Home
Class 12
MATHS
lim(nto oo){n" sin"(2pi)/(3n)."cos"(2pi)...

`lim_(nto oo){n" sin"(2pi)/(3n)."cos"(2pi)/(3n)}` =

A

`(2pi)/(3)`

B

`(pi)/(6)`

C

`(pi)/(3)`

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • KARNATAKA CET 2009

    KCET PREVIOUS YEAR PAPERS|Exercise MATHEMATICS|60 Videos

  • KARNATAKA CET 2012

    KCET PREVIOUS YEAR PAPERS|Exercise MATHEMATICS|60 Videos

Similar Questions

Explore conceptually related problems

lim_(n rarr oo) 1/n[sin(pi/(2n))+sin(pi/n)+sin((3pi)/2n)+........+sin(pi/2)] =

lim_(n rarr oo) (1-n^(2))/(sum n)=

lim_(n rarr oo) 5^(((2x)/(x+3)) =

lim_(n to oo) sum_(r = 1)^(n) 1/n sin(r pi)/(2pi) is :

lim_(n rarr oo) {1/n+1/(n+1)+1/(n+2)+…..+1/(3n)} =

The smallest positive integral value of n such that [(1+"sin"pi/8+i"cos"(pi)/8)/(1+"sin"(pi)/8-i"cos"(pi)/8)]^(n) is purely imaginary is n=

lim_(n to oo) [1/(n^2) "sec"^2 1/(n^2) + 2/(n^2) "sec"^(2) 4/(n^2) + …… + 1/n "sec"^(2) 1] equals :

Lim_(nto oo)(3^(n)+4^(n))^((1)/(n))=

underset(n to oo)lim 1/n [ tan pi/(4n) + tan (2pi)/(4n) + tan (3pi)/(4n) + …. + tan(npi)/(4n)] =

KCET PREVIOUS YEAR PAPERS-KARNATAKA CET 2010-Mathematics
  1. The sides of a triangle are 6+sqrt(12),sqrt(48) and sqrt(24). The tang...

    Text Solution

    |

  2. A simple graph contains 24 edges. Degree of each vertex is 3. The numb...

    Text Solution

    |

  3. lim(nto oo){n" sin"(2pi)/(3n)."cos"(2pi)/(3n)} =

    Text Solution

    |

  4. The function f(x)=[x], where [x] denotes the greatest than x, is

    Text Solution

    |

  5. If agtbgt0,sec^(-1)((a+b)/(a-b))=2"sin"^(-1)x, then x =

    Text Solution

    |

  6. If x!=npi,x!=(2n+1)(pi)/(2),nin then (sin^(-1)(cosx)+cos^(-1)(sinx))...

    Text Solution

    |

  7. The general solution of 1+sin^(2)x=3" sinx. Cosx, "tan"x!=(1)/(2) is

    Text Solution

    |

  8. The least positive integer n, for which ((1+i)^(n))/((1-i)^(n-2))is po...

    Text Solution

    |

  9. If x+i y=(-1+i sqrt(3))^(2010), then x=

    Text Solution

    |

  10. The greatest value of x satisfying 21-=385 (mod x) and 587-=167 (mod x...

    Text Solution

    |

  11. The number (49^(2)-4)(49^(3)-49) is divisible by

    Text Solution

    |

  12. The least positive integer x satisying 2^(2010)-=3x (mod 5) is

    Text Solution

    |

  13. If A and B are two square matrices of the same order such that AB=B an...

    Text Solution

    |

  14. If A is a 3xx3 nonsingular matrix and if |A|=3, then |(2A)^(-1)|=

    Text Solution

    |

  15. If A=[(3,2),(1,1)] then A^(2)+xA+yI=0 for (x,y) =

    Text Solution

    |

  16. The constant term of the polynomial |(x+3,x,x+2),(x,x+1,x-1),(x+2,2x,3...

    Text Solution

    |

  17. If vec a, vec b, vec c non zero coplanar vectors, then, [2 vec a - vec...

    Text Solution

    |

  18. A space vector makes the angle 150^(@) and 60^(@) with the positive di...

    Text Solution

    |

  19. If vec(a),vec(b) and vec(c) are unit vectors such that vec(a)+vec(b)+v...

    Text Solution

    |

  20. If hati,hatj,hatk are unit vectors along the positive direction of A,Y...

    Text Solution

    |