Home
Class 11
MATHS
If ""^nCr denotes the number of combinat...

If `""^nC_r` denotes the number of combinations of n things taken r at a time, then the expression `""^nC_(r+1)+""^nC_(r-1)+ 2xx""^nC_r` equals :

A

`""^(n+2)C_(r+1)`

B

`""^(n+1)C_(r)`

C

`""^(n+1)C_(r+1)`

D

`""^(n+2)C_(r)`.

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    MODERN PUBLICATION|Exercise EXERCISE|221 Videos
  • COMPLEX NUMBERS

    MODERN PUBLICATION|Exercise EXERCISE|291 Videos

Similar Questions

Explore conceptually related problems

Find the number of permutations of n things taken r at a time in which two particular things : never occur.

If ""^nC_r= ""^nC_s , then n is:

Find the number of permutations of n things, taken r at a time, in which 3 particular things : always occur.

Find the number of permutations of n things, taken r at a time, in which 3 particular things : will never occur.

Find the number of permutations of n things taken r at a time in which two particular things : always occur.

If n=7 and r= 5, then the value of ""^nC_r is :

If n=5 and r= 3, then the value of ""^nC_r is :

Find the number of permutations of n different things taken r at a time such that 3 specific things occur together ?

If 20C_(r+1)=^20C_(r-1) , then r is equal to:

MODERN PUBLICATION-BINOMIAL THEOREM-EXERCISE
  1. The number of ways in which 6 men and 5 women can sit at a round table...

    Text Solution

    |

  2. A student is to answer 10 out of 13 questions in an examination such t...

    Text Solution

    |

  3. If ""^nCr denotes the number of combinations of n things taken r at a ...

    Text Solution

    |

  4. The number of integral terms in the expansion of (sqrt3 + root(8)(5))^...

    Text Solution

    |

  5. The coefficient of t^24 in (1+t^2)^2 (1+ t^12) (1+ t^24) is:

    Text Solution

    |

  6. How many ways are there to arrange the letters in me word ‘GARDEN’ wit...

    Text Solution

    |

  7. If ^n-1Cr=(k^2-3)^n C(r+1),then k in

    Text Solution

    |

  8. The coefficient of the middle term in the binomial expansion in powers...

    Text Solution

    |

  9. Thr ciefficient of x^(n-2) in the polynomial (x-1)(x-2)(x-3)"…."(x-n),...

    Text Solution

    |

  10. If the letters of the word SACHIN are arranged in all possible ways ...

    Text Solution

    |

  11. A rectangle with sides (2m-1) and (2n -1) is divided into squares of u...

    Text Solution

    |

  12. The value of ""^50C4+ underset (r=1) overset (6) sum ""^(56-r)C3 is :

    Text Solution

    |

  13. If the coefficient of x^(7) " in " (ax^(2) + (1)/(bx))^(11) is equal ...

    Text Solution

    |

  14. The value of {:((30), (0))((30), (10))-((30), (1))((30),( 11)) +((30),...

    Text Solution

    |

  15. At an election, a voter may vote for any number of candidates not grea...

    Text Solution

    |

  16. For natural numbers m ,n ,if(1-y)^m(1+y)^n=1+a1y+a2y^2+... , and a1=a2...

    Text Solution

    |

  17. The letters of the word COCHIN are permuted and all the permutations a...

    Text Solution

    |

  18. The sum of series .^(20)C0-^(20)C1+^(20)C2-^(20)C3+....+^(20)C 10 is

    Text Solution

    |

  19. In the binomial expansion of (a -b)^n, nge5, the sum of the 5th and 6t...

    Text Solution

    |

  20. How many different words can be formed by jumbling the letters of the ...

    Text Solution

    |