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If (1)/(b+c) , (1)/(c+a) and (1)/(a+b) a...

If `(1)/(b+c) , (1)/(c+a) and (1)/(a+b)` are in AP, then `a^(2), b^(2) and c^(2)` are in

A

A.P.

B

G.P.

C

H.P.

D

none

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A
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If a,b,c are in A.P.prove that: (i) (1)/(bc),(1)/(ca),(1)/(ab) are in A.P.(ii) (b+c)^(2)-a^(2),(a+c)^(2)-b^(2),(b+a)^(2)-c^(2) are in A.P.

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ML KHANNA-PROGRESSIONS -PROBLEM SET - 5 (MULTIPLE CHOICE QUESTIONS)
  1. If H(1), H(2),…., H(n) be n harmonic means between a and b then (H(1) ...

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  2. If n is a root of the equation (1 - ab) x^(2) - (a^(2) + b^(2)) x - (1...

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  3. If (1)/(b+c) , (1)/(c+a) and (1)/(a+b) are in AP, then a^(2), b^(2) an...

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  4. If three numbers are in G.P., then the numbers obtained by adding the ...

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  5. If three numbers are in H.P., then the numbers obtained by subtracting...

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  6. If a ,b ,c ,d are in G.P., then prove that (a^3+b^3)^(-1),(b^3+c^3)^(-...

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  7. If a, b, c, d be four numbers of which the first three are in AP and t...

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  8. If S(k) denotes the sum of first k terms of a G.P. Then, S(n),S(2n)-S(...

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  9. If x, y, z be in A.P., then x + (1)/(yz), y + (1)/(zx), z + (1)/(xy) a...

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  10. Let the positive numebrs a,b,c,d be in A.P. Then abc,abd,acd,bcd re (A...

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  11. (1)/(b-a)+(1)/(b-c)=(1)/(a)+(1)/(c) then a,b,c are in:

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  12. <b>if a,b, c, d and p are distinct real number such that (a^(2) + b^...

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  13. sum(r = 1)^(10) (r)/(1 - 3r^(2) + r^(4))=

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  14. If 21(a^(2) + b^(2) + c^(2)) = (a + 2b + 4c)^(2) then a, b, c are in

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  15. If 4a^(2)+9b^(2)+16c^(2)=2(3ab+6bc+4ca)," where "a,b,c are non-zero nu...

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  16. alpha, beta, gamma are the geometric means between ca, ab, ab, bc, bc,...

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  17. If (a+b x)/(a-b x)=(b+c x)/(b-c x)=(c+dx)/(c-dx)(x!=0) , then show tha...

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  18. If a^(x) = b^(y) = c^(z) and a, b, c are in G.P. then x, y, z are in

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  19. If a^(x) = b^(y) = c^(z) = d^(u) and a, b, c, d are in G.P. then x, y,...

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  20. If for an exponential function y = a^(x) (a gt 0, ne 1) x(1), x(2),…x(...

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