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Question

If (sinα)x22x+b2 for all the real values of x1 and αϵ(0,π/2)(π/2,π), then the possible real values of b lies in

A
(2,4)
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B
(3,4)
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C
(4,5)
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D
(5,8)
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Solution

The correct option is A (3,4)
The minimum value of the quadratic takes place at 1sinα which is less than 1.
Thus, we check at 1 and then it should be valid for all x greater than 1.
Thus, sinα2+b>2
b4sinα
b(3,4)

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