Below is a table that lists countries region-wise. Each region-wise list is sorted first by birth rate and then alphabetically by name of country. We now wish to merge the region-wise list into one consolidated list and provide overall rankings to each country based first on birth rate and then on death rate. Thus, if some countries have the same birth rate, then the country with a lower death rate will be ranked higher. Further, countries having identical birth and death rates will get the same rank. For example, if two countries are tied for the third position, then both will be given rank 3, while the next country (in the ordered list) will be ranked 5.
| Rank | Country | Birth Rate | Death Rate | Region |
|---|---|---|---|---|
| 1 | South Africa | 36 | 12 | Africa |
| 2 | Egypt | 39 | 13 | Africa |
| 3 | Cameroon | 42 | 22 | Africa |
| 4 | Mozambique | 45 | 18 | Africa |
| 5 | Zaire | 45 | 18 | Africa |
| 6 | Ghana | 46 | 14 | Africa |
| 7 | Angola | 47 | 23 | Africa |
| 8 | Madagascar | 47 | 22 | Africa |
| 9 | Morocco | 47 | 16 | Africa |
| 10 | Tanzania | 47 | 17 | Africa |
| 11 | Ethiopia | 48 | 23 | Africa |
| 12 | Ivory Coast | 48 | 23 | Africa |
| 13 | Rhodesia | 48 | 14 | Africa |
| 14 | Uganda | 48 | 17 | Africa |
| 15 | Nigeria | 49 | 22 | Africa |
| 16 | Saudi Arabia | 49 | 19 | Africa |
| 17 | Sudan | 49 | 17 | Africa |
| 18 | Algeria | 50 | 16 | Africa |
| 19 | Kenya | 50 | 14 | Africa |
| 20 | Upper Volta | 50 | 28 | Africa |
| Rank | Country | Birth Rate | Death Rate | Region |
|---|---|---|---|---|
| 1 | Germany (FRG) | 10 | 12 | Europe |
| 2 | Austria | 12 | 13 | Europe |
| 3 | Belgium | 12 | 12 | Europe |
| 4 | Germany (DRG) | 12 | 14 | Europe |
| 5 | Sweden | 12 | 11 | Europe |
| 6 | Switzerland | 12 | 9 | Europe |
| 7 | U.K. | 12 | 12 | Europe |
| 8 | Netherlands | 13 | 8 | Europe |
| 9 | France | 14 | 11 | Europe |
| 10 | Italy | 14 | 10 | Europe |
| 11 | Greece | 16 | 9 | Europe |
| 12 | Bulgaria | 17 | 10 | Europe |
| 13 | Hungary | 18 | 12 | Europe |
| 14 | Spain | 18 | 8 | Europe |
| 15 | USSR | 18 | 9 | Europe |
| 16 | Yugoslavia | 18 | 8 | Europe |
| 17 | Czech Rep. | 19 | 11 | Europe |
| 18 | Portugal | 19 | 10 | Europe |
| 19 | Romania | 19 | 10 | Europe |
| 20 | Poland | 20 | 9 | Europe |
| Rank | Country | Birth Rate | Death Rate | Region |
|---|---|---|---|---|
| 1 | Japan | 16 | 6 | Asia |
| 2 | Korea (ROK) | 26 | 6 | Asia |
| 3 | Sri Lanka | 26 | 9 | Asia |
| 4 | Taiwan | 26 | 5 | Asia |
| 5 | Malaysia | 30 | 6 | Asia |
| 6 | China | 31 | 11 | Asia |
| 7 | Thailand | 34 | 10 | Asia |
| 8 | Turkey | 34 | 12 | Asia |
| 9 | India | 36 | 15 | Asia |
| 10 | Burma | 38 | 15 | Asia |
| 11 | Iran | 42 | 12 | Asia |
| 12 | Vietnam | 42 | 17 | Asia |
| 13 | Korea (DPRK) | 43 | 12 | Asia |
| 14 | Pakistan | 44 | 14 | Asia |
| 15 | Nepal | 46 | 20 | Asia |
| 16 | Bangladesh | 47 | 19 | Asia |
| 17 | Syria | 47 | 14 | Asia |
| Rank | Country | Birth Rate | Death Rate | Region |
|---|---|---|---|---|
| 1 | U.S.A. | 15 | 9 | N. America |
| 2 | Canada | 16 | 7 | N. America |
| 3 | Cuba | 20 | 6 | N. America |
| 4 | Mexico | 40 | 7 | N. America |
| 5 | Australia | 16 | 8 | Pacific |
| 6 | Philippines | 34 | 10 | Pacific |
| 7 | Indonesia | 38 | 16 | Pacific |
| 8 | Argentina | 22 | 10 | S. America |
| 9 | Chile | 22 | 7 | S. America |
| 10 | Colombia | 34 | 10 | S. America |
| 11 | Brazil | 36 | 10 | S. America |
| 12 | Venezuela | 36 | 6 | S. America |
| 13 | Guatemala | 40 | 14 | S. America |
| 14 | Peru | 40 | 13 | S. America |
| 15 | Ecuador | 42 | 11 | S. America |
The table provided displays the estimated cost (in lakh) for the construction of a canal between two points. Based on the information in the table, answer the questions that follow.
The following table gives the marks obtained by six students in six different subjects in an examination. The maximum marks for each subject are given in the brackets. Answer the questions that follow.
Consider the provided scenario and answer the following questions based on the given information.


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: