Home
Class 12
MATHS
Let x(n)=(2^(n)+3^(n))^(1//2n) for all n...

Let `x_(n)=(2^(n)+3^(n))^(1//2n)` for all natural number n.
Then

A

`lim_(n to oo)x_(n)=oo`

B

`lim_(n to oo)x_(n)=sqrt(3)`

C

`lim_(n to oo)x_(n)=sqrt(3)+sqrt(2)`

D

`lim_(n to oo)x_(n)=sqrt(5)`

Text Solution

Verified by Experts

The correct Answer is:
B
`lim_( nto oo)(3^(n))^(1//2n)(((2)/(3))^(n)+1)^(1//2n)`
Put `lim_(n to oo)sqrt(3)`
Promotional Banner

Topper's Solved these Questions

  • KVPY

    KVPY PREVIOUS YEAR|Exercise Part B- Mathematics|10 Videos

  • KVPY

    KVPY PREVIOUS YEAR|Exercise PART-1 MATHEMATICS|20 Videos

  • KVPY

    KVPY PREVIOUS YEAR|Exercise PART-II MATHEMATICS|10 Videos

  • KVPY 2021

    KVPY PREVIOUS YEAR|Exercise PART II MATHEMATICS|4 Videos

Similar Questions

Explore conceptually related problems

prove that 2nlt(n+2)! for all natural numbers n.

1+5+9+...+(4n-3)=n(2n-1) for all natural numbers n

Show that ""^(n)P_(n)=""^(n)P_(n-1) for all natural numbers n.

Let P(n) be a statement and let P(n) Rightarrow P(n+1) for all natural number n, then P(n) is true.

Prove that 1+2+2^(2)+ . . .+2^(n)=2^(n+1)-1 , for all natural number n.

Prove that 2n +1 lt 2^(n) for all natural numbers n ge3

Is 2^(3-n) a prime number for all natural numbers n?

A sequence x_(1),x_(2),x_(3),.... is defined by letting x_(1)=2 and x_(k)=(x_(k-1))/(k) for all natural numbers k,k>=2 Show that x_(n)=(2)/(n!) for all n in N.

Prove that (1)/(n+1)+(1)/(n+2)+...+(1)/(2n)>(13)/(24) ,for all natural number n>1

prove that 2+4+6+…2n=n^(2)+n , for all natural numbers n.

KVPY PREVIOUS YEAR-KVPY-Part A - Mathematics
  1. Let BC be a fixed line segment in the plane . The locus of a point A s...

    Text Solution

    |

  2. The number of solution pairs (x , y) of the simultaneous equations lo...

    Text Solution

    |

  3. The value of the limit lim(x to -oo) (sqrt(4x^(2) - x )+2x) is

    Text Solution

    |

  4. Let R be a relation on the set of all natural numbers given by a R hA...

    Text Solution

    |

  5. The fractional part of a real number x is x -[x] , where [x] is the g...

    Text Solution

    |

  6. The number of real solutions of the equation 2 sin 3x + sin 7x - 3 = 0...

    Text Solution

    |

  7. Suppose p,q,r and real number such that q=p(4-p),r=q(4-q),p=r(4-r). Th...

    Text Solution

    |

  8. The parabola y^(2)=4x+1 divides the disc x^(2)+y^(2) le 1 into two reg...

    Text Solution

    |

  9. A shooter can hit a given target with probability (1)/(4). She keeps f...

    Text Solution

    |

  10. Consider the following events: E(1): Six fair dices are rolled and at...

    Text Solution

    |

  11. For how many different values of a does the following system have at l...

    Text Solution

    |

  12. Let R be the set of real number and f:R to R be defined by f(x)=({x})/...

    Text Solution

    |

  13. Let x(n)=(2^(n)+3^(n))^(1//2n) for all natural number n. Then

    Text Solution

    |

  14. One of the solution of the equation 8 sin^(3) theta-7 sin theta+sqrt(...

    Text Solution

    |

  15. Let a,b,c,d,e, be real numbers such that a+b lt c+d , b+c lt d+e, c+d...

    Text Solution

    |

  16. If a fair coin is tossed 5 times, the porbability that heads does not ...

    Text Solution

    |

  17. Consider the following parametric equation of a curve : x(theta)=|co...

    Text Solution

    |

  18. Let A=(a(1),a(2)) " and " B=(b(1),b(2)) be two points in the plane wit...

    Text Solution

    |

  19. Let f(x) = " max " {3,x^(2),(1)/(x^(2))} for (1)/(2) le x le 2. Then t...

    Text Solution

    |

  20. Let a(i) = i+ (1)/(i) for i= 1 , 2 …………. , 20. Put p = (1)/(20) ( a(...

    Text Solution

    |