Half-life and rate constant for first order reaction are related by equation,

If decomposition of hydrogen peroxide is a first order reaction, it's rate law equation can be represented as

A reaction is first order with respective to $$\mathrm{A}$$ and second order with respective to $$\mathrm{B}$$. What is the effect on reaction rate if concentration of B is increased 3 times?

For the reaction $$\mathrm{A}+\mathrm{B} \rightarrow$$ product, rate of reaction is $$3.6 \times 10^{-2} \mathrm{mol~dm}^{-3} \mathrm{sec}^{-1}$$. When $$[\mathrm{A}]=0.2 \mathrm{~mol} \mathrm{dm}^{-3}$$ and $$[\mathrm{B}]=0.1 \mathrm{~mol} \mathrm{~dm}^{-3}$$, find rate constant of reaction if it is second order with respective to both reactants.