1. Draw the mean proportional between two line segments of lengths 4 cm and 3 cm.

2. If the product of three consecutive positive geometric numbers is 64, then the mean proportional between the first and the third is ______.

3. What is the mean proportional between 3 and 27?

(a) 9 (b) 10 (c) 11 (d) 12

4. If \(x\) is the mean proportional between \((x + 2)\) and \((x - 3)\), then the value of \(x\) is ___.

5. Determine the mean proportional between 4 cm and 3 cm using the geometric method. (In each step, only drawing markings should be shown).

6. If \(x\) is the mean proportional between \((x+2)\) and \((x-3)\), what is the value of \(x\)?

7. Using the geometric method, construct the mean proportional between 4 cm and 3 cm. (Only construction steps are to be shown.)

8. Determine the mean proportional between the positive numbers 5 and 80.

9. Determine the mean proportional between the positive numbers 8.1 and 2.5.

10. Determine the mean proportional between the positive numbers \(x^3y\) and \(xy^3\).

11. Determine the mean proportional between the positive numbers \((x - y)^2\) and \((x + y)^2\).

12. If \(x\) is the mean proportional between \((x + 2)\) and \((x - 3)\), then the value of \(x\) is ________.

13. A semicircle is drawn with AB as the diameter. From any point C on AB, a perpendicular is drawn to AB, which intersects the semicircle at point D. Prove that CD is the mean proportional between AC and CB.

14. Draw the mean proportional between straight line segments of lengths 9 cm and 5 cm, and determine the value of the mean proportional using a scale.

15. Draw the mean proportional between straight line segments of lengths 12 cm and 3 cm, and determine the value of the mean proportional using a scale.