Among PbS, CuS, HgS, MnS, Ag₂S, NiS, CoS, Bi₂S₃ and SnS₂ the total number of black coloured sulphides is

Consider all possible isomeric ketones including stereoisomers of MW = 100. All these isomers are independently reacted with NaBH₄ (Note : stereoisomers are also reacted separately). The total number of ketones that give a racemic product(s) is/are

Let $${n_1}\, < {n_2}\, < \,{n_3}\, < \,{n_4}\, < {n_5}$$ be positive integers such that $${n_1}\, + {n_2}\, + \,{n_3}\, + \,{n_4}\, + {n_5}$$ = 20. Then the number of such destinct arrangements $$\,({n_1}\,,\,{n_2},\,\,{n_3},\,\,{n_4}\,,{n_5})$$ is

A circle S passes through the point (0, 1) and is orthogonal to the circles $${(x - 1)^2}\, + \,{y^2} = 16\,\,and\,\,{x^2}\, + \,{y^2} = 1$$. Then