Once living objects of any age can be dated by carbon-14 method.
[A] True.
[B] False.

Hint: Carbon-14 method is used for the determination of age of materials. It uses the activity radioactive carbon present in the atmosphere and in the dead organism for calculating the age. It is also related to the half-life of the radioisotope which shows that we can use it on species which are a certain years old.

Complete step by step answer:
The Carbon-14 method is a radioactive method that we can use to determine the age of any object that contains organic materials. This process is carried out by a radioactive isotope of carbon, carbon-14. Therefore, this method is called the carbon-14 method or radiocarbon dating.
Now, we will discuss the principle of radiocarbon dating.
The carbon dioxide in our atmosphere is a mixture of $^{12}C{{O}_{2}}$, which is non-radioactive and is in maximum abundance and of $^{14}C{{O}_{2}}$, which is radioactive and it found in trace amounts. This mixture of carbon dioxides react with neutrons, nitrogen $\left( ^{14}{{N}_{7}} \right)$, which is present in the atmosphere and the cosmic rays of sun, ${}_{0}^{1}n$.
Therefore, we can write the reaction that

\[\begin{align}
  & ^{14}{{N}_{7}}+{}_{0}^{1}n\to {}_{6}^{14}{{C}^{*}}+{}_{1}^{1}H \\
 & ^{14}{{C}_{6}}+{{O}_{2}}\to {}^{14}C{{O}_{2}} \\
\end{align}\]

As long as the organism is alive, the ratio of the amount of carbon dioxides in the atmosphere is constant. But when it dies the radioactive carbon present in the organism starts to decay by emitting beta-particles. We can write the reaction as-
\[{}_{6}^{14}C\to {}_{7}^{14}N+{}_{-1}^{0}e+\bar{\nu }\]

The non-radioactive carbon remains intact and therefore, the ratio of the radioactive carbon and the non-radioactive carbon in the dead organism decreases. Thus we can calculate the age of the organism in terms of activity and half-life of the radioactive carbon by using the formula-

\[t=\dfrac{{{t}_{\dfrac{1}{2}}}\times 2.303}{0.693}\log \dfrac{activity\text{ of }{}^{14}C\text{ }of\,living\text{ organism}}{activity\text{ of }{}^{14}C\text{ of the dead organism}}\]

However, we cannot use this method to determine the age of very old rocks and other species due to the short half-life span of carbon. For example, we cannot determine the age of the bones of dinosaurs by this method because the half-life of carbon is only 5,730 years and we can determine only 50,000 years old species with this. For older species we will need an element with higher half-life span.
So, the given statement is incorrect.
So, the correct answer is “Option B”.

Note: In this method we make an assumption which also is a limitation. The assumption is that the intensity of the cosmic ray hence the ratio of non-radioactive carbon to radioactive carbon is constant in the atmosphere for many thousand years.