Home
Class 11
MATHS
If p, q. r in G.P and1/(p-a),1/(r-p),1/(...

If p, q. r in G.P and`1/(p-a),1/(r-p),1/(q-r)` are in AP.show that p+4q+r=0

Promotional Banner

Topper's Solved these Questions

  • MODEL QUESTION PAPERS-SET 1

    UNITED BOOK HOUSE|Exercise EXERCISE|50 Videos

  • MODEL QUESTION PAPERS-SET 11

    UNITED BOOK HOUSE|Exercise EXERCISE|46 Videos

Similar Questions

Explore conceptually related problems

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 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.

Let alpha and beta be the roots of equation px^(2)+qx+r=0" " pne0."If " p , q , r "are in A.P" and (1)/(alpha)+(1)/(beta)=4 , "then the value of " |alpha-beta| is -

If a ,b ,a n dc are in A.P. p ,q ,a n dr are in H.P., and a p ,b q ,a n dc r are in G.P., then p/r+r/p is equal to a. a/c+c/a b. a/c-c/a c. b/q + q/b d. b/q - q/b

If p+-a, q+- b, r+-c and abs((p,b,c),(a,q,c),(a,b,r)) = 0 show that p/(p-a)+q/(q-b)+r/(r-c)=2 .

If (p^2+q^2), (pq+qr), (q^2+r^2) are in GP then Prove that p, q, r are in G.P.

If the pth, qth, rth, and sth terms of an A.P. are in G.P., then p-q ,q-r ,r-s are in a. A.P. b. G.P. c. H.P. d. none of these

If the roots of the equation p(q-r)x^2+q(r-p)x+r(p-q)=0 be equal, show that 1/p+1/r=2/q .

If the roots of the equation p(q-r)x^2+q(r-p)x+r(p-q)=0 be equal ,show that 1/p+1/r=2/q

If pth, qth and rth terms of on AP are a. b and c, then show that a(q - r) + b(r - p) + c(p - q) = 0.

UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 10-EXERCISE
  1. Prove that ((i-sqrt3)/(i+sqrt3))^200+((i+sqrt3)/(-i+sqrt3))^200= -1

    Text Solution

    |

  2. If the sum of 1st n tenn of a GP is Sn=1 and S(2n)=4,show that S(3n):S...

    Text Solution

    |

  3. In the expansion of (x+P)^n,the 6th ,7th,8th and 9th terms are a,b,c a...

    Text Solution

    |

  4. Show that the straight lines x/a+y/b=1/c, x/b+y/c=1/a and x/c+y/a=1/b ...

    Text Solution

    |

  5. The co-ordinates of the end points of a diagonal of a rectangle are (...

    Text Solution

    |

  6. Find the equation of a circle which is passes through the point (4,3) ...

    Text Solution

    |

  7. Show that the points (0. 7, 10), (-1, 6, 6) and (-4, 9, 6) form a righ...

    Text Solution

    |

  8. Differentiate (from 1st principle) sinx/xwith respect to x

    Text Solution

    |

  9. Prove that the statement , “If all the angles of a triangle are equal,...

    Text Solution

    |

  10. Prove that sqrt2 irrational, (use the method of contradiction).

    Text Solution

    |

  11. Two unbiased dice are thrown. Find the probability that the upper fac...

    Text Solution

    |

  12. If x costheta=y cos (theta+(2pi)/3)=z cos(theta+(4pi)/3)show that xy +...

    Text Solution

    |

  13. if tan (theta/2)=sqrt((1-e)/(1+e))tan (varphi/2),then prove that cos v...

    Text Solution

    |

  14. If x=-1+i sqrt2 and the value of x^(4)+4x^(3)+6x^(2)+4x+9.

    Text Solution

    |

  15. If p, q. r in G.P and1/(p-a),1/(r-p),1/(q-r) are in AP.show that p+4q+...

    Text Solution

    |

  16. Solve graphically and find the common solution region of the system of...

    Text Solution

    |

  17. If the vertices of an equilateral traingle be represented by the compl...

    Text Solution

    |

  18. If the pointP(at^2,2at) is a end point of a chord of the parabolay^2=...

    Text Solution

    |

  19. Prove that the locus of the point of iter section of the linessqrt3x-y...

    Text Solution

    |

  20. Find the locus of the midpoints of the all chords drawn from the ends ...

    Text Solution

    |