JEE (Main) Mathematics - Relation between A.M. and G.M. MCQs (31-45)

1. 31. If the arithmetic mean (A.M.) and geometric mean (G.M.) of two positive numbers \( a \) and \( b \) are 6 and 4, respectively, what is the value of \( a \) and \( b \)?

   • a) 4 and 4
   • b) 5 and 5
   • c) 3 and 9
   • d) 2 and 8

   Answer: c) 3 and 9

2. 32. The relation between A.M. and G.M. for two positive numbers \( a \) and \( b \) is:

   • a) \( A.M. = G.M. \)
   • b) \( A.M. \geq G.M. \)
   • c) \( A.M. \leq G.M. \)
   • d) \( A.M. = 2G.M. \)

   Answer: b) \( A.M. \geq G.M. \)

3. 33. For two numbers \( a \) and \( b \), if \( A.M. = 8 \) and \( G.M. = 6 \), then the product \( ab \) is:

   • a) 36
   • b) 48
   • c) 64
   • d) 72

   Answer: a) 36

4. 34. If the arithmetic mean (A.M.) of two positive numbers is 10 and the geometric mean (G.M.) is 6, then the sum of the numbers is:

   • a) 16
   • b) 18
   • c) 20
   • d) 24

   Answer: c) 20

5. 35. Which of the following statements is correct regarding the relationship between A.M. and G.M.?

   • a) A.M. is always less than G.M.
   • b) A.M. is always greater than or equal to G.M.
   • c) A.M. is always equal to G.M.
   • d) A.M. and G.M. have no relation.

   Answer: b) A.M. is always greater than or equal to G.M.

6. 36. For two numbers \( a \) and \( b \), if \( A.M. = \frac{a+b}{2} \) and \( G.M. = \sqrt{ab} \), then the inequality between them is:

   • a) \( A.M. > G.M. \)
   • b) \( A.M. = G.M. \)
   • c) \( A.M. < G.M. \)
   • d) None of the above

   Answer: a) \( A.M. > G.M. \)

7. 37. If the arithmetic mean (A.M.) of two numbers \( a \) and \( b \) is 10, and the geometric mean (G.M.) is 8, then the sum of their squares is:

   • a) 128
   • b) 100
   • c) 96
   • d) 64

   Answer: b) 100

8. 38. For two positive numbers \( a \) and \( b \), if the A.M. is twice the G.M., what is the value of \( \frac{a}{b} \)?

   • a) 1
   • b) 2
   • c) 3
   • d) 4

   Answer: b) 2

9. 39. For two numbers \( a \) and \( b \), if \( A.M. = 12 \) and \( G.M. = 9 \), the difference between the numbers is:

   • a) 4
   • b) 6
   • c) 8
   • d) 10

   Answer: b) 6

10. 40. If \( A.M. \) and \( G.M. \) of two numbers are \( 15 \) and \( 10 \), respectively, then the two numbers are:

    • a) 10 and 20
    • b) 5 and 25
    • c) 8 and 22
    • d) 12 and 18

    Answer: d) 12 and 18

11. 41. The difference between the arithmetic mean and the geometric mean of two positive numbers is always:

    • a) Zero
    • b) A positive number
    • c) A negative number
    • d) Indeterminate

    Answer: b) A positive number

12. 42. If \( A.M. = 20 \) and \( G.M. = 15 \), the product of the two numbers is:

    • a) 225
    • b) 400
    • c) 450
    • d) 500

    Answer: c) 450

13. 43. If the A.M. of two numbers is 16 and their G.M. is 12, the two numbers must be:

    • a) 8 and 24
    • b) 10 and 22
    • c) 12 and 20
    • d) 14 and 18

    Answer: a) 8 and 24

14. 44. For two positive numbers, the arithmetic mean and geometric mean are related by which of the following inequality?

    • a) \( A.M. = G.M. \)
    • b) \( A.M. > G.M. \)
    • c) \( A.M. < G.M. \)
    • d) None of the above

    Answer: b) \( A.M. > G.M. \)

15. 45. If the A.M. of two numbers is 12 and the G.M. is 9, then the two numbers are:

    • a) 10 and 14
    • b) 8 and 16
    • c) 6 and 18
    • d) 9 and 15

    Answer: b) 8 and 16

   l    Next Page >>

Note/Caution: studentsbizz.com does not promise a job or an interview in exchange for money. Fraudsters may ask you to pay under the pretext of a registration fee or refundable fee, but please be aware that legitimate employers will not require such payments.

Join in Our Groups

Home Latest Jobs Syllabus Projects Previous Question Papers Entrance Exam Notifications Multiple Choice Question

@ 2025 Students Bizz Platform. All Rights Reserved.