KVPY SX SB Exam 2016 Question Paper

If P(x) be a polynomial with real coefficients such that $\mathit{P}\left({\sin }^2\mathit{x}\right)=\mathit{P}({\cos }^2\mathit{x}$), for all x ∈ [0, π/2]. Consider the following statements :
I. P(x) is an even function.
II. P(x) can be expressed as a polynomial in ${\left(2\mathit{x}-1\right)}^2$
III. P(x) is a polynomial of even degree
Then.