Which of the following statement(s) is/are TRUE?
I. Highest common factor of $$(3^{2002}-1)$$ and $$(3^{2002}+1)$$ is 4

II. $$(4^{84} - 1)$$ is exactly divisible by 5

$$\left(3^{2002}-1\right)\ gives\ a\ lowest\ factor\ of\ \left(3-1\right)=2.$$

And, $$\left(3^{2002}+1\right)gives\ a\ lowest\ factor\ of\ \left(3+1\right)=4.$$

So, they both have HCF of 2.

So, (I) is not correct.

Now,

$$\frac{4^{84}-1}{5}=\ \frac{\left(4\right)^{84}}{5}-\frac{1}{5}.$$

So, $$\frac{4^{84}}{5}=reminder\ of\ \left(-1\right)^{84}=\ reminder\ of\ 1.$$

So, $$\frac{4^{84}-1}{5}=\ \frac{\left(4\right)^{84}}{5}-\frac{1}{5}$$ , it will give a reminder of (1-1)=0.

So, (II) is correct .

B is correct choice.