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 limx→0[(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 C1/9 Given limit, limx→0(ax+bx2)2x =limx→0(1+ax+bx−22)2ax+bx−2Limx→0(ax−1+bx−1x) =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.