Home
Class 12
MATHS
The value of sum(r=0)^(3n-1)(-1)^r 6nC(...

The value of `sum_(r=0)^(3n-1)(-1)^r 6nC_(2r+1)3^r` is

A

`2^(3n)`

B

`2^(2n-1)`

C

`2^(6n-1)`

D

`0`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` `sum_(r=0)^(3n-1)(-1)^(r )'^(6n)C_(2r+1)3^(r )`
`="Imaginary part of" sum_(r=0)^(3n-1)(1)/(sqrt(3)i)*^(6n)C_(2r+1)(sqrt(3)i)^(2r+1)`
`=(1)/(sqrt(3)i)Im(1+sqrt(3))^(6n)`
`=(1)/(sqrt(3)i)Im(2^(6)(cos2pi+isin2pi))`
`=0`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE|Exercise Multiple Correct Answer|4 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Comprehension|11 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise JEE Previous Year|16 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|20 Videos

  • BINOMIAL THEORM

    CENGAGE|Exercise Question Bank|31 Videos

Similar Questions

Explore conceptually related problems

The value of sum_(r=0)^(3m)(-1)^(r).6mC_(2r) is

The value of sum_(r=1)^(3m)(-3)^(r-1).6mC_(2r-1) is

The value of sum_(r=0)^(n)r(n-r)(nC_(r))^(2) is equal to

The value of sum_(r=1)^(n) (2r+3)(3r+2)=

The value of sum_(r=0)^(n-1)(nC_(r))/(nC_(r)+^(n)C_(r+1)) is eqaul to

The value of sum_(n=0)^(1)sum_(i=1r<=pi)^( n)nC_(r)sC_(r) is

If the value of sum_(r=0)^(n)(2r+1)(-1)^(r) is a two digit number then the sum of digits is

Evaluate sum_(r=0)^n(r+1)^2*"^nC_r

The value of sum_(r=1)^(n)(sum_(p=0)^(n)nC_(r)^(r)C_(p)2^(p)) is equal to

CENGAGE-BINOMIAL THEOREM-Single correct Answer
  1. If a,b,c,d be four consecutive coefficients in the binomial expansion ...

    Text Solution

    |

  2. ("^(m)C(0)+^(m)C(1)-^(m)C(2)-^(m)C(3))+('^(m)C(4)+^(m)C(5)-^(m)C(6)-^(...

    Text Solution

    |

  3. The value of sum(r=0)^(3n-1)(-1)^r 6nC(2r+1)3^r is

    Text Solution

    |

  4. The coefficient of x^(50) in (x+^(101)C(0))(x+^(101)C(1)).....(x+^(101...

    Text Solution

    |

  5. In the expansion of (1+x)^(70), the sum of coefficients of odd powers ...

    Text Solution

    |

  6. The sum of all the coefficients of the terms in the expansion of (x+y+...

    Text Solution

    |

  7. The value of "^(12)C(2)+^(13)C(3)+^(14)C(4)+...+^(999)C(989) is

    Text Solution

    |

  8. If (1 +x+x^2)^25 = a0 + a1x+ a2x^2 +..... + a50.x^50 then a0 + a2 + ...

    Text Solution

    |

  9. If the sum of the coefficients in the expansion of (q+r)^(20)(1+(p-2)x...

    Text Solution

    |

  10. The sum S(n)=sum(k=0)^(n)(-1)^(k)*^(3n)C(k), where n=1,2,…. is

    Text Solution

    |

  11. If for n in I , n > 10 ;1+(1+x)+(1+x)^2++(1+x)^n=sum(k=0)^n ak*x^k ...

    Text Solution

    |

  12. Given "^(8)C(1)x(1-x)^(7)+2*^(8)C(2)x^(2)(1-x)^(6)+3*^(8)C(3)x^(3)(1-x...

    Text Solution

    |

  13. The value of 99^(50)-(99)/(1)*98^(50)+(99.98)/(1.2)97^(50)-……-(99.98)/...

    Text Solution

    |

  14. Let f(n)= (k=1)Σ^n k^2(n Ck)^ 2 then the value of f(5) equals

    Text Solution

    |

  15. The value of sum(r=1)^(n)(-1)^(r-1)((r )/(r+1))*^(n)C(r ) is

    Text Solution

    |

  16. The value of ((100),(0))((200),(150))+((100),(1))((200),(151))+......+...

    Text Solution

    |

  17. Let t(100)=sum(r=0)^(100)(1)/(("^(100)C(r ))^(5)) and S(100)=sum(r=0)^...

    Text Solution

    |

  18. Let S(1)=underset(0 le i lt j le 100)(sumsum)C(i)C(j), S(2)=underset(0...

    Text Solution

    |

  19. "^(74)C(37)-2 is divisibl by

    Text Solution

    |

  20. If "^(n)C(0)-^(n)C(1)+^(n)C(2)-^(n)C(3)+...+(-1)^(r )*^(n)C(r )=28 , t...

    Text Solution

    |