Home
Class 12
MATHS
If (1+x+x^(2))^(n) = a(0)+a(1) x+a(2) x^...

If `(1+x+x^(2))^(n) `= `a_(0)+a_(1) x+a_(2) x^(2)+.. .+a_(2 n) x^(2 n) ` then the value of `a_(0)+a_(3)+a_(6)+.. ` . . is

A

(3^(n)-1)/(2)

B

(3^(n)+1)/(2

C

3^(n)+(1)/(2

D

3^(n)-(1)/(2)

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DIFFERENTIATION

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|221 Videos

  • CIRCLES

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|272 Videos

Similar Questions

Explore conceptually related problems

If (1+x+x^(2))^(n) = a_(0)+a_(1) x+a_(2) x^(2)+..+a_(2 n) x^(2 n) then the value of a_(1)+a_(4)+a_(7)+.. . . is

If (1 +x + x^(2))^(n) = a_(0) + a_(1) x + a_(2) x^(2) + … + a_(2n) x^(2n) , then a_(0) + a_(2) + a_(4) + … + a_(2n) equals

If (1+2 x+x^(2))^(n)=sum_(r=0)^(2 n) a_(r) x^(r) , then a_(r) =

If (1+x-2 x^(2))^(6)=1+a_(1) x+a_(z) x^(2)+l .. .+a_(12) x^(12) then a_(2)+a_(4)+..+a_(12) =

If 1, a_(1), a_(2). ..., a_(n-1) are n roots of unity, then the value of (1 - a_(1)) (1 - a_(2)) .... (1 - a_(n-1)) is :

Let n in N . If (1+x)^(n)=a_(0)+a_(1)x+a_(x)x^(2)+ . . . .+a_(n) x^(n) and a_(n-3),a_(n-2),a_(n-2),a_(n-1) are in A.P. then:

Let alpha and beta be the roots of equation x^(2) - 6x -2 = 0 . If a_(n) = a^(n) - beta^(n), for n ge l , then the value of (a_(10) - 2 a_(8))/(2 a_(9)) is equal to :

If (1+x+x^(2))^(n) = sum_(r=0)^(2 n) a_(r). x^(r) then a_(1)-2 a_(2)+3 a_(3)-..-2 n. a_(2n) =

If a_(1)=2 and a_(n)=2a_(n-1)+5 for ngt1 , the value of sum_(r=2)^(5)a_(r) is

The number of real roots of : 1 + a_(1)X + a_(2) x^(2) .... + a_(n) x^(n) = 0 , where |x| lt (1)/(3) and | a_(n) | lt 2 , is :

HIMALAYA PUBLICATION-BINOMIAL THEOREM-QUESTION BANK
  1. If the coefficients of r^(th) and (r+1)^(th) term in the expansion o...

    Text Solution

    |

  2. Sum of the odd binomial coefficients of (1+x)^(50) is

    Text Solution

    |

  3. If (1+x+x^(2))^(n) = a(0)+a(1) x+a(2) x^(2)+.. .+a(2 n) x^(2 n) then ...

    Text Solution

    |

  4. The coefficient of the term independent of x in the expansion of (sqrt...

    Text Solution

    |

  5. If C(0),C(1),C(2), . . . .,C(n) are binomial coefficients of order n,...

    Text Solution

    |

  6. The sum of the coefficients in the expansion of (1+x-3x^(2))^(3148)

    Text Solution

    |

  7. The middle term in the expansion of((x-(1))/(x))^(18) is...

    Text Solution

    |

  8. If the value of C(0)+2C(1)+3C(2)+ . . .+(n+1)C(n)=576, then n is

    Text Solution

    |

  9. The ninth term of the expansion((3x) (-1)/(2x))^(8) is

    Text Solution

    |

  10. The coefficient of x^(5) in (1+x^(2))^(5)(1+x)^(4) is

    Text Solution

    |

  11. If the coefficient of the r^(th) term and the (r+1)^ (th) term is th...

    Text Solution

    |

  12. The co-efficient of x^(-9) in the expansion of ((x^(2))/(2)-(2)/(x)...

    Text Solution

    |

  13. Let (1+x^(2))^(2)(1+x)^(n) = sum(k=0)^(n+4) a(k) x^(k) . If a(1) , a...

    Text Solution

    |

  14. If in the expansion of (1+x)^(m)(1-x)^(n) the coefficients of x and x^...

    Text Solution

    |

  15. The term independent of x in the expansion of (x^(2)-(1)/(x))^(6) ...

    Text Solution

    |

  16. sum(r=0)^(m)( n+r )C(n)=

    Text Solution

    |

  17. If (1+2 x+x^(2))^(n)=sum(r=0)^(2 n) a(r) x^(r), then a(r) =

    Text Solution

    |

  18. (C(0))/(1)-(C(1))/(2)+(C(2))/(3)+.. . .+((-1)^(n))/(n+1). C(n) =

    Text Solution

    |

  19. The value of C(1)+4C(2)+7C(3)+ . . .+(2n-2)C(n) is

    Text Solution

    |

  20. If T, denotes the r^(th) term in the expansion of (x+(1)/(y))^(23)...

    Text Solution

    |