Home
Class 12
MATHS
If a and x are positive integers such th...

If a and x are positive integers such that x `lt `a and `sqrt(a - x ), sqrt(x), sqrt(a + x)` are in A.P , then least possible value of a is

A

5

B

7

C

11

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • RELATIONS

    DIPTI PUBLICATION ( AP EAMET)|Exercise Exercise|49 Videos
  • SETS ( APPENDIX - 1)

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE|70 Videos

Similar Questions

Explore conceptually related problems

Let f(x) = (sqrt(x - 2 sqrt(x - 1)))/(sqrt(x - 1) - 1)x , then

sqrt x = sqrt(2x - 1) "then" x = ...

Lt_(x to 0) (""^(n) sqrt(a-x)-""^(n) sqrt(a))/(x)=

Lt_(x to 0) sqrt(|x|-x)=

Lt_(x to oo) {sqrt(x^(2)-sqrt(x^(4)+1))-x sqrt(2)}=

Lt_(x to 0)(sqrt(1-cos2x))/(sqrt(2)x)=

underset(x to 1)"Lt" sqrt(1-x)=

"lt"_(x to 0) (sqrt(x+1)-1)/(x)

DIPTI PUBLICATION ( AP EAMET)-SEQUENCES AND SERIES -EXERCISE
  1. If the sum of four numbers in A.P is 24 and the sum of their square is...

    Text Solution

    |

  2. Let T(r) be the rth term of an A.P, for r = 1,2 …. If for some positiv...

    Text Solution

    |

  3. If a and x are positive integers such that x lt a and sqrt(a - x ), sq...

    Text Solution

    |

  4. If the length of sides of right angled triangle are in A.P., then the ...

    Text Solution

    |

  5. If three positive real numbers a,b, c are in A.P such that abc = 4, th...

    Text Solution

    |

  6. If log(5) 2, log(5) (2^(x)-5 ) log(5) (2^(x) - 7//2) are in A.P ., th...

    Text Solution

    |

  7. If a(1),a(2),a(3),………. are in A.P. such that a(1) + a(5) + a(10) + a(1...

    Text Solution

    |

  8. Four numbers are in arithmetic progression. The sum of first and last ...

    Text Solution

    |

  9. The ratio of the sums of m arithmatic means and n arithmatic means bet...

    Text Solution

    |

  10. Between 1 and 31 are inserted m arithmetic means, so that the ratio of...

    Text Solution

    |

  11. If a(1), a(2) ……… a(n) are in A.P with common difference d ne 0, then ...

    Text Solution

    |

  12. Value of underset(n rarr infty )(Lim) sum(r = 1)^(n) Tan^(-1) ((1)/(2r...

    Text Solution

    |

  13. Given that n A.M.s are inserted between two sets of numbers a , 2b and...

    Text Solution

    |

  14. If pth, qth, rth terms of an A.P are a,b,c then a(q - r ) + b(r - p ) ...

    Text Solution

    |

  15. If mth terms of an A.P . Is n and nth term is m, then (m + n)th term i...

    Text Solution

    |

  16. If the mth term of an A.P is n and nth term is m , then pth term =

    Text Solution

    |

  17. If 100 times the 100^(th) term of an A.P with non zero common differen...

    Text Solution

    |

  18. If the sum of m terms of an A.P, is equal to the sum of n terms of the...

    Text Solution

    |

  19. If a(1), a(2) …… a(n) are in A.P then (sqrt(a(1)) + sqrt(a(n)))/( sqrt...

    Text Solution

    |

  20. If the ratio of sum of n terms in two A.P' s is 2n : n + 1, then the ...

    Text Solution

    |