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Which of the following statement (s) is ...

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

A

Sum of the reciprocal of all the n harmonic means inserted between a and b is equal to n times the harmonic mean between two given numbers a and b.

B

Sum of the cubes of first n natural number is equal to square of the sum of the first a natural numbers.

C

If `a , A_(1), A_(2), A_(3), ….., A_(2n), b` are in A.P. then `sum _( I =1) ^(2n) A_(l) =n (a+b).`

D

If the first term of the geometric progression `g _(1), g _(2), g _(3), ……, oo` is unity, then the value of the common ratio of the progression such that `(4g _(2)+5g _(3))` is minimum equals `2/5.`

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The correct Answer is:
B, C
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VIKAS GUPTA (BLACK BOOK)-SEQUENCE AND SERIES -EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
  1. If first and (2n-1)^th terms of an AP, GP. and HP. are equal and the...

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

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

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

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

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