“Between the year 1946 and the year 1955, I did not file any income tax returns.” With that [1] statement, Ramesh embarked on an account of his encounter with the income tax department. "I originally owed Rs. 20,000 in unpaid taxes. With [2] and [3], the 20,000 became 60,000. The Income Tax Department then went into action, and I learned first hand just how much power the Tax Department wields. Royalties and trust funds can be [4]; automobiles may be [5], and auctioned off. Nothing belongs to the [6] until the case is settled.”
Consider the following statements: Statement I: \( 5 + 8 = 12 \) or 11 is a prime. Statement II: Sun is a planet or 9 is a prime.
Which of the following is true?
For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which \[ (a_1)^1 \times (a_2)^2 \times \dots \times (a_{20})^{20} \;<\; a_{21} \times a_{22} \times \dots \times a_{20+m} \] is: