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Question

If a and b are chosen randomly from the set consisting of numbers 1, 2, 3, 4, 5, 6 with replacement. Then the probability that limx0[(ax+bx)/2]2/x=6 is

A
1/3
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B
1/4
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C
1/9
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D
2/9
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Solution

The correct option is C 1/9
Given limit,
limx0(ax+bx2)2x
=limx0(1+ax+bx22)2ax+bx2Limx0(ax1+bx1x)
=elogab=ab=6
Total number of possible ways in a,b can take values is 6X6=36.Total possible ways are (1,6),(6,1),(2,3),(3,2).The total number of possible ways is 4.Hence, the required probability is 4/36=1/9.

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