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Let f(x) be a non-constant twice differe...

Let `f(x)` be a non-constant twice differentiable function defined on `(-oo,oo)` such that `f(x)=f(1-x)a n df^(prime)(1/4)=0.` Then

A

f'' (x) is vanishes atleast twice on [0,1]

B

`f'(1/2)=0`

C

`int_(-1//2)^(1//2) f(x+1/2)sin x dx=0`

D

`int_(0)^(1//2) f(t)e^(sin pit) =int_(1//2)^(1) f(1-t)e^(sin pi t)dt`

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A, B, C, D
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