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If a is the A.M. of ba n dc and the two ...

If `a` is the A.M. of `ba n dc` and the two geometric mean are `G_1a n dG_2,` then prove that `G1 3+G2 3=2a b cdot`

A

1

B

2

C

3

D

4

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If G is the geometric mean of x and y then prove that (1)/(G^(2)-x^(2))+(1)/(G^(2)-y^(2))=(1)/(G^(2))

If the ratio of A.M. and G.M. of two positive numbers a and b is m : n, then prove that : a:b=(m+sqrt(m^(2)-n^(2))):(m-sqrt(m^(2)-n^(2)))

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ML KHANNA-PROGRESSIONS -PROBLEM SET - 5 (MULTIPLE CHOICE QUESTIONS)
  1. If A is the arithmetic mean and p and q be two geometric means between...

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

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

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

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

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

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

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

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

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

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  13. If 2(y-a) is the harmonic mean between y-x and y-z then x-a, y—a and z...

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  14. IF a(1),a(2),a(3),"...."a(10) be in AP and h(1),h(2),h(3),"...."h(10) ...

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  15. If a(1), a(2), a(3) and h(1), h(2), h(3) are the A.M.'s and H.M.'s bet...

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  16. If H(1), H(2),…., H(n) be n harmonic means between a and b then (H(1) ...

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  17. If n is a root of the equation (1 - ab) x^(2) - (a^(2) + b^(2)) x - (1...

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  18. If (1)/(b+c) , (1)/(c+a) and (1)/(a+b) are in AP, then a^(2), b^(2) an...

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  19. If three numbers are in G.P., then the numbers obtained by adding the ...

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  20. If three numbers are in H.P., then the numbers obtained by subtracting...

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