Home
Class 11
MATHS
If P-th ,q-th and r-th terms of an AP as...

If P-th ,q-th and r-th terms of an AP as well those of a GP are a,b,c respectively,then prove that `a^(b-c):b^(c-a):c^(a-b)=1`

Promotional Banner

Topper's Solved these Questions

  • ANNUAL EXAMINATION QUESTION PAPERS 2017

    UNITED BOOK HOUSE|Exercise EXERCISE|50 Videos

  • Bethune Collegiate School, Question Paper

    UNITED BOOK HOUSE|Exercise Exercise |21 Videos

Similar Questions

Explore conceptually related problems

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

If the 3rd, 4th. 5th and sixth term in the expansion of (x+alpha)^n are a,b,c,d respectively, then prove that ((b^2-ac)/(c^2-bd))=(5a)/(3c).

The 5th, 8th and 11th terms of a GP are a,b,c respectively. Show that, b^2=ac

If the p^("th"), q^("th") and r^("th") terms of a G.P. are a, b and c, respectively. Prove that a^(q – r) b^(r-p) c^(P - q) = 1.

If the pth ,qth and rth terms of a G.P are a,b and c respectively show that (q-r)loga+(r-p)logb+(p-q)logc=0

The p^(th), q^(th) and r^(th) terms of an A.P. are a, b, c, respectively. Show that (q-r) a+(r-p) b+(p-q)c = 0

The p th ,q th and r th terms of an A.P are a,b,c respectively. Show that (p-r)a+(r-p)b+(p-q) c=0

If the p^(th) , q^(th) and r^(th) terms of a G.P. are x , y , z respectively. then show that : x^(q-r) . y^(r-p).z^(p-q)=1

If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in GP.

If the p-th, q-th and the r-th terms of a H.P. be x, y, z respectively, prove that, yz (q-r) + zx(r-p)+xy(p-q) = 0

UNITED BOOK HOUSE-ANNUAL EXAMINATION QUESTION PAPERS 2018-EXERCISE
  1. Prove that in any /\ABC.(b-c)cot(A/2)+(c-a)cot (B/2)+(a-b)cot (C/2)=0

    Text Solution

    |

  2. Solve secx-tanx=sqrt3

    Text Solution

    |

  3. If P-th ,q-th and r-th terms of an AP as well those of a GP are a,b,c ...

    Text Solution

    |

  4. Using the principle of mathematical induction ,prove that x^n-y^nis di...

    Text Solution

    |

  5. If z=x+iy andw=(1-iz)/(1+iz)such that |w|=1.then show that z is purely...

    Text Solution

    |

  6. Find the rank of the word 'MOTHER' in dicitonary format.

    Text Solution

    |

  7. If the coefficients of 2nd,3rd and 4th terms in the (1+x)^(2n)are in A...

    Text Solution

    |

  8. (2a,0) and (0,a) are the extremities of the base of an isosceles trian...

    Text Solution

    |

  9. A variable straight line passes through the point of intersection of t...

    Text Solution

    |

  10. The abscissae of two points A and B are the roots of the equation x^2+...

    Text Solution

    |

  11. If 2f(x)+f(-x)=1+x,find f'(10),where f'(x) denote derivative of f(x).

    Text Solution

    |

  12. Evaluate lim(xrarrpi//4)(4sqrt2-(cosx+sinx)^5)/(1-sin2x)

    Text Solution

    |

  13. Write the negation of each of the following statements:p:for every rea...

    Text Solution

    |

  14. Write the negation of each of the following statements:q:For every rea...

    Text Solution

    |

  15. "Mathematics is fun"check whether this sentence is a statement .

    Text Solution

    |

  16. p: If x is a real number such that x^3+4x=0,then x=0,prove that p is t...

    Text Solution

    |

  17. p: If x is a real number such that x^3+4x=0,then x=0,prove that p is t...

    Text Solution

    |

  18. A bag contains 5 white and 4 black balls.If 3 balls are drawn at rando...

    Text Solution

    |

  19. The arithmetic mean and standard deviation of 7 observations are respe...

    Text Solution

    |

  20. Prove that if x=a(costheta+sin thetasin2theta)and y=a(sintheta+costhet...

    Text Solution

    |