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If a,b,c are in 3 distinct numbers in H....

If a,b,c are in 3 distinct numbers in H.P. `a,b,c gt 0,` then :

A

`(b+c-a)/(a ) , (a +b-c)/(b ), (a +b-c)/(c )` are in AP

B

`(b+c)/(a), (c+a)/(b ), (a +b)/(c )` ar in A.P.

C

`a ^(5) +c ^(5) ge 2b^(5)`

D

`(a-b)/(b-c) =a/c`

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The correct Answer is:
A, B, C, D
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VK JAISWAL ENGLISH-SEQUENCE AND SERIES -EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
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  2. If a, b, c are distinct positive real numbers such that the quadratic ...

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  3. If a,b,c are in H.P, where a gt c gt 0, then :

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  4. In an A.P. let T(r) denote r ^(th) term from beginning, T(p) - (1)/(q ...

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  5. Which of the following statement (s) is (are) correct ?

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  6. If a,b,c are in 3 distinct numbers in H.P. a,b,c gt 0, then :

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  7. All roots of equation x ^(5) -40 x ^(4) + alphax ^(3) + beta x ^(2) + ...

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  8. Let a (1), a(2), a(3)……. be a sequence of non-zero rela numbers with a...

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  9. Given a,b,c are in A.P. b,c,d are in G.P. and c,d,e are in H.P. if a =...

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  10. The numbers a,b,c are in A.P. and a+b+c=60. The numbers (a-2), b, (c+3...

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  11. If (x ^(2) +x+1) + (x^(2) + 2x +3) + (x^(2) + 3x +5) + ….. + (x ^(2) +...

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  12. For Delta ABC, if 81 + 144 a ^(4) + 16b ^(4) + 9c ^(4) =144 abc, (whe...

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  13. Let x,y,z in (0, (pi)/(2)) are first three consecutive terms of an ari...

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  14. If the number 16, 20, 16, d form a A.G.P. then d can be equal to :

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  15. Given then which of the following true

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  16. If S(r) = sqrt(r+sqrt(r+sqrt(r+sqrt(r+.....oo)))),r gt 0, then which o...

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  17. Consider the A.P. 50,48,46,44 ……. If S (n) denotes the sum to n terms ...

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  18. Sum of the n terms of the series (3)/(1^(2))+(5)/(1^(2)+2^(2))+(7)/(1^...

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  19. For Delta ABC, if 81 + 144 a ^(4) + 16b ^(4) + 9c ^(4) =144 abc, (whe...

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