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Let f(x)=([a]^(2)-5[a]+4)x^(3)-(6{a}^(2)...

Let `f(x)=([a]^(2)-5[a]+4)x^(3)-(6{a}^(2)-5{a}+1)x-(tan x) xx sin x` be an even function for all `x in R`. Then the sum of all possible values of a is (where `[.]` and `{.}` denote gretest integer function and fractional part function, respectively )

A

`(17)/(6)`

B

`(53)/(6)`

C

`(31)/(3)`

D

`(35)/(3)`

Text Solution

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The correct Answer is:
D
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