Home
Class 11
MATHS
If a,b,c are in HP and agtcgt0, then 1/(...

If a,b,c are in HP and `agtcgt0, then 1/(b-c)-1/(a-b)`.

A

is positive

B

is zero

C

is negative

D

has no fixed sign

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    PATHFINDER|Exercise QUESTION BANK|41 Videos

  • QUADRATIC EQUATION

    PATHFINDER|Exercise QUESTION BANK|19 Videos

Similar Questions

Explore conceptually related problems

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

If a, b, c are in H.P., prove that, (1)/(bc), (1)/(ca), (1)/(ab) are in H.P.

If a,b,c are in HP , thn the value of (b+a)/(b-a)+(b+c)/(b-c) is

If a, b, c are in HP and if ((a + b)/(2a - b)) + ((c + b)/(2c - b)) gt sqrt(lambdasqrt(lambdasqrt(lambda ....infty))) , then the value of lambda must be

If a,b,c are in H.P. show that a/(b+c),b/(c+a),c/(a+b) are also in H.P.

If a ,b ,c are in G.P. and a-b ,c-a ,a n db-c are in H.P., then prove that a+4b+c is equal to 0.

If a,b,c are in AP and a^2,b^2,c^2 are in HP, then

If a, b, c are in H.P., prove that, (a)/(b+c-a), (b)/(c+a-b), (c )/(a+b-c) are in H.P.

If a, b, c are in H.P., prove that (a)/(b+c), (b)/(c+a) and (c )/(a+b) are also in H.P.

If a, b, c are in H.P., prove that, (a)/(a-b) = (a+c)/(a-c)

PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. Consider an infinite geometric series with first term a and common rat...

    Text Solution

    |

  2. The value of a^(logb(x))=(where, a=0.2,b=sqrt5), x=(1/4+1/8+1/16+........

    Text Solution

    |

  3. If a,b,c are in HP and agtcgt0, then 1/(b-c)-1/(a-b).

    Text Solution

    |

  4. Let the positive numbers a,b,c,d be in AP , Then abc, abd,acd,bcd are

    Text Solution

    |

  5. If a,b,c are in HP , thn the value of (b+a)/(b-a)+(b+c)/(b-c) is

    Text Solution

    |

  6. If x1gt0,i=1,2.....50 and x1+x2+.....x50=50 then the minimum value of ...

    Text Solution

    |

  7. If three positive real number a,b,c are in AP with abc =4 , then the m...

    Text Solution

    |

  8. The sum of 10 terms of the series 0.7+.77+.777+.... is

    Text Solution

    |

  9. Find the sum of the series upto n terms 1.3.5+3.5.7+5.7.9+....

    Text Solution

    |

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

    Text Solution

    |

  11. If the sum to infinity to the series 1+4x+7x^2+10x^3+..... is 35/16 th...

    Text Solution

    |

  12. Consider an AP with first term a and the common difference 'd' Let Sk...

    Text Solution

    |

  13. If p,q,r are three positive real number are in AP , then the roots of ...

    Text Solution

    |

  14. The solution of the equation (8)^((1+[cosx absdivcos^2xabsdiv cos^3x]d...

    Text Solution

    |

  15. If (1+x)(1+x^2)(1+x^4)....(1+x^128)=sum(r=0)^nx^r then n is

    Text Solution

    |

  16. If angt1 for all ninN,then log(a2)a1+log(a3)a2+.....+log(an)a(n-1)+log...

    Text Solution

    |

  17. Let Sk=underset(nrarrinfty)limsum(i=0)^n1/(k+1)^i. Then sum(k=1)^nkSk...

    Text Solution

    |

  18. If a1,a2,a3...an are in HP and f(k)=sum(r=1)^nar-ak, then a1/(f(1)),a...

    Text Solution

    |

  19. sum(r=1)^nr^2-sum(m=1)^nsum(r=1)^mr is equal to

    Text Solution

    |

  20. The sum of the integer from 1 to 100 which is not divisible by 3 or 5 ...

    Text Solution

    |