Home
Class 12
MATHS
Lt(nrarroo) {(n!)/(kn)^n}^(1/n), k!=0, i...

`Lt_(nrarroo) {(n!)/(kn)^n}^(1/n), k!=0`, is equal to (A) `k/e` (B) `e/k` (C) `1/(ke)` (D) none of these

A

ke

B

`(e )/(k)`

C

`(k)/(e )`

D

`(1)/(ke)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Chapter Test 2|60 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Exercise|147 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA|Exercise Exercise|86 Videos

  • DERIVATIVE AS A RATE MEASURER

    OBJECTIVE RD SHARMA|Exercise Exercise|26 Videos

Similar Questions

Explore conceptually related problems

Lt_(nrarroo) sum_(r=1)^n (2r)^k/n^(k+1),k!=-1 , is equal to (A) 2^k/(k-1) (B) 2^k/k (C) 1/(k+1) (D) 2^k/(k+1)

lim_(x rarr oo)n^(2)(x^((1)/(n))-x^((1)/((n+1)))),x>0, is equal to (a)0(b)e^(x)(c)(log)_(e)x(d) none of these

Lt_(nrarroo)((n!)/n^n)^(1/n)= (A) e^(-2) (B) e^(-1) (C) e^3 (D) e

lim_(nrarroo) (1-x+x.root n e)^(n) is equal to

Let lim_(n rarr oo)(((kn)!)/(n^(kn)))^(1/n)=lambda(k) where k in N

The coefficient of x^k d in the expansion of 1+(1+x)+(1+x_)^2+……+(1+x)^n is (A) ^nC_k (B) ^(n+1)C_k (C) ^(n+1)C_(k+1) (D) none of these

Lt_(nrarroo) sum_(r=1)^(6n) 1/(n+r)= (A) log6 (B) log7 (C) log5 (D) 0

lim_(nrarroo) sum_(r=1)^n 1/n e^(r/n) is (A) 1-e (B) e-1 (C) e (D) e+1

" If "Lt_(nrarroo) ((prod_(k=1)^(n)(1+(k)/(n))))^(1/n)" has the value of equal to "ke^(-1)" where "k in N" ,then the value of "K" is "

If A=[a_(ij)] is a scalar matrix of order n xx n such that a_(ii)=k for all i, then trace of A is equal to nk(b)n+k(c)(n)/(k) (d) none of these

OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Chapter Test 1
  1. Let I(n)=int(0)^(pi//2) sin^(n)x dx, nin N. Then

    Text Solution

    |

  2. If f(x)=int(0)^(x) sin^(4)t dt, then f(x+2pi) is equal to

    Text Solution

    |

  3. int(0)^(pi) (1)/(1+3^(cosx)) dx is equal to

    Text Solution

    |

  4. Let int(0)^(a) f(x)dx=lambda and int(0)^(a) f(2a-x)dx=mu. Then, int(...

    Text Solution

    |

  5. The value of int(pi//4)^(3pi//4) (x)/(1+sin x) dx is equal to

    Text Solution

    |

  6. Let I(n)=int(0)^(pi//2) cos^(n)x cos nx dx. Then, I(n):I(n+1) is equal...

    Text Solution

    |

  7. The value of int(-1)^(1) max[2-x,2,1+x] dx is

    Text Solution

    |

  8. int(0)^(pi//4) sin(x-[x]) dx is equalto

    Text Solution

    |

  9. The value of the integral int(-1)^(1) (x-[2x])dx,is

    Text Solution

    |

  10. Let f:R in R be a continuous function such that f(1)=2. If lim(x to 1)...

    Text Solution

    |

  11. Let f:R in R be a continuous function such that f(x) is not identicall...

    Text Solution

    |

  12. Let f(x)=int(0)^(x) |xx-2|dx, ge 0. Then, f'(x) is

    Text Solution

    |

  13. Lt(nrarroo) {(n!)/(kn)^n}^(1/n), k!=0, is equal to (A) k/e (B) e/k (C)...

    Text Solution

    |

  14. Let f(x) be an integrable function defined on [a,b],b gt a gt 0. If I(...

    Text Solution

    |

  15. int(0)^(sqrt(2)) [x^(2)]dx, is

    Text Solution

    |

  16. Let f(x) be a function satisfying f'(x)=f(x) with f(0)=1 and g(x) be a...

    Text Solution

    |

  17. (sum(n=1)^10int(-2n-1)^(-2n)sin^(27)(x)dx+sum(n=1)^10int(2n)^(2n+1)sin...

    Text Solution

    |

  18. If f(y)=e^(y)=e^(y),g(y)=y, y gt 0 and F(t)=int(0)^(t) f(t-y)g(y) dy, ...

    Text Solution

    |

  19. If I(n)=int(0)^(pi//2) x^(n) sin x dx, then I(4)+12I(2) is equal to\

    Text Solution

    |

  20. int(0)^(1) sin{2 tan^(-1)sqrt((1+x)/(1-x))}dx=

    Text Solution

    |