Home
Class 11
MATHS
The coefficient of x^(6) in the expansi...

The coefficient of` x^(6)` in the expansion of `(1 + x + x^(2))^(-3)` is

A

6

B

5

C

4

D

3

Text Solution

Verified by Experts

The correct Answer is:
d
We have,
`(1 + x + x^(2))^(-3) = ((1 - x^(3))/(1 -x))^(-3)`
`rArr (1 + x + x^(2))^(-3) = (1 - x^(3))(1 -x^(3))^(-3)`
`rArr (1 + x + x^(2))^(-3) = (1 -3x + 3x^(2)- x^(3))(1 + 3x^(3) + 6x^(6) + ...)`
`therefore ` Coefficient of `x^(6)` in `(1 + x + x^(2))^(-3) = 6 - 3 = 3.` .
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM AND ITS APPLCIATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Assertion Reason Type|13 Videos

  • BINOMIAL THEOREM AND ITS APPLCIATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|103 Videos

  • BINOMIAL THEOREM AND ITS APPLCIATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|58 Videos

  • CARTESIAN CO-ORDINATE SYSTEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|27 Videos

Similar Questions

Explore conceptually related problems

The coefficient of x^5 in the expansion of (x+3)^8

The coefficient of x^(6) in the expansion of (1+x+x^(2))^(6) is

The coefficient of x^(4) in the expansion of (1+x+x^(2))^(6) is

The coefficient of x^(6) in the expansion of (1+x+x^(2)+x^(3))(1-x)^(6) is

The coefficient of x^(5) in the expansion of (x +3)^(6) ,is

The coefficient of x in the expansion of (x+3)^(3) is

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

The coefficient of x^(4) in the expansion of (1+x+x^(2)+x^(3))^(11) is where ({:(n),(r):}) = nC_(r)

The coefficient of x^(8) in the expansion of (1+x+x^(2)+x^(3))^(4) is

The coefficients of x^(11) in the expansion of (2x^(2)+x-3)^(6) is

OBJECTIVE RD SHARMA ENGLISH-BINOMIAL THEOREM AND ITS APPLCIATIONS -Section I - Solved Mcqs
  1. The value of sum(r=1)^(10) r. (""^(n)C(r))/(""^(n)C(r-1) is equal to

    Text Solution

    |

  2. 7^(103) when divided by 25 leaves the remainder .

    Text Solution

    |

  3. The coefficient of x^(6) in the expansion of (1 + x + x^(2))^(-3) is

    Text Solution

    |

  4. If (x^(2) + x)/(1-x) = a(1) x + a(2) x^(2) + ... to infty , |x| lt 1,...

    Text Solution

    |

  5. The sum of the series ""^(4)C(0) + ""^(5)C(1) x + ""^(6)C(2) x^(2)...

    Text Solution

    |

  6. the sum of the series ""^(2)C(0) + ""^(3)C(1) x^2 + ""^(4)C(2) x^(4)...

    Text Solution

    |

  7. If Sn=sum(r=0)^n 1/(nCr) and tn=sum(r=0)^n r/(nCr), then tn/Sn=

    Text Solution

    |

  8. If sn=sum(r < s) (1/(nCr)+1/(nCs)) and tn=sum(r < s)(r/(nCr)+s/(nCs)),...

    Text Solution

    |

  9. The coefficient of x^5 in the expansion of (x^2-x-2)^5 is -83 b. -82 c...

    Text Solution

    |

  10. If ar is the coefficient of x^r in the expansion of (1+x+x^2)^n, the...

    Text Solution

    |

  11. If n be a positive integer and Pn denotes the product of the binomial ...

    Text Solution

    |

  12. Prove that in the expansion of (1+x)^(n) (1+y)^(n) (1+z)^(n), the sum ...

    Text Solution

    |

  13. If 1/(sqrt(4x+1)){((1+sqrt(4x+1))/2)^n-((1-sqrt(4x+1))/2)^n}=a0+a1x t...

    Text Solution

    |

  14. If f(x)=x^n ,f(1)+(f^1(1))/1+(f^2(1))/(2!)+(f^n(1))/(n !),w h e r ef^r...

    Text Solution

    |

  15. the coefficient of x^(r) in the expansion of (1 - 4x )^(-1//2), is

    Text Solution

    |

  16. In the expansion of (x^(2) + 1 + (1)/(x^(2)))^(n), n in N,

    Text Solution

    |

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

    Text Solution

    |

  18. The value of ""(n)C(1). X(1 - x )^(n-1) + 2 . ""^(n)C(2) x^(2) (1 -...

    Text Solution

    |

  19. sum(r=1)^(n) {sum(r1=0)^(r-1) ""^(n)C(r) ""^(r)C(r(1)) 2^(r1)} is equ...

    Text Solution

    |

  20. The coefficients of x^(13) in the expansion of (1 - x)^(5) (1 + x...

    Text Solution

    |