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If S(r) = sqrt(r+ sqrt(r+sqrt(r+sqrt(......

If `S_(r) = sqrt(r+ sqrt(r+sqrt(r+sqrt(......oo)))) , r gt 0` then which the following is\are correct.

A

`S_(2), S_(6), S_(13), S _(20) ` are in A.P.

B

`S_(4), S_(9), S_(16)` are irrational

C

`(2S_(3)-1) ^(2), (2S_(4)-1)^(2) , (2S_(2)-1)^(2)` are in A.P.

D

`S_(2), S_(12), S_(36)` are in G.P.

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The correct Answer is:
A, B, C, D
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VK JAISWAL-SEQUENCE AND SERIES -EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
  1. If the first and (2n-1)^(th) terms of an A.P, a G.P and an H.P of posi...

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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 number a, b, c in that order form a term A.P and a + b + c = 60. T...

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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(......oo)))) , r gt 0 then which...

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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. Let S(n)be the sum to n terms of the series (2)/(1 ^(2)) + (5)/(1 ^(2)...

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

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