1. The number of factors of 1800 that are multiple of 6 is ________
18
2. The number of real solutions of the equation \( (x^2 – 15x + 55)^{x^2 – 5x + 6} = 1 \) is______ .
81
3. The following table shows the number of employees and their median age in eight companies located in a district.
| Company | Number of Employees | Median Age |
|---|---|---|
| A | 32 | 24 |
| B | 28 | 30 |
| C | 43 | 39 |
| D | 39 | 45 |
| E | 35 | 49 |
| F | 29 | 54 |
| G | 23 | 59 |
| H | 16 | 63 |
It is known that the age of all employees are integers. It is known that the age of every employee in A is strictly less than the age of every employee in B, the age of every employee in B is strictly less than the age of every employee in C. The age of every employee in G is strictly less than the age of every employee in H.
The highest possible age of an employee of company A is ______
81
4. In a group of 150 students, 52 like tea, 48 like juice and 62 like coffee. If each student in the group likes at least one among tea, juice and coffee, then the maximum number of students that like more than one drink is _____ .
12
5. Let ABC be a triangle right-angled at B with AB = BC = 18. The area of largest rectangle that can be inscribed in this triangle and has B as one of the vertices is ______
81
6. A fruit seller has oranges, apples and bananas in the ratio 3:6:7. If the number of oranges is a multiple of both 5 and 6, then the minimum number of fruits the seller has is ______
81