Para-Jumble Arrange the sentences in a coherent order:
The task is to arrange the given jumbled sentences to form a coherent paragraph. Let's analyze the options one by one to understand the logical sequence:
Based on this logical sequence, the correct order of sentences is A-D-C-B:
This sequence creates a coherent paragraph that introduces a problem (A), explains the persistence of this problem (D), contextualizes it in a dynamic environment (C), and then proposes a solution (B).
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: