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If m is the A.M. of two distinct real nu...

If m is the A.M. of two distinct real numbers `l and n(l, n>1) and G_1, G_2 and G_3`, are three geometric means between `I and n`, then `G_1^4+2G_2^4+G_3^4` equals-

A

`4 lmn^(2)`

B

`4 l^(2)m^(2)n^(2)`

C

`4 l^(2)mn`

D

`4 lm^(2)n`

Text Solution

Verified by Experts

The correct Answer is:
D
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ALLEN-SEQUENCE AND PROGRESSION-Exercise (JM)
  1. If m is the A.M. of two distinct real numbers l and n(l, n>1) and G1, ...

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  2. If the 2nd , 5th and 9th terms of a non-constant A.P. are in G.P...

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  3. If the sum of the first ten terms of the series (1 3/5)^2+(2 2/5)^2+(3...

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  4. If, for a positive integer n , the quadratic equation, x(x+1)+(x-1)(x+...

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  5. For any three positive real numbers a, b and c, 9(25a^2+b^2)+25(c^2-3a...

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  6. Let a, b, c in R. If f (x) = ax^(2) + bx + c is such that a + b + c = ...

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  7. Let a(1), a(2), a(3).... A(49) be in A.P. such that sum(k =0)^(12) a(4...

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  8. Let A be the sum of the first 20 terms and B be the sum of the first 4...

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  9. If a, b and c be three distinct real number in G.P. and a + b + c = xb...

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  10. Let a(1), a(2) ......, a(30) be an A.P., S = sum(i=1)^(30) a(i) and T...

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  11. Find sun of first 15 term of series 1+6+(9(1^2+2^2+3^2))/(7)+(12(1^2+...

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  12. If x and y are positive real numbers and m, n are any positive integ...

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  13. If sin^4 alpha + 4 cos^4 beta + 2 = 4sqrt2 sin alpha cos beta ; alpha,...

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  14. The sum of all natural number 'n' such that 100 lt n lt 200 and H.C.F....

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  15. If a ,b ,a n dc are in G.P., then the equations a x^2+2b x+c=0a n ddx^...

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  16. Let the sum of the first n terms of a non-constant A.P., a(1), a(2), a...

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  17. The sum (3 xx 1^(3))/(1^(2)) + (5 xx (1^(3) + 2^(3)))/(1^(2) + 2^(2)) ...

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  18. Let numbers a(1),a(2)…a(16) are in AP and a(1)+a(4)+a(7)+a(10)+a(13)+a...

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  19. Let a,b and c be in G.P. with common ratio r, where a != 0 and 0 lt r ...

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  20. If alpha and beta are the roots of the equation 375 x^(2) - 25x - 2 = ...

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