Home
Class 12
MATHS
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 _________.

Text Solution

Verified by Experts

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}`
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise ARCHIVES ( JEE MAIN )(SINGLE CORRECT ANSWER TYPE )|16 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise ARCHIVES ( JEE ADVANCED )(SINGLE CORRECT ANSWER TYPE )|3 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise EXERCIESE ( MATRIX MATCH TYPE )|3 Videos

  • PROBABILITY II

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

Similar Questions

Explore conceptually related problems

Number of positive integral ordered pairs of (x,y), so that 8,x,y are in H.P. is a. 0 b. 1 c. 2. d. 3

Find the number of positive integral solutions of x y z=21600.

Find the number of positive integral solutions of the equation x+y+z=12.

The number of positive integral solutions of x^4-y^4=3789108 is a. 0 b. 1 c. 2 d. 4

Let the harmonic mean of two positive real numbers a and b be 4. If q is a positive real number such that a,5,q,b is an arithmetic progression , then the value (s) of abs(q - a) is (are)

Find the total number of positive integral solutions for (x ,y ,z) such that x y z=24. Also find out the total number of integral solutions.

Let a ,b be positive real numbers. If a, A_1, A_2, b be are in arithmetic progression a ,G_1, G_2, b are in geometric progression, and a ,H_1, H_2, b are in harmonic progression, show that (G_1G_2)/(H_1H_2)=(A_1+A_2)/(H_1+H_2)

Let a ,b , c be positive integers such that (b)/(a) is an integer . If a , b , c are in geometric progression and the arithmetic mean of a , b , c , is b + 2 , then value of (a^(2)+a-14)/(a+1)

Let a, b , c be positive integers such that b/a is an integer. if a, b , c are in geometric progression and the arithmetic mean of a , b , c is b + 2, then the value of (a^2 + a -14)/(a + 1) is

Number of ordered pairs (s) , (a,b) of real numbers such that (a+ib)^(2008)=a-ib holds good is

CENGAGE PUBLICATION-PROGRESSION AND SERIES-EXERCIESE ( NUMERICAL VALUE TYPE )
  1. The terms a1, a2, a3 from an arithmetic sequence whose sum s 18. The t...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  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 ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |