JEE Main - Insertion of arithmetic and geometric means Online Test (MCQ Quiz)

1. If 3 numbers are in arithmetic progression, their sum is 45. If 1, 4, and 19 are added to them respectively, the new numbers are in geometric progression. Find the numbers.

A) 10, 15, 20 B) 5, 15, 25 C) 15, 15, 15 D) 12, 15, 18

2. Insert 2 arithmetic means between 4 and 16.

A) 8, 12 B) 6, 10 C) 7, 11 D) 8, 10

3. Insert 3 geometric means between 2 and 162.

A) 6, 18, 54 B) 4, 12, 36 C) 6, 12, 24 D) 3, 9, 27

4. If 4 numbers are in geometric progression, their product is 256. If 2, 6, 8, and 50 are added to them respectively, the new numbers are in arithmetic progression. Find the numbers.

A) 1, 2, 4, 8 B) 2, 4, 8, 16 C) 4, 8, 16, 32 D) 1/2, 2, 8, 32

5. Insert 4 arithmetic means between -2 and 18.

A) 2, 6, 10, 14 B) 3, 7, 11, 15 C) 0, 4, 8, 12 D) 1, 5, 9, 13

6. The arithmetic mean of two numbers is 6 and their geometric mean is 4. Find the numbers.

A) 2, 10 B) 4, 8 C) 3, 9 D) 6, 6

7. Insert 2 geometric means between 1/2 and 1/16.

A) 1/4, 1/8 B) 1/3, 1/9 C) 1/5, 1/10 D) 1/6, 1/12

8. If a, b, c are in geometric progression, then which of the following is true?

A) b = (a+c)/2 B) b^2 = ac C) a^2 = bc D) c^2 = ab

9. Insert 5 arithmetic means between 10 and 40.

A) 15, 20, 25, 30, 35 B) 16, 22, 28, 34, 40 C) 10, 15, 20, 25, 30 D) 12, 18, 24, 30, 36

10. If a, b, c are in arithmetic progression, then which of the following is true?

A) b^2 = ac B) b = (a+c)/2 C) a = (b+c)/2 D) c = (a+b)/2

11. Insert 3 geometric means between 3 and 48.

A) 6, 12, 24 B) 3, 6, 12 C) 9, 18, 36 D) 4, 8, 16

12. The product of three numbers in geometric progression is 1000. If 6 and 8 are added to the first and second numbers respectively, then the new numbers are in arithmetic progression. Find the numbers.

A) 2, 10, 50 B) 4, 10, 25 C) 5, 10, 20 D) 10, 10, 10

13. Insert 4 geometric means between 1/3 and 243.

A) 1, 3, 9, 27 B) 3/2, 9/2, 27/2, 81/2 C) 3, 9, 27, 81 D) 1/2, 3/2, 9/2, 27/2

14. If the arithmetic mean of two positive numbers is twice their geometric mean, then the numbers are in the ratio.

A) 2:1 B) 4:1 C) 3:1 D) 1:1

15. Insert 2 arithmetic means between 7 and 25.

A) 13, 19 B) 10, 16 C) 11, 17 D) 12, 18

16. If a, b, c are in geometric progression, then log a, log b, log c are in:

A) Geometric progression B) Arithmetic progression C) Harmonic progression D) None of these

17. Insert 3 geometric means between 1/4 and 16.

A) 1/2, 1, 2 B) 1/4, 1, 4 C) 1/2, 2, 8 D) 1, 2, 4

18. The sum of two numbers is 12 and their geometric mean is 6. Find the numbers.

A) 6, 6 B) 3, 9 C) 4, 8 D) 2, 10

19. Insert 5 geometric means between 2 and 128.

A) 4, 8, 16, 32, 64 B) 2, 4, 8, 16, 32 C) 3, 6, 12, 24, 48 D) 2, 4, 8, 16, 64

20. If a, b, c are in arithmetic progression and b, c, d are in geometric progression, then which of the following is true?

A) b^2 = ac B) c^2 = bd C) a^2 = cd D) d = c^2/b

21. Insert 3 arithmetic means between 1 and 17.

A) 4, 7, 10 B) 5, 9, 13 C) 3, 7, 11 D) 2, 7, 12

22. If the geometric mean of two numbers is 6 and their arithmetic mean is 7.5, find the numbers.

A) 3, 12 B) 5, 10 C) 4, 11 D) 6, 9

23. Insert 4 arithmetic means between 5 and 25.

A) 9, 13, 17, 21 B) 7, 11, 15, 19 C) 6, 10, 14, 18 D) 8, 12, 16, 20

24. If a, b, c are in geometric progression, then log(a), log(b), log(c) are in:

A) Arithmetic progression B) Geometric progression C) Harmonic progression D) None of these

