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As the given function is not periodic because of x^3 part and also by refering to the link  https://www.desmos.com/calculator/cwpyyqjjmx we do not get any periodicity in the resultant graph.

For Even function F(-x) = F(x)

For Odd function F(-x) = -F(x)

Replacing x with -x in above function we get -(x^3) + x sin(x) which  is neither even nor odd

The above function is  Constant because it does involve constant term when we place the value of x then a constant will be there in the form of x^3 along with x sin(x)

Hence it will be Constant function

So option A is Correct.

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