Home
Class 11
MATHS
If a,b,c are in H.P. , then...

If a,b,c are in H.P. , then

A

`(1)/(a),b,(1)/(c)` are in A.P.

B

`(1)/(bc),(1)/(ca),(1)/(ab)` are in H.P

C

ab,bc,ca are in H.P.

D

`(a)/(b),(b)/(c),(c)/(a)` are in H.P.`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|129 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 positive quantities a,b,c are in H.P. , then which of the following is not true ?

If a,b,c,d are in H.P., then ab+bc+cd is equal to

Assertion: x-a,y-a,z-a are in G.P., Reason: If a,b,c are in H.P. then a- b/2, b- b/2, c- b/2 are in G.P. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

If three positive unequal numbers a, b, c are in H.P., then

If a,b,c ,d are in H.P., then show that ab + bc + cd =3ad

If a ,b ,c are in A.P., the a/(b c),1/c ,1/b will be in a. A.P b. G.P. c. H.P. d. none of these

If positive numbers a ,b ,c are in H.P., then equation x^2-k x+2b^(101)-a^(101)-c^(101)=0(k in R) has (a)both roots positive (b)both roots negative (c)one positive and one negative root (d)both roots imaginary

If positive numbers a ,b ,c are in H.P., then equation x^2-k x+2b^(101)-a^(101)-c^(101)=0(k in R) has (a)both roots positive (b)both roots negative (c)one positive and one negative root (d)both roots imaginary

STATEMENT-1 : If a^(x) = b^(y) = c^(z) , where x,y,z are unequal positive numbers and a, b,c are in G.P. , then x^(3) + z^(3) gt 2y^(3) and STATEMENT-2 : If a, b,c are in H,P, a^(3) + c^(3) ge 2b^(3) , where a, b, c are positive real numbers .

Statement - 1 : If non-zero numbers a , b , c are in H.P. , then the equation (x)/(a) + (y)/(b) = (1)/(c) represents a family of concurrent lines . Statement- 2 : A linear equation px + qy = 1 in x , y represents a family of straight lines passing through a fixed point iff there is a linear relation between p and q .

OBJECTIVE RD SHARMA ENGLISH-SEQUENCES AND SERIES-Chapter Test
  1. The sum of the integers from 1 to 100 which are not divisible by 3 or ...

    Text Solution

    |

  2. Let the harmonic mean and geometric mean of two positive numbers be in...

    Text Solution

    |

  3. The sum of the series 1 + 2.2+ 3.2^(2) + 4.2^(3) + 5.2^(4) + ….. +...

    Text Solution

    |

  4. If a\ (1/b+1/c),\ b(1/c+1/a),\ c(1/a+1/b) are in A.P. prove that a ,\ ...

    Text Solution

    |

  5. If the m^(th),n^(th)andp^(th) terms of an A.P. and G.P. be equal and b...

    Text Solution

    |

  6. The 7th term of a H.P. is (1)/(10) and 12 th term is (1)/(25), find th...

    Text Solution

    |

  7. The length of side of a square is 'a' metre. A second square is formed...

    Text Solution

    |

  8. The harmonic mean of the roots of the equation (5+sqrt(2))x^2-(4+sqrt(...

    Text Solution

    |

  9. If three positive real numbers a,b,c, (cgta) are in H.P., then log(a+c...

    Text Solution

    |

  10. In an A.P., the p^(th) term is 1/q and the q^(th) term is 1/p. fin...

    Text Solution

    |

  11. The sum of the series 2/3+8/9+(26)/(27)+(80)/(81)+ to n terms is (a) n...

    Text Solution

    |

  12. If a,b,c are in H.P. , then

    Text Solution

    |

  13. The odd value of n for which 704+1/2(704)+… upto n terms = 1984-1/2(1...

    Text Solution

    |

  14. The positive interger n for which 2xx2^2+3xx 2^3+4xx2^4+….+nxx2^4=2^(n...

    Text Solution

    |

  15. If 1^2+2^2+3^2++2003^2=(2003)(4007)(334) and (1)(2003)+(2)(2002)+(3)(2...

    Text Solution

    |

  16. The sum to n terms of the series (n^(2)-1^(2))+2(n^(2)-2^(2))+3(n^(2...

    Text Solution

    |

  17. The sum of the series a-(a+d)+(a+2d)-(a+3d)+... up to (2n+1) terms is:...

    Text Solution

    |

  18. If Hn=1+1/2+...+1/ndot , then the value of Sn=1+3/2+5/3+...+(99)/(50) ...

    Text Solution

    |

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

    Text Solution

    |

  20. If a(n)=1+(1)/(2)+(1)/(3)+(1)/(4)+(1)/(5)+ . . . .+(1)/(2^(n)-1), then

    Text Solution

    |