Consider the reaction, 

2A + B → Products 

When concentration of B alone was doubled, the half-life did not change. When the concentration of A alone was doubled, the rate increased by two times. The unit of rate constant for this reaction is

2A+B→Product

When conc. of B is doubled, the half life did not change, hence reaction is of first order w.r.t. B. When concentration of A is doubled, reaction rate is doubled, hence reaction is of first order w.r.t. A. 

Hence over all order of reaction is 1 + 1 = 2

So, unit of rate constant ${\mathrm{mol}}^{-1}{\text{ lit s }}^{-1}\text{. }$

Hence, (1) is correct