In this paper, we study some new selection principles using the star operator which was introduced by Bal and Bhowmik (2017) [7]. If the Alexandroff duplicate A(X) of a space X has the property U1⋆(O,O) (Ufin⋆(O,O)), then X has the property U1⋆(O,O) (Ufin⋆(O,O)). If a space has the property Ufin⋆(O,O), then its inverse image under perfect open map has the property Ufin⋆(O,O). The product of a space having Ufin⋆(O,O) property with σ-compact has the property Ufin⋆(O,O). If for each k, Xk has the property U1⋆(O,O) (Ufin⋆(O,O)), then X has the property U1⋆(O,Owgp) (Ufin⋆(O,Owgp)). If a subspace A of a space X is weakly Menger (weakly Rothberger), then Cl(A) has the property Ufin⋆(O,Ogp) (Ufin⋆(O,Ogp)). The above-mentioned results answer two published open questions of Song and Xuan from [10].