Home
Class 12
MATHS
If one G.M., G and two A.M.\'s p and q b...

If one G.M., G and two A.M.\'s p and q be inserted between two given quantities, show that `G^2=(2p-q)(2q-p)`.

A

G

B

`G^(2)`

C

`2G^(2)`

D

2G

Text Solution

Verified by Experts

The correct Answer is:
2
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    AAKASH INSTITUTE|Exercise Assignment (SECTION - C) More than one option are correct|11 Videos
  • SEQUENCES AND SERIES

    AAKASH INSTITUTE|Exercise Assignment (SECTION - D) Linked Comprehension|12 Videos
  • SEQUENCES AND SERIES

    AAKASH INSTITUTE|Exercise Assignment (SECTION - A) One option is correct|60 Videos
  • RELATIONS AND FUNCTIONS

    AAKASH INSTITUTE|Exercise Assignment (Section - J) Aakash Challengers Questions|8 Videos
  • SETS

    AAKASH INSTITUTE|Exercise SECTION-I(Aakash Challengers Questions)|5 Videos

Similar Questions

Explore conceptually related problems

If one A.M. A and two G.M.\'s p and q be inserted between two given numbers, shwo that p^2q+q^2/p=2A

one AM,a and two GM's, pand q be inserted between any two given numbers then show that p^(3)+q^(3)=2apq

If one geometric mean G and two arithmetic means p,q be inserted between two given numbers,then prove that,G^(2)=(2p-q)(2q-p)

If odd number of G.M.\'s are inserted between two given quantities a and b, show that the middle G.M.= sqrt(ab)

If one A.M.A and tow geometric means G_(1) and G_(2) inserted between any two positive numbers,show that (G_(1)^(1))/(G_(2))+(G_(2)^(2))/(G_(1))=2A

If p ,q be two A.M. ' s and G be one G.M. between two numbers, then G^2= a)(2p-q)(p-2q) (b) (2p-q)(2q-p) c)(2p-q)(p+2q) (d) none of these

AAKASH INSTITUTE-SEQUENCES AND SERIES -Assignment (SECTION - B) One option is correct
  1. Four geometric mens are inserted between the number 2^(11) - 1 an...

    Text Solution

    |

  2. Find the values of x in (-pi,pi) which satisfy the equation 8^(1+|cosx...

    Text Solution

    |

  3. If one G.M., G and two A.M.\'s p and q be inserted between two given q...

    Text Solution

    |

  4. the sum of three numbers in G.P. is 56. If we subtract 1,7,21 from the...

    Text Solution

    |

  5. Let a, b be the roots of the equation x^(2) - 4 x k(1) = 0 and c ,...

    Text Solution

    |

  6. If a ,b ,c are three distinct real numbers in G.P. and a+b+c=x b , the...

    Text Solution

    |

  7. Sum of the series 1+2.2+3.2^2 +4.2^3+.....+100.2^99 is

    Text Solution

    |

  8. If 3+1/4(3+p)+1/(4^2)(3+2p)+... + oo=8, then p

    Text Solution

    |

  9. The value of 2^(1/4).4^(1/8).8^(1/16),,,,,,,oo is equal to.

    Text Solution

    |

  10. Let S denotes the infinite sum 2 + 5x + 9x^(2) + 14x^(3) + 2x^(4) ...

    Text Solution

    |

  11. The value of x + y + z is 15 if a, x, y, z, b are in A.P. while t...

    Text Solution

    |

  12. If x , y, z are positive reals satisfying 4xy + 6yz + 8 zx = 9 , ...

    Text Solution

    |

  13. (p)/(q) + (q)/(p) = (c)/(a) - (a)/(c)

    Text Solution

    |

  14. The sum to 100 terms of the series 1.2.3. + 2.3.4. + 3.4.5. + …+ n...

    Text Solution

    |

  15. The sum of n terms of the series 1^2+2.2^2+3^2+2.4^2+5^2+2.6^2+.... is...

    Text Solution

    |

  16. If x,y, z and w are non-zero real numbers and x^(2) + 5y^(2) + 5z^...

    Text Solution

    |

  17. If x^(18)=y^(21)=z^(28), then 3,3 log(y)x,3log(z)y,7log(x)z are in

    Text Solution

    |

  18. The coefficient of x^(101) in the expansion of (1 - x) (1- 2x) (1 ...

    Text Solution

    |

  19. If a, b, c, are in A.P. ., p , q,r, are in H.P. and ap ,bq, cr are i...

    Text Solution

    |

  20. Let C be a circle with centre P(0) and AB be a diameter of C . supp...

    Text Solution

    |