1. A solid vertical cylindrical cone has both its diameter and height equal to 21 cm. Find the volume of the largest possible sphere that can be obtained from this cone. Also, determine the ratio of the volumes of the cone and the sphere.

2. y is equal to the sum of two variables—one that varies directly with x and another that varies inversely with x. When x = y, then y = –1, and when x = 3, then y = 5. Determine the relationship between x and y.

3. When Mr. Subir retired from his job, he received a lump sum of ₹6,00,000 from his Provident Fund and Gratuity. He wants to divide this amount between the post office and the bank in such a way that he earns ₹34,000 annually as interest. If the annual simple interest rates of the post office and the bank are 6% and 5% respectively, determine how much money he should deposit in each.

4. When a spherical gas balloon is inflated and its radius increases from 7 cm to 21 cm, determine the ratio of its surface areas before and after inflation.

5. If the rationalizing factor of \(\sqrt{5}\) is \(\sqrt{x}\), then calculate and write the smallest possible value of \(x\), where \(x\) is a whole number.

6. \25 farmers of a cooperative society cultivate 2400 bighas of land in 36 days. After the society buys a tractor, it is found that half of the land can be cultivated in 30 days. Using the concept of ratio (ভেদতত্ত্ব), determine the equivalent farming capacity of one tractor in terms of number of farmers.