Home
Class 12
MATHS
Consider the set A(n) of point (x,y) suc...

Consider the set `A_(n)` of point (x,y) such that `0 le x le n, 0 le y le n` where n,x,y are integers. Let `S_(n)` be the set of all lines passing through at least two distinct points from `A_(n)`. Suppose we choose a line l at random from `S_(n)`. Let `P_(n)` be the probability that l is tangent to the circle `x^(2)+y^(2)=n^(2)(1+(1-(1)/(sqrt(n)))^(2))`. Then the limit `lim_(n to oo)P_(n)` is

A

0

B

1

C

`1/pi`

D

`1/sqrt2`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • QUESTION PAPER 2020

    KVPY PREVIOUS YEAR|Exercise PART-II(MATHEMATICS)|10 Videos

  • SOLVED PAPER 2019

    KVPY PREVIOUS YEAR|Exercise EXAMPLE|26 Videos

Similar Questions

Explore conceptually related problems

(1+x)^n le 1+ x^n where

The probability that the roots of the equation x^(2)+nx+(1)/(2)+(n)/(2)=0 are real where n in N such that n le 5 , is

Let P (n) be the statement C_(r) le n! for 1 le r le n then P(n + 1) = ________

The set S’ = {n : n is an integer, 1 le n le 50 }. If an element of S is selected at random, find the probability that it does not contain the digit '2' at all.

Let A_(n) be the area bounded by the curve y=x^(n)(n>=1) and the line x=0,y=0 and x=(1)/(2). If sum_(n=1)^(n)(2^(n)A_(n))/(n)=(1)/(3) then find the value of n .

KVPY PREVIOUS YEAR-SOLVED PAPER 2018-EXAMPLE
  1. Let a=cos 1^(@) and b= sin 1^(@). We say that a real number is algebra...

    Text Solution

    |

  2. A rectangle with its sides parallel to the x-axis and y-axis is inscib...

    Text Solution

    |

  3. Let f(x)=x|sin x|,x in R. Then

    Text Solution

    |

  4. Let f:[-1,1] to R be a function defined by f(x)={x^(2)|cos((pi)/(x))| ...

    Text Solution

    |

  5. The value of the integral int(0)^(pi)(1-|sin 8x|)dx is

    Text Solution

    |

  6. Let in x denote the logarithm of x with respect to the base e. Let S s...

    Text Solution

    |

  7. Let S be the set of real numbers p such that there is no nonzero conti...

    Text Solution

    |

  8. The porbability of men getting a certain disease is (1)/(2) and that o...

    Text Solution

    |

  9. The number of function f:[0,1] to [0,1]" satisfying " |f(x)-f(x)|=|x-...

    Text Solution

    |

  10. Suppose A is a 3xx3 matrix consisting of integer entries that are chos...

    Text Solution

    |

  11. Let x^(2)=4ky,k gt 0 be a parabola with vertex A. Let BC be its latus ...

    Text Solution

    |

  12. Let f:[0'1] to [-1,1] and g:[-1,1] to [0,2] be two functions such that...

    Text Solution

    |

  13. Let R be a rectangle , C be a circle, and T be a triangle in the plane...

    Text Solution

    |

  14. The number of different possible values for the sum x+y+z, where x,y,z...

    Text Solution

    |

  15. Let Gamma be a circle with diameter AB and centre O.Let l be the tange...

    Text Solution

    |

  16. The number of solution x of the equation sin (x+x^(2))- sin(x^(2))= si...

    Text Solution

    |

  17. The number of polynomials p:R to R satisfying p(0)=0,p(x) gtx^(2) for ...

    Text Solution

    |

  18. Consider the set A(n) of point (x,y) such that 0 le x le n, 0 le y le ...

    Text Solution

    |

  19. The maximum possible area bounded by the parabola y=x^2+x+10 and a cho...

    Text Solution

    |

  20. Suppose z is any root of 11z^8+20iz^7+10iz-22=0 where i=sqrt-1.Then,S=...

    Text Solution

    |