Is a racemic mixture optically active, if yes,why?

no, a racemic mixture is not optically active as it has 50 - 50 per cent of both the d and l form of enantiomers , as they rotate the plane of polarised light in opposite direction so the effect caused by these two type of enentiomers cancel out each other and the mixture becomes optically inactive.

YES,   Recimic mixture have same physical  properties. melting point ,boilind point,density.but they have same specific notation,but they opposite sings. that's why recimic mixture optically active.