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The sum of the squares of three distinct...

The sum of the squares of three distinct real
numbers which are in GP is `S^(2)` , if their sum is `alpha S`, then

A

`1ltalpha^(2)lt3`

B

`(1)/(3)ltalpha^(2)lt3`

C

`1ltalphalt3`

D

`(1)/(3)ltalphalt3`

Text Solution

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The correct Answer is:
B
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OBJECTIVE RD SHARMA ENGLISH-SEQUENCES AND SERIES-Exercise
  1. If a, b, c are distinct positive real numbers in G.P and logca, logbc,...

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  2. If lta(n)gtandltb(n)gt be two sequences given by a(n)=(x)^((1)/(2^(n))...

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  3. The sum of the squares of three distinct real numbers which are in G...

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  4. If there be n quantities in G.P., whose common ratio is r and S(m) den...

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  5. The value of sum(r=1)^(n)log((a^(r))/(b^(r-1))), is

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  6. If n arithmetic means are inserted between 2 and 38, then the sum of t...

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  7. An A.P., and a H.P. have the same first and last terms and the same od...

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  8. If a ,b ,a n dc be in G.P. and a+x ,b+x ,and c+x in H.P. then find the...

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  9. The maximum sum of the series 20+19 1/3+18 2/3+ is 310 b. 300 c. 0320 ...

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  10. If 2 (y - a) is the H.M. between y - x and y - z then x-a, y-a...

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  11. If the roots of the equation x^3-12x^2 +39x -28 =0 are in AP, then the...

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  12. If the sum of the first n natural numbers is 1/5 times the sum of the ...

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  13. log3 2, log6 2, log12 2 are in

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  14. The value of 9^(1//3)xx9^(1//9)xx9^(1//27)xx…… to oo is

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  15. The following consecutive terms 1/(1+sqrtx), 1/(1-x), 1/(1-sqrtx) of ...

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  16. The sum of all two digit odd numbers is

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  17. If the sum of the series 2, 5, 8, 11, ... is 60100, then find the valu...

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  18. Given two numbers a and b. Let A denote the single A.M. and S denote t...

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  19. If underset(r=1)overset(n)Sigmar^4=I(n), " then "underset(r=1)overset(...

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  20. 0. 423 is equivalent to the fraction (94)/(99) (b) (49)/(99) (c) ...

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