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Question

Let f(x)=1+eln(lnx)ln(k2+25) and g(x)=1|x|1. If limx1+(f(x))g(x)=k(2sin2α+3cosβ+5) for k>0 and α,βR, then which of the following is (are) CORRECT?

A
The value of k is equal to 5
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B
The value of sin10α+cos5βsin2α+cosβ is equal to 1
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C
cos2β+sin4α=2
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D
sin2α>cosβ
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