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Q.

Let ƒ(x)  be a function defined by ƒ(x)=(aba22)x0x(cos4t+sin2t2)dt.  If ƒ(x)  is a decreasing function for all  xR and for all aR , where a is independent of x, then b belongs to

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a

(,3)

b

(3,)

c

(3,3)

d

(2,3)(3,2)

answer is C.

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Detailed Solution

ƒ'(x)<0,xR ab-a2-2-cos4x+sin2x-2<0 ab-a2-2-cos4x+1-cos2x+2<0 ab-a2-34-cos2x-122<0 aba234<0 a2-ab+34>0 b23<0(Δ<0)

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