Home
Class 12
MATHS
For positive integers K=1,2,3,……….n Let ...

For positive integers `K=1,2,3,……….n` Let `S_(k)` denotes the area of `DeltaOAB_(k)` (where `O` is the origin) such that `/_AOB_(k)=(Kpi)/(2n),OA=1` and `OB_(K)=K`. The value of the `lim_(nto oo)1/(n^(2)).sum_(K=1)^(n)S_(K)` is

A

`(2)/(pi^(2))`

B

`(4)//(pi^(2))`

C

`(8)/(pi^(2))`

D

`(1)/(2pi^(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE AND DEFINITE INTEGRATION

    VK JAISWAL ENGLISH|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|15 Videos

  • INDEFINITE AND DEFINITE INTEGRATION

    VK JAISWAL ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|16 Videos

  • HYPERBOLA

    VK JAISWAL ENGLISH|Exercise Exercise-4 : Subjective Type Problems|3 Videos

  • INVERSE TRIGONOMETRIC FUNTIONS

    VK JAISWAL ENGLISH|Exercise Exercise-5 : Subjective Type Problems|6 Videos

Similar Questions

Explore conceptually related problems

For positive integers k=1,2,3,....n,, let S_k denotes the area of triangleAOB_k such that angleAOB_k=(kpi)/(2n) , OA=1 and OB_k=k The value of the lim_(n->oo)1/n^2sum_(k-1)^nS_k is

The value of lim_(n->oo) sum_(k=1)^n log(1+k/n)^(1/n) ,is

The value of lim _( n to oo) sum _(k =1) ^(n) ((k)/(n ^(2) +n +2k))=

Evaluate ("lim")_(n rarr oo)sum_(k=1)^nk/(n^2+k^2)

Find the sum_(k=1)^(oo) sum_(n=1)^(oo)k/(2^(n+k)) .

The value of lim_(n->oo)sum_(k=1)^n(6^k)/((3^k-2^k)(3^(k+1)-2^(k+1)) is equal to

The value of \lim_{n \to \infty } sum_(k=1)^n (n-k)/(n^2) cos((4k)/n) equals to

If S_n=sum_(k=1)^n a_k and lim_(n->oo)a_n=a , then lim_(n->oo)(S_(n+1)-S_n)/sqrt(sum_(k=1)^n k) is equal to

Evaluate : sum_(k=1)^n (2^k+3^(k-1))

If a_(K)=(1)/(K(K+1)) for K=1, 2, 3....n , then (sum_(K=1)^(n)a_(K))^(2)=

VK JAISWAL ENGLISH-INDEFINITE AND DEFINITE INTEGRATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. For positive integers K=1,2,3,……….n Let S(k) denotes the area of Delta...

    Text Solution

    |

  2. int (x+ ( cos^(-1)3x )^(2))/(sqrt(1-9x ^(2)))dx = (1)/(k (1)) ( sqrt(1...

    Text Solution

    |

  3. If int (0)^(oo) (x ^(3))/((a ^(2)+ x ^(2)))dx = (1)/(ka ^(6)), then fi...

    Text Solution

    |

  4. int( (x^2+1)dx)/x

    Text Solution

    |

  5. If int (x ^(6) +x ^(4)+x^(2)) sqrt(2x ^(4) +3x ^(2)+6) dx = ((ax ^(6) ...

    Text Solution

    |

  6. int( x^2+3)/(x^2+2)dx

    Text Solution

    |

  7. The value of int (tan x )/(tan ^(2) x + tan x+1)dx =x -(2)/(sqrtA) tan...

    Text Solution

    |

  8. Let int (0)^(1) (4x ^(3) (1+(x ^(4)) ^(2010)))/((1+x^(4))^(2012))dx = ...

    Text Solution

    |

  9. Let int ( 1) ^(sqrt5)(x ^(2x ^(2)+1) +ln "("x ^(2x ^(2x ^(2+1)))")")dx...

    Text Solution

    |

  10. If int (dx )/(cos ^(3) x-sin ^(3))=A tan ^(-1) (f (x)) +bln |(sqrt2+f ...

    Text Solution

    |

  11. Find the value of |a| for which the area of triangle included between ...

    Text Solution

    |

  12. Let I = int (0) ^(pi) x ^(6) (pi-x) ^(8)dx, then (pi ^(15))/((""^(15) ...

    Text Solution

    |

  13. int( x^3)/(x^2-3)dx

    Text Solution

    |

  14. If a continuous function f on [0,a] satisfies f(x)f(a-x)=1,agt0, then ...

    Text Solution

    |

  15. If {x} denotes the fractional part of x, then I = int (0) ^(100) (sqrt...

    Text Solution

    |

  16. int( x^3)/(x^2-2)dx

    Text Solution

    |

  17. If M be the maximum value of 72 int (0) ^(y) sqrt(x ^(4) +(y-y^(2))^(2...

    Text Solution

    |

  18. Find the number points where f (theta) = int (-1)^(1) (sin theta dx )/...

    Text Solution

    |

  19. Find the vlaur of lim (n to oo) (1)/(sqrtn)(1+ (1)/(sqrt2) +(1)/(sqrt3...

    Text Solution

    |

  20. The maximum value of int (-pi/2) ^((3pi)/2) sin x. f (x) dx, subject t...

    Text Solution

    |

  21. Given a function g, continous everywhere such that g (1)=5 and int (0)...

    Text Solution

    |