Home
Class 11
MATHS
If x^2+9y^2+25 z^2=x y z((15)/x+5/y+3/z)...

If `x^2+9y^2+25 z^2=x y z((15)/x+5/y+3/z),` then `x ,y ,a n dz` are in a. H.P. b. A.P. c. G.P. d. None of These

A

A.P.

B

G.P.

C

A.G.P.

D

H.P.

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`x^(2)+9y^(2)+25z^(2)=xyz((15)/(x)+(5)/(y)+(3)/(z))`
`rArr" "x^(2)+9y^(2)+25z^(2)-15yz-5xz-3xy=0`
`rArr" "(x^(2)-6xy+9y^(2))+(9y^(2)+25z^(2)-30yz)+(x^(2)-10xz+25z^(2))=0`
`rArr" "(x-3y)^(2)+(3y-5z)^(2)+(x-5z)^(2)=0`
`rArr" "x-3y=0,3y-5z=andx-5z=0`
`rArr" "x=3y=5z`
`rArr" "(x)/(1)=(y)/(1//3)=(z)/(1//5)=(1)/(lamda)" (say)"rArrx=(1)/(lamda),y=(1)/(3lamda),z=(1)/(5lamda)`
Clearly, x,y,z are in H.P.
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|80 Videos

  • SEQUENCES AND SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|13 Videos

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|50 Videos

  • SETS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

If x^2+9y^2+25 z^2=x y z((15)/x+5/y+3/z),t h e n x ,y ,a n dz are in H.P. b. 1/x ,1/y ,1/z are in A.P. c. x ,y ,z are in G.P. d. 1/a+1/d=1/b=1/c

If x ,y ,z are real and 4x^2+9y^2+16 z^2-6x y-12 y z-8z x=0,t h e nx , y,z are in a. A.P. b. G.P. c. H.P. d. none of these

If the lines a x+2y+1=0,b x+3y+1=0a n dc x+4y+1=0 are concurrent, then a ,b ,c are a. A.P. b. G.P. c. H.P. d. none of these

If the lines a x+2y+1=0,b x+3y+1=0a n dc x+4y+1=0 are concurrent, then a ,b ,c are in (a). A.P. (b). G.P. (c). H.P. (d). none of these

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 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), then x y z are in AP (b) GP (c) HP (d) none of these

If a,b,c are proper fractiion are in H.P. and x sum_(n=1)^oo a^n, y=sum_(n=1)^oo b^n, z= sum_(n=1)^oo c^n then x,y,z are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

If x ,y ,a n dz are distinct prime numbers, then (a). x , y , a n dz may be in A.P. but not in G.P. (b) x , y , a n dz may be in G.P. but not in A.P. (c). x , y , a n dz can neither be in A.P. nor in G.P. (d).none of these

If normals at two points A(x_1, y_1) and B(x_2, y_2) of the parabola y^2 = 4ax , intersect on the parabola, then y_1, 2sqrt(2)a, y_2 are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

OBJECTIVE RD SHARMA ENGLISH-SEQUENCES AND SERIES-Chapter Test
  1. If x^2+9y^2+25 z^2=x y z((15)/x+5/y+3/z), then x ,y ,a n dz are in a...

    Text Solution

    |

  2. Let H(n)=1+(1)/(2)+(1)/(3)+ . . . . .+(1)/(n), then the sum to n terms...

    Text Solution

    |

  3. Sum of the first n terms of the series 1/2+3/4+7/8+(15)/(16)+............

    Text Solution

    |

  4. If A(1),A(2) are between two numbers, then (A(1)+A(2))/(H(1)+H(2)) is ...

    Text Solution

    |

  5. If the (m+1)t h ,(n+1)t h ,a n d(r+1)t h terms of an A.P., are in G.P....

    Text Solution

    |

  6. Given that n arithmetic means are inserted between two sets of numbers...

    Text Solution

    |

  7. If a,b, and c are in G.P then a+b,2b and b+ c are in

    Text Solution

    |

  8. If in a progression a1, a2, a3, e t cdot,(ar-a(r+1)) bears a constant...

    Text Solution

    |

  9. If in an AP, t1 = log10 a, t(n+1) = log10 b and t(2n+1) = log10 c then...

    Text Solution

    |

  10. Find the sum of the series: 1^2-2^2+3^2-4^2+.....-2008^2+2009^2.

    Text Solution

    |

  11. If 4a^(2)+9b^(2)+16c^(2)=2(3ab+6bc+4ca)," where "a,b,c are non-zero nu...

    Text Solution

    |

  12. If Sn denotes the sum of n terms of an A.P. whose common difference is...

    Text Solution

    |

  13. The sides of a right angled triangle are in A.P., then they are in the...

    Text Solution

    |

  14. Find the sum of all the 11 terms of an AP whose middle most term is 30...

    Text Solution

    |

  15. The maximum sum of the series 20+19 1/3+18 2/3+ is 310 b. 300 c. 0320 ...

    Text Solution

    |

  16. If three numbers are in G.P., then the numbers obtained by adding the ...

    Text Solution

    |

  17. If p ,q ,r are in A.P., show that the pth, qth and rth terms of any G....

    Text Solution

    |

  18. Let a,b,c be three positive prime number. The progrrssion in which sqr...

    Text Solution

    |

  19. If 1/(b-a)+1/(b-c)=1/a+1/c , then (A). a ,b ,a n dc are in H.P. (B). a...

    Text Solution

    |

  20. If three numbers are in H.P., then the numbers obtained by subtracting...

    Text Solution

    |

  21. The first three of four given numbers are in G.P. and their last three...

    Text Solution

    |