Home
Class 12
MATHS
If (1+x+x^(2))^(n) = sum(r=0)^(2 n) 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) `=

A

a)0

B

b)1

C

c) `n `

D

d) `-n `

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 (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) =

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=

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

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

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 (1+x)^(n)=sum_(r=0)^(n)a_(r)x^(r) and b_(r)=1+(a_(r))/(a_(r-1)), and prod_(r=1)^(n)b_(r)=((101)^(100))/(100!) then n 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_(1)+a_(4)+a_(7)+.. . . is

If a_(n) = (n^(2))/(2^(n)) , then find a_(7) .

HIMALAYA PUBLICATION-BINOMIAL THEOREM-QUESTION BANK
  1. If C(0), C(2), C(4).. . are the binomial coefficients in the expansi...

    Text Solution

    |

  2. The largest term in the expansion of (3+2x)^(50) where x=1/5 is:

    Text Solution

    |

  3. 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

    |

  4. If C(n) is the coefficient of x^(n) in the expansion of (1+x)^(n) ...

    Text Solution

    |

  5. Term independent of x in (2 x^(2)+(3)/(x^(3)))^(15) is

    Text Solution

    |

  6. The coefficients of the middle term in the expansion of (1+x)^(40) is

    Text Solution

    |

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

    Text Solution

    |

  8. The coefficients of x^(-n) in (1+x)^(n)(1+(1)/(x))^(n) is

    Text Solution

    |

  9. The sum of the coefficients in the expansion of (1+x-3 x^(2))^(171) i...

    Text Solution

    |

  10. If (1+x)^(n) = C(0)+C(1).x+C(2). x^(2)+..+C(n). x^(n) then C(0)+2. ...

    Text Solution

    |

  11. In the expansion of (1+x)^(n) the coefficients of pth and (p+1)^(t...

    Text Solution

    |

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

    Text Solution

    |

  13. The first three terms in the expansion of (1+a x)^(n ne 0) are 1,6 x...

    Text Solution

    |

  14. The coefficient of x^(n) in the expansion of (1+x)(1-x)^(n) is

    Text Solution

    |

  15. The coeffient of the middle term in the binomial expansion in powers o...

    Text Solution

    |

  16. The number of integral terms in the expansion of (sqrt(3)+root(8)(5))^...

    Text Solution

    |

  17. If the coefficient of rth, (r+1)th and (r+2)th terms in the binomial e...

    Text Solution

    |

  18. If the coefficient of x^(7) in [ax^(2)+((1)/(bx))]^(11) equals the coe...

    Text Solution

    |

  19. Let nge5 and bne0. In the binomial expansion of (a-b)^(n), the sum of ...

    Text Solution

    |

  20. The coefficient of x^(53) is sum(r=0)^(100) 100 C(r).(x-3)^(100-r). ...

    Text Solution

    |