Home
Class 12
MATHS
lim(n to oo) {(n!)/((kn)^n)}^(1/n), wher...

`lim_(n to oo) {(n!)/((kn)^n)}^(1/n)`, where `k != 0` is a constant and `n in N`, equals :

A

`ke`

B

`ke^(-1)`

C

`k^(-1)e`

D

`k^(-1)e^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    MODERN PUBLICATION|Exercise LATEST QUESTIONS FROM AIEEE/JEE EXAMINATION|13 Videos

  • DEFINITE INTEGRALS

    MODERN PUBLICATION|Exercise RECENT COMPETITIVE QUESTIONS|21 Videos

  • DEFINITE INTEGRALS

    MODERN PUBLICATION|Exercise RECENT COMPETITIVE QUESTIONS|21 Videos

  • COMPLEX NUMBERS

    MODERN PUBLICATION|Exercise Questions from karnataka CET & COMED|15 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Recent competitive Questions|10 Videos

Similar Questions

Explore conceptually related problems

lim_(n rarr oo) (4^(n)+5^(n))^(1/n) =

lim_(n rarr oo) (4^(n)+5^(n))^(1/n) =

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

lim_(x rarr oo) (1+2/n)^(2n)=

Lt_(n to oo)(1 + 2/n)^(2n) =

lim_(n to oo) sum_(r = 1)^(n) 1/n e^(r/n) is :

lim_(n rarr oo) 1/2 [(n+1)(n+2)…….2n]^(1/n) =

lim_(n rarr oo) (nsqrt(n^(2)+1)-n) =

lim _( n to 0) ( 1+ 2n )^( (1)/( n) )

MODERN PUBLICATION-DEFINITE INTEGRALS-MULTIPLE CHOICE QUESTIONS (LEVEL - II)
  1. sum(n = 1)^(1000) int(n - 1)^(n) e^(x-[x]) dx, whose [x] is the greate...

    Text Solution

    |

  2. If f(x) = |(sin x + sin 2x + sin 3x, sin 2x , sin 3x),(3 + 4 sin x, 3,...

    Text Solution

    |

  3. lim(n to oo) {(n!)/((kn)^n)}^(1/n), where k != 0 is a constant and n i...

    Text Solution

    |

  4. If f(x) is a quadratic polynomial such that f(0) = 2, f(0) = -3 and f'...

    Text Solution

    |

  5. lim(n to oo) ((n)/(1 + n^2) + n/(2^2 + n^2) + n/(3^2 + n^2) + ……. + n/...

    Text Solution

    |

  6. int0^(pi) (x tanx dx)/(sec x+ cosx) =

    Text Solution

    |

  7. Let f : R to R be a differentiable function and f(1) = 4, then the val...

    Text Solution

    |

  8. For any integer n, the integral : int0^(pi) e^(cos^2) cos^(3) (2n + 1)...

    Text Solution

    |

  9. If In = int0^(pi//4) tan^n theta d theta, then for any +ve integer n, ...

    Text Solution

    |

  10. int0^1 |sin 2 pi x| dx is equal to :

    Text Solution

    |

  11. If f(x) = f(a - x), then int0^(a) xf(x) dx is equal to :

    Text Solution

    |

  12. Let f(x) = {:[(e^(cos x) sinx",", "for" |x| le 2),(2,"otherwise"):} th...

    Text Solution

    |

  13. The value of integral int(e^(-1))^(e^2) |(loge x)/(x)| dx is :

    Text Solution

    |

  14. Let g(x) = int0^(x) f(t) dt, where 1/2 le f(t) < 1, t in [0,1] and 0 <...

    Text Solution

    |

  15. Let f : (0, oo ) to R and F(x) = int0^x f(t) dt. If F(x^2) = x^2(1 +...

    Text Solution

    |

  16. If (1 sin t)/(1 + t) dt = alpha, then that value of the integral : i...

    Text Solution

    |

  17. The integral int(-1//2)^(1//2) ([x] + ln ((1 + x)/(1 - x)))dx equals :

    Text Solution

    |

  18. Let f(x) = int1^x sqrt(2 - t^2)dt. Then the real roots of the equation...

    Text Solution

    |

  19. Let T > 0 be a fixed real number. Suppose f is a continuous function s...

    Text Solution

    |

  20. Let d/(dx) F(x) = ((e^(sin x))/(x)) , x > 0. If int1^4 3/x e^(sin x^3)...

    Text Solution

    |