Home
Class 12
MATHS
If (n) is an odd positive integer and ...

If `(n)` is an odd positive integer and
`(1+x+x^(2)+x^(3))^(n) = sum_(r=0)^(3 n) a_(r) x^(r) ` then, `a_(0)-a_(1)+a_(2)-a_(3)+.. .-a_(3 n) =`

A

`4^(circ) `

B

1

C

-1

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
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+2 x+x^(2))^(n)=sum_(r=0)^(2 n) a_(r) x^(r) , then a_(r) =

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) =

Let (1+x^(2))^(2)(1+x)^(n) = sum_(k=0)^(n+4) a_(k) x^(k) . If a_(1) , a_(2) , a_(3) are in A.P., then n=

8,A_(1),A_(2),A_(3),24.

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+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+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

If sin ^(3) x sin 3 x=sum_(r=0)^(n) a_(r) cos r x is an identity in x, then n=

If a_(1), a_(2) ,a_(3)"….." is an A.P. such that : a_(1) + a_(5) + a_(10)+a_(15)+a_(20)+a_(24)=225 , then a_(1) + a_(2)+a_(3) +"….." a_(23) + a_(24) is :

HIMALAYA PUBLICATION-BINOMIAL THEOREM-QUESTION BANK
  1. The greatest term in the expansion of (1+3 x)^(54) , when x=(1)/(3) ...

    Text Solution

    |

  2. The sum of the last eight coefficients in the expansion of (1+x)^(15)...

    Text Solution

    |

  3. If C(0), C(1), C(2), C(3),.., C(n) are the binomial coefficients in t...

    Text Solution

    |

  4. Greatest term in the expansion of sqrt(3)(1+(1)/(sqrt(3)))^(20) is

    Text Solution

    |

  5. The term independent of x in expansion of ((x+1)/(x^(2//3)-x^(1//3)+1)...

    Text Solution

    |

  6. The coefficient of x^(4) in ((x)/(2)-(3)/(x^(2)))^(10) is

    Text Solution

    |

  7. The greatest coefficient in the expansion of (1+x)^(2n) is

    Text Solution

    |

  8. If the coefficients of r^(th) and (r+1)^(th) terms in the expansion o...

    Text Solution

    |

  9. The coefficient of x^(5) in the expansion of (1+x^(2))^(5).(1+x)^(4)...

    Text Solution

    |

  10. The coefficient of x^(-10)in(x^(2)-(1)/(x^(3)))^(10) is

    Text Solution

    |

  11. The approximate value of (1.0002)^(3000) is

    Text Solution

    |

  12. If (1+x+x^(2))^(n) = sum(r=0)^(2 n) a(r). x^(r) then a(1)-2 a(2)+3 a...

    Text Solution

    |

  13. The coefficient of x^(5) in the expansion of (x^(2)-x-2)^(5) is

    Text Solution

    |

  14. The total number of terms in the expansion of (x+y)^(100)+(x-y)^(100) ...

    Text Solution

    |

  15. In the binomial expansion of (1+x)^(15), the coefficients of x^(r ) an...

    Text Solution

    |

  16. If (n) is an odd positive integer and (1+x+x^(2)+x^(3))^(n) = sum(r...

    Text Solution

    |

  17. If r^(th) (r+1)^(th) terms in the expansion of (p+q)^(n) are equal ,th...

    Text Solution

    |

  18. If x^(r) occurs in the expansion of (x+(1)/(x))^(n), then is coefficie...

    Text Solution

    |

  19. If n C(1)+2. n C(2)+..n. n C(n) = 2 n^(2), then n =

    Text Solution

    |

  20. If (1 +x + x^(2))^(n) = a(0) + a(1) x + a(2) x^(2) + … + a(2n) x^(2n) ...

    Text Solution

    |