Which of the following is a correct pair of masculine and feminine gender?

Duke: Duchess

"Duke" is a title given to a male member of nobility or a high-ranking position, while "Duchess" is the corresponding title for the female counterpart. 

The Feminine Gender of the horse is Mare.

 The feminine form of the noun 'bachelor' is 'bachelorette'.

A cook is a gender-neutral word which explains the person who is a professional in cooking, culinary abilities and know-how in culinary arts.

 The feminine of 'duke' is 'Duchess'.