Home
Class 12
MATHS
If two different numbers are taken from ...

If two different numbers are taken from the set {0, 1, 2, 3, …, 10}, then the probability that their sum as well as absolute difference are both multiples of 4, is

A

`(6)/(55)`

B

`(12)/(55)`

C

`(14)/(45)`

D

`(7)/(55)`

Text Solution

Verified by Experts

The correct Answer is:
A
Total number of ways of selecting 2 different numbers from {0,1,2,…..10}=`^(11)C_2=55`
Let two numbers selected be x and y
Then, `x + y = 4m " " …(i)`
and `x - y =4n " "…(ii)`
`rArr 2x=4(m+n) and 2y=4(m+n)`
`rArr x=2(m+n) and y=2(m-n)`
`therefore` x and y both even numbers

`therefore " Required probility "=6/(55)`
Promotional Banner

Similar Questions

Explore conceptually related problems

If two different numbers are taken from the set {0,1,2,3, ,10}; then the probability that their sum as well absolute difference are both multiple of 4, is: (14)/(45) (2) 7/(55) (3) 6/(55) (4) (12)/(55)

Two different numbers are taken from the set {0,1,2,3,4,5,6,7,8,9,10}dot The probability that their sum and positive difference are both multiple of 4 is x//55 , then x equals ____.

A number is selected from the set {2,3,…,30}. The probability that the selected number is a prime number is

A number is selected from the set {1, 2, 3,.., 20} . The probability That the selected number is divisible by 3 or 4 is

A two digit number is to be formed from the digits 0,1,2,3,4. Repetition of the digit is allowed . Find the probability that the number so formed is a - multiple of 4

A number is selected from the set {1,2,3, . . .20}. The probability that the selected number is divisible by 3 or 4 is . . .

A two digit number is to be formed from the digits 0,1,2,3,4. Repetition of the digit is allowed . Find the probability that the number so formed is a - multiple of 11.