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Question

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 multiple of 4, is:

A
655
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B
1255
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C
1445
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D
755
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Solution

The correct option is A 655
From the given conditions,
x1+x2=4α and x1x2=±4β
Solving the two equations, we get
x1=2(α±β)
i.e, x1 is multiple of 2.
x1x204,826,1040,862,1080,4102,6
​​​​There are total 12 possibilities. Since (x1,x2) and (x2,x1) are same in this case, there is only 6 possibilities.
Hence, required probability =611C2=655

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