Home
Class 12
MATHS
The coefficient of x^(n) in the expansi...

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

A

`(-1)^(a-1).(n-1)^(2) `

B

`(-1)^(n)(1-n) `

C

`n-1 `

D

`(-1)^(n-1). n `

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

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

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

The coefficients of x^(n) in the expansion of (1+x)^(2n) and (1+x)^(2n-1) are in the ratio

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

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

The coefficient of x^(3) in the expansion of (1-x+x^(2))^(5) is

The coefficient of x^(5) in the expansion of (1+x)^(21)+(1+x)^(22)+.. .+(1+x)^(30) is

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

The coefficient of x^(7) in the expansion of (1-x-x^(2)+x^(3))^(6) is:

HIMALAYA PUBLICATION-BINOMIAL THEOREM-QUESTION BANK
  1. The coefficient of x^(5) in the expansion of (x^(2)-x-2)^(5) is

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. Coefficient of t^(24) in (1+t^(2))^(12)(1+t^(12))(1+t^(24)) is:

    Text Solution

    |

  12. In the expansion of (1+x)^(50), the sum of the coefficients of odd pow...

    Text Solution

    |

  13. Given the integers rgt1,ngt2 and coefficients of (3r)th and (r+2)nd te...

    Text Solution

    |

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

    Text Solution

    |

  15. The coefficient of x^(4) in the expansion of ((x)/(2)-(3)/(x^(2)))^(...

    Text Solution

    |

  16. In the expansion of (1+x)^(n) , coefficients of 2^(text (nd )) 3^(r...

    Text Solution

    |

  17. The coefficients of x in the expansion of (x^(2)+(c)/(x))^(5) is equ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |