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If (1)/(a)+(1)/(c)+(1)/(a-b)+(1)/(c-b)=0...

If `(1)/(a)+(1)/(c)+(1)/(a-b)+(1)/(c-b)=0`, than prove that `a,b,c` are in HP, unless `b=a+c`.

A

H.P.

B

G.P.

C

A.P.

D

none of these

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The correct Answer is:
A
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OBJECTIVE RD SHARMA ENGLISH-SEQUENCES AND SERIES-Exercise
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  2. If log(x+z)+log(x-2y+z)=2log(x-z)," then "x,y,z are in

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  3. If (1)/(a)+(1)/(c)+(1)/(a-b)+(1)/(c-b)=0, than prove that a,b,c are in...

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  4. If arithmetic mean of two positive numbers is A, their geometric mean ...

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  5. If (1-p)(1+3x+9x^2+27 x^3+81 x^4+243 x^5)=1-p^6,p!=1 , then the value ...

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  6. If a, b, c are in G.P, then loga x, logb x, logc x are in

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  7. If the sum of series 1+(3)/(x)+(9)/(x^(2))+(27)/(x^(3))+ . . .. " to "...

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  8. If H be the H.M. between a and b, then the value of (H)/(a)+(H)/(b) is

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  9. The sum of n terms of two arithmetic progressions are in the ratio 2n+...

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  10. If x = underset(n-0)overset(oo)sum a^(n), y= underset(n =0)overset(oo)...

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  11. Show that X^((1)/(2))*X^((1)/(4))*X^((1)/(8))... Upto oo = X

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  12. If a,b,c be in arithmetic progession, then the value of (a+2b-c) (2b+c...

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  13. If a, b, c are distinct positive real numbers in G.P and logca, logbc,...

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

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

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

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

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

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

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  20. 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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