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Question

All x satisfying the inequality (cot1x)27(cot1x)+10>0, lie in the interval :

A
(cot5,cot4)
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B
(cot2,)
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C
(,cot5)(cot4,cot2)
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D
(,cot5)(cot2,)
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Solution

The correct option is B (cot2,)
(cot1x)27(cot1x)+10>0(cot1x)25(cot1x)2(cot1x)+10>0(cot1x)[(cot1x)5]2[(cot1x)5]>0(cot1x2)(cot1x5)>0cot1x(,2)(5,) (1)

We know that cot1x(0,π) (2)
So, from (1) and (2)
0<cot1x<2
As, cot1x is decreasing function,
x(cot2,)


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