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The number of positive integral ordered ...

The number of positive integral ordered pairs of `(a ,b)` such that `6,a ,b` are in harmonic progression is _________.

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The correct Answer is:
7
6,a,b in H.P.
`rArr1/6,1.a,1/b` are in A.P.
`rArr2/a=1/6+1/b`
or `1/b=2/a-1/6`
or `1/b=(12-a)/(6a)`
or `b=(6a)/(12-a)`
`ain{3,4,6,7,9,10,11}`
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CENGAGE ENGLISH-PROGRESSION AND SERIES-EXERCIESE ( NUMERICAL VALUE TYPE )
  1. The terms a1, a2, a3 from an arithmetic sequence whose sum s 18. The t...

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  2. Let the sum of first three terms of G.P. with real terms be 13/12 and ...

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  3. The first term of an arithmetic progression is 1 and the sum of the fi...

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  4. A person drops a ball from an 80 m tall building and each time the bal...

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  5. Metals have conductivity in the order of ohm^(-1) cm^(-1)

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  6. The number of positive integral ordered pairs of (a ,b) such that 6,a ...

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  7. If the roots of 10 x^3-n x^2-54 x-27=0 are in harmonic oprogresi...

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  8. 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=2 ...

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  9. Let Sk be sum of an indinite G.P whose first term is 'K' and commmon r...

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  10. The value of the sum Sigma(i=1)^(20) i(1/i+1/(i+1)+1/(i+2)+.....+1/(2)...

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  11. The difference between the sum of the first k terms of the series 1^3+...

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  12. The vlaue of the Sigma(n=0)^(oo) (2n+3)/(3^n) is equal to .

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  13. The sum of the infinite Arithmetico -Geometric progression3,4,4,… is .

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  14. Sigma(r=1)^(50)(r^2)/(r^2+(11-r)^2) is equal to .

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  15. If Sigma(r=1)^(50) (2)/(r^2+(11-r^2)), then the value of n is

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  16. Let lt an gt be an arithmetic sequence of 99 terms such that sum of it...

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  17. Find the sum of series upto n terms ((2n+1)/(2n-1))+3((2n+1)/(2n-1))^2...

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  18. Let S=Sigma(n=1)^(999) (1)/((sqrt(n)+sqrt(n+1))(4sqrt(n)+4sqrtn+1)) , ...

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  19. Let S denote sum of the series 3/(2^3)+4/(2^4 .3)+5/(2^6 .3)+6/(2^7 .5...

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  20. The sum (7)/(2^2xx5^2)+13/(5^2xx8^2)+19/(8^2xx11^2)+…10 terms is S, th...

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