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If the arithmetic means of two positive number a and b `(a gt b )` is twice their geometric mean, then find the ratio a: b

A

`2 + sqrt(3) : 2 - sqrt(3)`

B

`7 + 4 sqrt(3) : 7 - 4 sqrt(3)`

C

`2 : 7 + 4 sqrt(3)`

D

`2 : sqrt(3)`

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The correct Answer is:
A
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ML KHANNA-PROGRESSIONS -PROBLEM SET - 5 (MULTIPLE CHOICE QUESTIONS)
  1. The A.M. of two numbers exceeds their G.M. by 15 and H.M. by 27. The n...

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  2. If the harmonic mean between two positive numbers is to their G.M. as ...

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  3. If the arithmetic means of two positive number a and b (a gt b ) is tw...

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  4. If first and (2n−1)^(th) terms of an A.P., G.P. and H.P. are equal a...

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  5. If a ,a1, a2, a3, a(2n),b are in A.P. and a ,g1,g2,g3, ,g(2n),b . are...

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  6. Given that n arithmetic means are inserted between two sets of numbers...

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  7. If A(1),A(2) are between two numbers, then (A(1)+A(2))/(H(1)+H(2)) is ...

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  8. Two A.M.'s A(1) and A(2), two G.M.'s G(1) and G(2) and two H.M's H(1) ...

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  9. If A is the arithmetic mean and p and q be two geometric means between...

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  10. If one G.M., G and two A.M.\'s p and q be inserted between two given q...

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  11. If a is the A.M. of ba n dc and the two geometric mean are G1a n dG2, ...

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  12. If p, q, r are + ive, then the minimum value of p^(log q - log r) + q^...

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  13. (i) The value of x + y + z is 15. If a, x, y, z, b are in AP while the...

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  14. If a,b,c,d are in H.P., then ab+bc+cd is equal to

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  15. If a(a), a (2), a (3),…., a(n) are in H.P. and f (k)=sum (r =1) ^(n) a...

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  16. If A, G & H are respectively te A.M., G.M. & H.M. of three positive nu...

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  17. In an H.P., T(p) = q (p + q), T(q) = p (p + q), then p and q are the r...

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  18. If four positive numbers a, b, c, d are in H.P. then which one of the ...

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  19. The A.M., G.M. and H.M. between two positive numbers a and b are equal...

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  20. The AM, HM and GM between two numbers are (144)/(15), 15 and 12, but n...

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