25. Insert 2 geometric means between 5 and 45.

A) 15, 45 B) 10, 30 C) 5 * sqrt(3), 15 * sqrt(3) D) 15, 25

26. The sum of three numbers in geometric progression is 39, and their product is 729. Find the numbers.

A) 3, 9, 27 B) 1, 9, 81 C) 9, 9, 9 D) 3, 13, 39

27. Insert 3 geometric means between 1/8 and 128.

A) 1/2, 2, 8 B) 1/4, 1, 4 C) 1/2, 1, 2 D) 1, 2, 4

28. If a, b, c are in arithmetic progression and a, b, c are also in geometric progression, then:

A) a = b = c B) a = b != c C) a != b = c D) a, b, c are not necessarily equal

29. Insert 4 geometric means between 3 and 96.

A) 6, 12, 24, 48 B) 3, 6, 12, 24 C) 4, 8, 16, 32 D) 3, 9, 27, 81

30. The arithmetic mean of two numbers is 15 and their geometric mean is 9. Find the numbers.

A) 3, 27 B) 5, 25 C) 6, 24 D) 9, 15

31. Insert 2 arithmetic means between 10 and 30.

A) 15, 20 B) 12, 18 C) 14, 16 D) 10, 20

32. If a, b, c are in geometric progression, then a/(b+a) + c/(b+c) is equal to:

A) 2 B) 1 C) b/a D) b/c

33. Insert 3 geometric means between 8 and 1/27.

A) 4, 2, 1 B) 4, 2, 1/2 C) 8/3, 8/9, 8/27 D) 2, 1, 1/2

34. The sum of three numbers in arithmetic progression is 21 and their product is 231. Find the numbers.

A) 3, 7, 11 B) 5, 7, 9 C) 1, 7, 13 D) 7, 7, 7

35. Insert 4 geometric means between 1/2 and 16.

A) 1, 2, 4, 8 B) 1/4, 1/2, 1, 2 C) 1/2, 1, 2, 4 D) 1/2, 1, 2, 4, 8

36. If a, b, c are in geometric progression, then (a+b+c)(a-b+c) is equal to:

A) a^2 + b^2 + c^2 B) a^2 - b^2 + c^2 C) a^2 + b^2 - c^2 D) a^2 - b^2 - c^2

37. Insert 2 arithmetic means between -5 and 13.

A) -1, 7 B) 1, 9 C) 3, 9 D) 0, 6

38. The geometric mean of two numbers is 8. If 6 is added to the first number and 4 is added to the second number, the resulting numbers are equal. Find the numbers.

A) 4, 16 B) 2, 32 C) 8, 8 D) 1, 64

39. Insert 5 arithmetic means between 2 and 20.

A) 5, 8, 11, 14, 17 B) 4, 7, 10, 13, 16 C) 3, 6, 9, 12, 15 D) 6, 9, 12, 15, 18

40. If a, b, c are in arithmetic progression and b, c, d are in geometric progression, then a, c, d^2 are in:

A) Arithmetic progression B) Geometric progression C) Harmonic progression D) None of these

41. Insert 3 geometric means between 1/27 and 27.

A) 1/9, 1, 9 B) 1/3, 1, 3 C) 3, 9, 27 D) 1, 3, 9

42. If the arithmetic mean of two numbers is A and their geometric mean is G, find the numbers.

A) A + sqrt(A^2 - G^2), A - sqrt(A^2 - G^2) B) A + sqrt(G^2 - A^2), A - sqrt(G^2 - A^2) C) G + sqrt(G^2 - A^2), G - sqrt(G^2 - A^2) D) A + sqrt(A^2 + G^2), A - sqrt(A^2 + G^2)

43. Insert 4 arithmetic means between 1 and 16.

A) 4, 7, 10, 13 B) 2, 5, 8, 11 C) 3, 6, 9, 12 D) 5, 8, 11, 14

44. If a, b, c are in geometric progression, then log(a^x), log(b^x), log(c^x) are in:

A) Arithmetic progression B) Geometric progression C) Harmonic progression D) None of these

45. Insert 2 geometric means between 1/4 and 1/64.

A) 1/8, 1/16 B) 1/16, 1/32 C) 1/8, 1/32 D) 1/4, 1/16

46. If the sum of three numbers in geometric progression is 21 and their product is 729, find the numbers.

A) 3, 9, 27 B) 1, 9, 81 C) 9, 9, 9 D) 7, 7, 7

47. Insert 3 arithmetic means between 10 and 26.

A) 14, 18, 22 B) 12, 16, 20 C) 11, 15, 19 D) 13, 17, 21

48. If a, b, c are in arithmetic progression and a, b, c are in geometric progression, then which statement is true?

A) a=b=c B) a=b!=c C) a!=b=c D) a,b,c are distinct

49. Insert 4 geometric means between 1/2 and 128.

A) 1, 2, 4, 8 B) 2, 4, 8, 16 C) 1/2, 1, 2, 4 D) 1, 4, 16, 64

50. If the arithmetic mean of two numbers is 10 and their geometric mean is 8, find the numbers.

A) 4, 16 B) 2, 18 C) 5, 15 D) 6, 14

Insertion of arithmetic and geometric means - Online Test

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