Home
Class 12
MATHS
For a in R (the set of all real numbers...

For `a in R` (the set of all real numbers), `a!=-1),` `(lim)_(nvecoo)((1^a+2^a++n^a)/((n+1)^(a-a)[(n a+1)+(n a+2)+&(n a+n)])=1/(60.)` Then `a=` `5` (b) 7 (c) `(-15)/2` (d) `(-17)/2`

A

5

B

7

C

`(-15)/2`

D

`(-17)/2`

Text Solution

Verified by Experts

The correct Answer is:
B, D
Given limit `=(lim_(n to oo) 1/n sum_(r=1)^(n)(r/n)^(a))/(lim_(n to oo) (1+1/n)^(a-1)lim_(n to oo) 1/n sum_(r=1)^(n)(a+r/n))=(int_(0)^(1)x^(a)dx)/(int_(0)^(1)(a+x)dx)`
`=2/((2a+1)(a+1))=2/120`
`:.a=7` or `-17/2`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE|Exercise JEE Main Previous Year|12 Videos

  • CURVE TRACING

    CENGAGE|Exercise Exercise|24 Videos

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

For a in R (the set of all real numbers), a!=-1), (lim)_(n->oo)((1^a+2^a++n^a)/((n+1)^(a-1)[(n a+1)+(n a+2)+......(n a+n)])=1/(60.) Then a= (a) 5 (b) 7 (c) (-15)/2 (d) (-17)/2

lim_(n->oo)((n^2-n+1)/(n^2-n-1))^(n(n-1)) is

Evaluate: ("lim")_(nvecoo)((a1 1/x+a2 1/x++a n1/x)/n)^(n x)

lim_(n->oo)(n(2n+1)^2)/((n+2)(n^2+3n-1)) is equal to (a)0 (b) 2 (c) 4 (d) oo

Evaluate: ("lim")_(nvecoo)n^(-n^2){(n+2^0)(n+2^(-1))(n+2^(-2))(n+2^(-n+1))}^n

Discuss the continuity of f(x)=(lim)_(nvecoo)(x^(2n)-1)/(x^(2n)+1)

("lim")_(nvecoo)"{"(n/(n+1))^(alpha)+sin(1/n)]^n (when alpha in Q ) is equal to (a) e^(-alpha) (b) -alpha (c) e^(1-alpha) (d) e^(1+alpha)

Evaluate: lim_(n->oo)[1/(n a)+1/(n a+1)+1/(n a+2)++1/(n b)]

lim_(n to oo)((1)/(n^2)+(2)/(n^2)+(3)/(n^2)+"………."+(n)/(n^2)) is

CENGAGE-DEFINITE INTEGRATION -JEE Advanced Previous Year
  1. about to only mathematics

    Text Solution

    |

  2. Let S be the area of the region enclosed by y=e^-x^2,y=0,x=0,a n dx=1....

    Text Solution

    |

  3. For a in R (the set of all real numbers), a!=-1), (lim)(nvecoo)((1^a...

    Text Solution

    |

  4. Let f be a continuous function on [a ,b]dot Prove that there exists a ...

    Text Solution

    |

  5. Let f:(0,oo) in R be given f(x)=overset(x)underset(1//x)int e^-(t+(1...

    Text Solution

    |

  6. The option(s) with the values of aa n dL that satisfy the following eq...

    Text Solution

    |

  7. Given A = {2,4,5 }, B = {2, 5}, C = {3, 4} and D = {1, 3, 5}, check if...

    Text Solution

    |

  8. ("lim")(xvecoo)((n^2)/(n^2))^(n(n-1)i se q u a lto e (b) e^2 (c) e^(...

    Text Solution

    |

  9. Let f: RvecR be a continuous function which satisfies f(x)= int0^xf(t...

    Text Solution

    |

  10. int(1)/(x(logx)log(logx))dx=

    Text Solution

    |

  11. Evaluate the following integrals using properties of integration : i...

    Text Solution

    |

  12. The total number for distinct x epsilon[0,1] for which int(0)^(x)(t^(2...

    Text Solution

    |

  13. Given that for each a epsilon(0,1),lim(hto 0^(+)) int(h)^(1-h)f^(-a)(1...

    Text Solution

    |

  14. Let f: R->R be a twice differentiable function such that f(x+pi)=f(x) ...

    Text Solution

    |

  15. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

    Text Solution

    |

  16. If f:R→R and g:R→R be two functions defined as below, then find (fog)(...

    Text Solution

    |

  17. about to only mathematics

    Text Solution

    |

  18. Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0),x in R , wher...

    Text Solution

    |

  19. The value of int0^1 4x^3{(d^2)/(dx^2)(1-x^2)^5}dxi s

    Text Solution

    |

  20. Let f: RvecR be a continuous odd function, which vanishes exactly at o...

    Text Solution

    |