5/2
4(5/2)+4(2/5)=58/5