If f (x)= [{:((sin [x^(2)]pi)/(x ^(2)-3x...

If `f (x)= [{:((sin [x^(2)]pi)/(x ^(2)-3x+8)+ax ^(3)+b,,, 0 le x le 1),( 2 cos pix + tan ^(-1)x ,,, 1 lt x le 2):}` is differentiable in `[0,2]` then: ([.] denotes greatest integer function)

A

`a = (1)/(6), b = (pi)/(4) - (13)/(6)`

B

`a =-(1)/(6), b = (pi)/(4)`

C

`a=-(1)/(6), b = (pi)/(4) - (13)/(6)`

D

None of these

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The correct Answer is:

A

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