How to find the units of the rate constant? Consider the reaction $$\ce{2A + B -&gt; Products},$$ when the concentration of $\ce{B}$ alone was doubled, the half-life did not change. When the concentration of $\ce{A}$ alone was doubled, the rate increased by two times. The units of the rate constant is:
a) $\mathrm{s^{-1}}$
b) $\mathrm{L\ mol^{-1}\ s^{-1}}$
c) Unitless
d) $\mathrm{mol\ L^{-1}\ s^{-1}}$

I have tried it solving through this method:
According to me, when the concentration of $\ce{A}$ alone was doubled, reaction rate also increased by two time, implies that reaction is first order according to $\ce{A}$. In same way, the reaction should be 0th order according to $\ce{B}$. So the net order would be 1. So this gives me answer $\mathrm{s^{-1}}$ but the answer is $\mathrm{L\ mol^{-1}\ s^{-1}}$. Where am I going wrong?
You are doing it wrong in situation when concentration of B alone was doubled but half life did not change.

In this situation, the reaction order should be 1 according to B as Half life in first order reaction doesn't depend upon initial concentration of reactants.

$$t_{1/2} = \ln2 / k $$

So the final order will be $2$ and the answer of the question will be b.