Home
Class 12
MATHS
If ak is the coefficient of x^k in the e...

If `a_k` is the coefficient of `x^k` in the expansion of `(1 +x+x^2)^n` for k = 0,1,2,……….,2n then `a_1 +2a_2 + 3a_3 + ………+2n.a_(2n) =`

A

`-a_0`

B

`3^n`

C

`n.3^n`

D

`-n.3^n`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    AAKASH SERIES|Exercise PRACTICE EXERCISE|95 Videos

  • BINOMIAL THEOREM

    AAKASH SERIES|Exercise EXERCISE - 1.1 (Level - 1) |52 Videos

  • BINOMIAL THEOREM

    AAKASH SERIES|Exercise EXERCISE - I|27 Videos

  • AREAS

    AAKASH SERIES|Exercise Exercise-3.2|21 Videos

  • CIRCLE

    AAKASH SERIES|Exercise EXERCISE -1.4|38 Videos

Similar Questions

Explore conceptually related problems

The coefficient of x^p in the expansion of (x^2+(1)/(x))^(2n) is

Find the coefficient of x^n in the expansion of (1+ 2x + 3x^2 + 4x^3 + …..)^2

The coefficient of x^(n) in the expansion of (1+ax+x^(2))/(e^(x)) is

If n=3m then the coefficient of x^(n) in the expansion of log(1+x+x^(2)) is

The coefficient of x^(n) in the expansion of log_(e)(1+3x+2x^(2)) is

If a_r is the coefficient x^r in the expansion of (1+x+x^2)^n then a_1 - 2a_2 + 3a_3 -…..-2na_(2n) =

AAKASH SERIES-BINOMIAL THEOREM-EXERCISE - II
  1. (1 +x)^15 = a0 + a1x +…..+a15 x^15 rArr sum(r = 1)^15 r (ar)/(a(r - 1)...

    Text Solution

    |

  2. The value of sum(r = 1)^15 r^2 ((""^15Cr)/(""^15C(r - 1)) ) of is equa...

    Text Solution

    |

  3. If ak is the coefficient of x^k in the expansion of (1 +x+x^2)^n for k...

    Text Solution

    |

  4. Find the sum of the following (""^(15)C(1))/(""^(15)C(0))+2(""^(15)C...

    Text Solution

    |

  5. If a0, a1 , a2 …..an are binomial coefficients then (1 + a1/a0)(1 +a2/...

    Text Solution

    |

  6. ((C0 + C1)(C1 + C2)(C2 + C3)………(C(n-1) + Cn) )/(C0C1C2…Cn)

    Text Solution

    |

  7. If (1+x)(1+x+x^2)(1+x+x^2+x^3)……(1+x+x^2+……+x^(n-1)) = a0 + a1x + a2x^...

    Text Solution

    |

  8. If (1 -x + x^2)^n = a0 +a1x + a2x^2+….+a(2n)x^(2n) then a0 + a2 +a4 +...

    Text Solution

    |

  9. If (1)/(1!(n-1)!) + (1)/(3!(n-3)!) + (1)/(5!(n-5)!) +…. =

    Text Solution

    |

  10. C0 + C1 + 2.C2(3) + 3.C3(3^2)+ 4.C4(3^3) + ……+n.Cn 3^(n-1) =

    Text Solution

    |

  11. (1 + x+x^2)^8 = a0 + a1x +…….+a16 x^16 then a0 - a2 + a4 - a6 + ……..+a...

    Text Solution

    |

  12. If ar is the coefficient x^r in the expansion of (1+x+x^2)^n then a1 -...

    Text Solution

    |

  13. If (1+2x +3x^2)^10 = a0 +a1x +a2x^2 + ……+a20x^20 then a2/a1 =

    Text Solution

    |

  14. ""^15C2 + 2.""^15C3 + 3. ""^15C4 + …..+ 14.""^15C15 =

    Text Solution

    |

  15. ""^20C10.""^15C0 + ""^20C9.""^15C1 + ""^20C8.""^15C2 + …..+""^20C0.""^...

    Text Solution

    |

  16. ""^10C1 . ""^9C5 + ""^10C2. ""^9C4 + ""^10C3. ""^9C3 + ""^10C4. ""^9C2...

    Text Solution

    |

  17. sum(r=1)^(10) r. (""^nCr)/(""^nC(r-1)) =

    Text Solution

    |

  18. sum(r = 0)^(n-1) (Cr)/(Cr + C(r+1)) =

    Text Solution

    |

  19. The sum of the coefficients in the binomial expansion of (1/x + 2x)^n ...

    Text Solution

    |

  20. If (1)/((1 - 2x)(1 + 3x)) is to tbe expanded as a power series of x, t...

    Text Solution

    |