Home
Class 11
MATHS
Determine n if (i) .^(2n) C2: "^n C2=...

Determine n if
(i) ` .^(2n) C_2: "^n C_2=12 :1`
(ii) `.^(2n) C_3: "^n C_3=11 :1`

Text Solution

Verified by Experts

The correct Answer is:
`n = 2`
Promotional Banner

Topper's Solved these Questions

  • PERMUTATION AND COMBINATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise G|34 Videos

  • PERMUTATION AND COMBINATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise H|10 Videos

  • PERMUTATION AND COMBINATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise E|8 Videos

  • MATHEMATICAL REASONING

    NAGEEN PRAKASHAN ENGLISH|Exercise Misellaneous exercise|7 Videos

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 4.1|1 Videos

Similar Questions

Explore conceptually related problems

Determine n if (i) ""^(2n)C_(3) : ""^(n)C_(3) = 12:1 (ii) ""^(2n)C_(3): ""^(n)C_(3)= 11:1

Find n if (^(2n)C_2)/(^(n)C_2)= 12:1

If C (2n,3) : C ( n,2)=12 : 1 find n,

If .^(2n)C_(3):^(n)C_(3)=11:1 , find the value of n.

Prove that .^n C_0 . ^(2n) C_n- ^n C_1 . ^(2n-2)C_n+^n C_2 . ^(2n-4)C_n-=2^ndot

Prove that: (i) r.^(n)C_(r) =(n-r+1).^(n)C_(r-1) (ii) n.^(n-1)C_(r-1) = (n-r+1) .^(n)C_(r-1) (iii) .^(n)C_(r)+ 2.^(n)C_(r-1) +^(n)C_(r-2) =^(n+2)C_(r) (iv) .^(4n)C_(2n): .^(2n)C_(n) = (1.3.5...(4n-1))/({1.3.5..(2n-1)}^(2))

If C_(0), C_(1), C_(2),..., C_(n) denote the binomial coefficients in the expansion of (1 + x)^(n) , then . 1^(2). C_(1) - 2^(2) . C_(2)+ 3^(2). C_(3) -4^(2)C_(4) + ...+ (-1).""^(n-2)n^(2)C_(n)= .

If C_(0),C_(1), C_(2),...,C_(n) denote the cefficients in the expansion of (1 + x)^(n) , then C_(0) + 3 .C_(1) + 5 . C_(2)+ ...+ (2n + 1) C_(n) = .

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n) , prove that C_(0)^(2) - C_(1)^(2) + C_(2)^(2) -…+ (-1)^(n) *C_(n)^(2)= 0 or (-1)^(n//2) * (n!)/((n//2)! (n//2)!) , according as n is odd or even Also , evaluate C_(0)^(2) - C_(1)^(2) + C_(2)^(2) - ...+ (-1)^(n) *C_(n)^(2) for n = 10 and n= 11 .

The value of determinant |[ ^n C_(r-1), ^n C_r, (r+1)^(n+2)C_(r+1)],[ ^n C_r, ^n C_(r+1),(r+2)^(n+2)C_(r+2)],[ ^n C_(r+1), ^n C_(r+2), (r+3)^(n+2)C_(r+3)]| is n^2+n-2 b. 0 c. ^n+3C_(r+3) d. ^n C_(r-1)+^n C_r+^n C_(r+1)

NAGEEN PRAKASHAN ENGLISH-PERMUTATION AND COMBINATION -Exercise F
  1. If .^(16)C(r) = .^(16)C(r+6), then find .^(5)C(r).

    Text Solution

    |

  2. Determine n if (i) ^2n C2:^n C2=12 :1 (ii) ^2n C3:^n C3=11 :1

    Text Solution

    |

  3. Determine n if (i) .^(2n) C2: "^n C2=12 :1 (ii) .^(2n) C3: "^n C...

    Text Solution

    |

  4. Determine n if (i) ^2n C2:^n C2=12 :1 (ii) ^2n C3:^n C3=11 :1

    Text Solution

    |

  5. If .^(15)C(r): .^(15)C(r-1) = 1:5, then find r.

    Text Solution

    |

  6. If .^(n-1)P3 :^(n+1)P3 = 5 : 12, find n.

    Text Solution

    |

  7. If .^(n)P(r) = 720 and .^(n)C(r) = 120, then find r. .

    Text Solution

    |

  8. If .^(n+1)C(r+1.): ^nCr: ^(n-1)C(r-1)=11:6:3 find the values of n and ...

    Text Solution

    |

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

    Text Solution

    |

  10. If alpha=\ \ ^m C2,\ then find the value of \ ^(alpha)C2dot

    Text Solution

    |

  11. In how many ways can a team of 11 players be selected from 14 players?

    Text Solution

    |

  12. In how many ways 2 persons can be selected from 4 persons?

    Text Solution

    |

  13. In how many ways can a person invites his 2 or more than 2 friends out...

    Text Solution

    |

  14. In how many ways can 11 players be selected from 14 players if (i) a...

    Text Solution

    |

  15. In how many ways can 5 subjects be chosen from 9 subjects if three sub...

    Text Solution

    |

  16. In how many ways can 4 books be chosen from 12 books if (i) there is...

    Text Solution

    |

  17. A bag contains 5 black and 6 red balls. Determine the number of way...

    Text Solution

    |

  18. In 25 cricket players, there are 10 batsmen, 9 bowlers, 4 all-rounders...

    Text Solution

    |

  19. There are 8 math's books and 6 science books in a almirah. In how many...

    Text Solution

    |

  20. There are 3 parts A,B and C in a question paper of Math's, which inclu...

    Text Solution

    |