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If p,q ,r are in G . P, and the equation...

If `p,q ,r` are in `G . P`, and the equations, `p x^2+2 q x+r=0` and `d x^2+2 e x+f=0` have a common root, then show that `d/p, e/q, f/r` are in `A . P`

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V PUBLICATION-SEQUENCES AND SERIES-QUESTIONBANK
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  2. If a, b, c, d and p are different real numbers such that (a^2+b^2+c^2)...

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  3. If p,q ,r are in G . P, and the equations, p x^2+2 q x+r=0 and d x^2+2...

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  4. Show that the sum of (m+n)^(th) and (m-n)^(th) terms of an A . P is eq...

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  5. If the sum of three numbers in an. A.P. is 24 and their product is 440...

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  6. If S1,S2 and S3 are respectively the sums of n, 2n and 3n terms of an ...

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  7. Find the sum of multiple of 7 between 200 and 400.

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  8. Find the sum of integers from 1 to 100 that are divisible-by 2 or 5 .

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  9. Find the sum of all two digit numbers which when divided by 4, yields ...

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  10. If f is a function satisfying f(x+y)=f(x) . f(y) 'for all x, y in N su...

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  11. The sum of some terms of G.P.is 315 . whose first term and the common ...

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  12. The first term of a G.P is 1. The sum of the third and fifth terms is ...

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  13. The sum of three numbers in G.P is 56 : If we subtract 1,7,21 from the...

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  14. A G.P consists of an even number of terms. If the sum of all the term...

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  15. The sum of the first four terms of an A.Pis 56. The sum of the last fo...

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  16. If (a+b x)/(a-b x)=(b+c x)/(b-c x)=(c+d x)/(c-d x)(x ne 0), then show ...

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  17. Let S be the sum, P, the product and R the sum of reciprocals of n ter...

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  18. The p^ (th) , q^ (th) and r^ (th) terms of an A.P. are a, b, c respe...

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  19. If a (1/b+1/c), b(1/c+1/a), c(1/a+1/b) are in A.P. Prove that a, b, c ...

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  20. If a, b, c, d are in G.P. Prove that (a^n+b^n),(b^n+c^n),(c^n+d^n) are...

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