Home
Class 12
MATHS
The coefficient of 1//x in the expansion...

The coefficient of `1//x` in the expansion of `(1+x)^n(1+1//x)^n` is `(n !)/((n-1)!(n+1)!)` b. `((2n)!)/((n-1)!(n+1)!)` c. `((2n)!)/((2n-1)!(2n+1)!)` d. none of these

A

`(n!)/((n-1)!(n+1)!)`

B

`(2(n)!)/((n-1)!(n+1)!)`

C

`(2(n)!)/((2n-1)!(2n+1)!)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    VMC MODULES ENGLISH|Exercise LEVEL 2|50 Videos
  • BINOMIAL THEOREM

    VMC MODULES ENGLISH|Exercise NUMERICAL VALUE TYPE FOR JEE MAIN|14 Videos
  • BINOMIAL THEOREM

    VMC MODULES ENGLISH|Exercise JEE Archive|56 Videos
  • CIRCLES

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ( ARCHIVE )|68 Videos

Similar Questions

Explore conceptually related problems

The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (a). (n !)/((n-1)!(n+1)!) (b). ((2n)!)/((n-1)!(n+1)!) (c). ((2n)!)/((2n-1)!(2n+1)!) (d). none of these

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

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

If x^m occurs in the expansion (x+1//x^2)^(2n) , then the coefficient of x^m is a. ((2n)!)/((m)!(2n-m)!) b. ((2n)!3!3!)/((2n-m)!) c. ((2n)!)/(((2n-m)/3)!((4n+m)/3)!) d. none of these

The middle term in the expansion of ((2x)/3-3/(2x^2))^(2n) is a. \ ^(2n)C_n b. (-1)^n\ ^(2n)C_(n\ )x^(-n) c. \ ^(2n)C_n x^(-n) d. none of these

If A and B are the coefficients of x^n in the expansion (1 + x)^(2n) and (1 + x)^(2n-1) respectively, then

If A and B are the coefficients of x^n in the expansion (1 + x)^(2n) and (1 + x)^(2n-1) respectively, then

The coefficient of x^(n) in the polynomial (x+""^(2n+1)C_(0))(X+""^(2n+1)C_(1)) (x+""^(2n+1)C_(2))……(X+""^(2n+1)C_(n)) is

If |x|<1, then the coefficient of x^n in expansion of (1+x+x^2+x^3+)^2 is a. n b. n-1 c. n+2 d. n+1

Prove that the term independent of x in the expansion of (x+1/x)^(2n) \ is \ (1. 3. 5 ... (2n-1))/(n !). 2^n .

VMC MODULES ENGLISH-BINOMIAL THEOREM-LEVEL 1
  1. (sum(r=0)^(10) ""^(10)C(r) ) (sum(r=0)^(10)(-1)^(m) (""^(10)C(m))/(2^(...

    Text Solution

    |

  2. The coefficient of x^n in (1+x)^(101)(1-x+x^2)^(100) is non zero, then...

    Text Solution

    |

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

    Text Solution

    |

  4. If the coefficients of 2nd, 3rd and 4th terms in the expansion of (...

    Text Solution

    |

  5. If in the expansion of (1+x)^(n),a,,b,c are three consecutive coeffici...

    Text Solution

    |

  6. The coefficient of x in the expansion of (1+x)(1+2x)(1+3x)….(1+100x) i...

    Text Solution

    |

  7. If the coefficients of three consecutive terms in the expansion of (1 ...

    Text Solution

    |

  8. Find sum of sum(r=1)^n r . C (2n,r) (a) n*2^(2n-1) (b) 2^(2n-1) (c) 2^...

    Text Solution

    |

  9. In the expansion of (1+x)^(50), find the sum of coefficients of odd po...

    Text Solution

    |

  10. If (1+x) ^(15) =a(0) +a(1) x +a(2) x ^(2) +…+ a(15) x ^(15), then the ...

    Text Solution

    |

  11. If ( 1 + x - 2x^(2))^(20) = sum(r=0)^(40) a(r) x^(r) , then find ...

    Text Solution

    |

  12. ""^(n-2)C(r)+2""^(n-2)C(r-1)+""^(n-2)C(r-2) equals :

    Text Solution

    |

  13. ""^(15)C(8) + ""^(15)C(9) - ""^(15)C(6) - ""^(15)C(7) is equal to ………....

    Text Solution

    |

  14. If ""^(18)C(15)+2(""^(18)C(16))+""^(17)C(16)+1=""^(n)C(3), then n is e...

    Text Solution

    |

  15. Let (1 + x)^(n) = sum(r=0)^(n) a(r) x^(r) . Then ( a+ (a(1))/(a(0))...

    Text Solution

    |

  16. sum(r=0)^(n-1) (""^(n)C(r))/(""^(n)C(r) + ""^(n)C(r+1)) is equal to

    Text Solution

    |

  17. Find the coefficient of x^7 in the expansion of (1 - x -x^2 + x^3)^(6)...

    Text Solution

    |

  18. Statement - 1 sum(r=0)^(n) (r + 1) ""^(n)C(r) = (n+2)*2^(n-1) Stat...

    Text Solution

    |

  19. if n>=2, ""^(n+1)C(2)+2(""^(2)C(2)+""^(3)C(2)+""^(4)C(2)+....+""^(n)...

    Text Solution

    |

  20. In the coefficients of rth, (r+1)t h ,a n d(r+2)t h terms in the binom...

    Text Solution

    |