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 lim_(x→0)[(a^x+b^x)/2]^(2/x)]=6

March 30, 2022

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Maths Problems

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 $\lim _{x\rightarrow 0}\left[ \dfrac{a^{x}+b^{x}}{2}\right] ^{\dfrac{2}{x}}=6$

(A) 1/3

(B) 1/4

(D) 2/9

Answer : option (C)

Solution :

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 lim_(x→0)[(a^x+b^x)/2]^(2/x)]=6