Home
Class 12
MATHS
sum(r=0)^(n)(P(r))/(r!) is equal to...

`sum_(r=0)^(n)(P_(r))/(r!)` is equal to

A

`2^(n-1)`

B

`2^(n)`

C

`2^(n)+1`

D

`2^(n-1)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS & COMBINATIONS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|163 Videos
  • PERMUTATIONS & COMBINATIONS

    AAKASH SERIES|Exercise EXERCISE-I|60 Videos
  • PARTIAL FRACTIONS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|31 Videos
  • PROBABILITY

    AAKASH SERIES|Exercise Practise Exercise|165 Videos

Similar Questions

Explore conceptually related problems

If a_(n)=sum_(r=0)^(n)(1)/(""^(n)C_(r)) then sum_(r=0)^(n)(r)/(""^(n)C_(r)) equal to

""^(m)C_(r+1)+ sum_(k=m)^(n)""^(k)C_(r) is equal to :

If sum_(r=1)^(n)Cos^(-1)x_(r)=0," then "sum_(r=1)^(n)x_(r) equals to

If (1+x)^(n)=sum_(r=0)^(n)""^(n)C_(r )x^(r ) and if sum_(r=0)^(n) (1)/(""^(n)C_(r ))=lambda , then show that sum_(0 leilen) sum_(0 le j len) ((i)/(""^(n)C_(i)) +(j)/(""^(n)C_(j)))=n(n+1)lambda

overset(10)underset(r=0)sum^(40-r)C_(5) is equal to

""^(n-2)C_(r)+2.""^(n-2)C_(r-1)+""^(n-2)C_(r-2) is equal to

If sum_(r = 0)^(2n) a_(r ) (x-2)^(r ) = sum_(r = 0)^(2n) b_(r ) (x-3)^(r ) and a_(k ) =1 for all k ge n then show that b_(n ) =""^((2n+1)) C_((n+1)) .

AAKASH SERIES-PERMUTATIONS & COMBINATIONS-EXERCISE-II
  1. Assertion (A): The number of ways in which 5 boys and 5 girls can sit ...

    Text Solution

    |

  2. Assertion (A) : The number of ways in which 6 persons can sit around a...

    Text Solution

    |

  3. sum(r=0)^(n)(P(r))/(r!) is equal to

    Text Solution

    |

  4. If ""^(n)P(r)=""^(n)P((r+1))and ""^(n)C(r) = ""^(n)C(r-1), then (n,...

    Text Solution

    |

  5. IF ""^(n) P(r)=720,""^(n)C(r)=120then (n,r)=

    Text Solution

    |

  6. ""^(2n)C(n+1)+2. ""^(2n)C(n) + ""^(2n) C(n-1) =

    Text Solution

    |

  7. the value of ""^50C(4) + underset( r=1) overset( 6 ) sum ""^(56...

    Text Solution

    |

  8. sum( r=0 )^ ( 10) ( 40 -r)C (5)=

    Text Solution

    |

  9. If ""^(n-1)C(3)+""^(n-1)C(4)gt""^(n)C(3), then

    Text Solution

    |

  10. If ""^(n)C(4),""^(n)C(5),""^(n)C(6) are in A.P., then the value of n i...

    Text Solution

    |

  11. If ""^(n)C(r-1)=36,""^(n)C(r)=84 and ""^(n)C(r+1)=126, then r is equal...

    Text Solution

    |

  12. The value of 2^(n)n!(1.3.5.....(2n-1)) is

    Text Solution

    |

  13. If a(n)=sum(r=0)^(n)(1)/(""^(n)C(r)) then sum(r=0)^(n)(r)/(""^(n)C(r))...

    Text Solution

    |

  14. ""^(n)C(r)+4.""^(n)C(r-1)+6.""^(n)C(r-2)+4.""^(n)C(r-3)+""^(n)C(r-4) i...

    Text Solution

    |

  15. The sum sum(i=0)^(m)((10)/(i))((20)/(m-i)) is maximum when m is

    Text Solution

    |

  16. In a football championship there were played 153 matches. Every two te...

    Text Solution

    |

  17. From a group of persons the number of ways of selecting 5 persons is e...

    Text Solution

    |

  18. In a chess tournament where the participants were to play one game wit...

    Text Solution

    |

  19. A teacher takes 3 children from her class to the zoo at a time as ofte...

    Text Solution

    |

  20. From 0 to 9, four digited numbers can be formed such that the digits a...

    Text Solution

    |