A radioactive nucleus can decay by two different process . The half life for first process is $\;t_{1}\;$ and that for second process is $\;t_{2}\;$. Find the effective half life of nucleus

Question

$(a)\;t_{1}+t_{2}\qquad(b)\;t_{1}\qquad(c)\;t_{2}\qquad(d)\;\large\frac{t_{1} t_{2}}{t_{1}+t_{2}}$