Home
Class 11
MATHS
If (a-x)/(p x)=(a-y)/(q y)=(a-z)/(rz) an...

If `(a-x)/(p x)=(a-y)/(q y)=(a-z)/(rz) and p ,q ,and r` are in A.P., then prove that `x ,y ,z` are in H.P.

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|9 Videos
  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

If a^(x) = b^(y) = c^(z) and a, b, c, are in G.P., prove that x, y, z are in H.P.

Let a(a != 0) is a fixed real number and (a-x)/(p x) = (a-y)/(qy) = (a-z)/(r z) . If p, q, r are in A.P., show that (1)/(x), (1)/(y), (1)/(z) are in A.P.

If x ,1,a n dz are in A.P. and x ,2,a n dz are in G.P., then prove that x ,a n d4,z are in H.P.

If (y/z)^a.(z/x)^b.(x/y)^c=1 and a,b,c are in A.P ,show that x,y,z are in G.P.

If x^(1/a)=y^(1/b)=z^(1/c) where a,b,c are in A.P,,than show that x,y,z are in G.P.

If (1)/(x+y),(1)/(2y),(1)/(y+t) are in A.P . Prove that x,y,t are in G.P.

If p, q, r are in A.P., q, r, s are in G.P. and r, s, t are in H.P., prove that p, r, t are in G.P.

If x = a - (1)/(a), y = b - (1)/(b) and z = c - (1)/(c ) and a, b, c are in G.P., then show that (x+z)/(y) = r + (1)/(r ) , where r is the common ratio of the G.P.

If sin(y+z-x),sin(z+x-y),"sin"(x+y-z) are in A.P., then t a n x ,tany ,tanz are in (a)A.P. (b) G.P. (c) H.P. (d) none of these

If a, b, c are in G.P. and a^(1/x) =b^(1/y)=c^(1/z) , prove that x, y , x are in A.P

CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. The AM of two given positive numbers is 2. If the larger number is inc...

    Text Solution

    |

  2. Find the sum of the series 1+3x+5x^2+7x^3+..........upto n terms.

    Text Solution

    |

  3. If (a-x)/(p x)=(a-y)/(q y)=(a-z)/(rz) and p ,q ,and r are in A.P., the...

    Text Solution

    |

  4. Find the sum of n terms of the series 1+4/5+7/(5^2)+10/5^3+......

    Text Solution

    |

  5. Find the sum (1^2)/2-(3^2)/(2^2)+(5^2)/(2^3)-(7^2)/(2^4)+....oodot

    Text Solution

    |

  6. If H is the harmonic mean between P and Q then find the value of H//P+...

    Text Solution

    |

  7. If Tr=r(r^2-1), then find sum(r=2)^oo1/Trdot

    Text Solution

    |

  8. Insert four H.M.’s between 2/3 and 2/13.

    Text Solution

    |

  9. If a , b ,a n dc are respectively, the pth, qth , and rth terms of a G...

    Text Solution

    |

  10. The A.M. and H.M. between two numbers are 27 and 12, respectively, t...

    Text Solution

    |

  11. If a ,a1, a2, a3, a(2n),b are in A.P. and a ,g1,g2,g3, ,g(2n),b . are...

    Text Solution

    |

  12. If nine arithmetic means and nine harmonic means are inserted between ...

    Text Solution

    |

  13. If x ,1,a n dz are in A.P. and x ,2,a n dz are in G.P., then prove tha...

    Text Solution

    |

  14. Find two numbers whose arithmetic mean is 34 and the geometric mean is...

    Text Solution

    |

  15. If a,b,c ,d and p are distinct real number such that (a^2+b^2+c^2)p^2-...

    Text Solution

    |

  16. If A.M. and G.M. between two numbers is in the ratio m : n then prove...

    Text Solution

    |

  17. Prove that (666....6)^2+(888....8)=4444.....4.

    Text Solution

    |

  18. If a is the A.M. of b and c and the two geometric mean are G1 and G2...

    Text Solution

    |

  19. If a,b,c ,d are distinct integer in AP such that d=a^2+b^2+c^2, then a...

    Text Solution

    |

  20. The 8th and 14th term of a H.P. are 1/2 and 1/3, respectively. Find it...

    Text Solution

    |