Home
Class 11
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

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • ARITHMETIC PROGRESSIONS

    RD SHARMA ENGLISH|Exercise All Questions|248 Videos

  • BRIEF REVIEW OF CARTESIAN SYSTEM OF RECTANGULAR COORDINATES

    RD SHARMA ENGLISH|Exercise All Questions|77 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 .

RD SHARMA ENGLISH-BINOMIAL THEOREM-All Questions
  1. Find the term independent o f x in the expansion of the following expr...

    Text Solution

    |

  2. If A and B respectively denote the sum of the odd terms and sum of the...

    Text Solution

    |

  3. If the coefficient of x in the expansion of (x^2 +k/x)^5 is 270, then...

    Text Solution

    |

  4. The coefficient of x^4 in (x//2-3//x^2)^10 is (405)/(256) b. (504)...

    Text Solution

    |

  5. The number of terms in the expansion of (x+a)^100+(x-a)^100 after simp...

    Text Solution

    |

  6. If T2/T3 in the expansion of (a + b)^n and T3/T4 in the expansion o...

    Text Solution

    |

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

    Text Solution

    |

  8. The sum of the binomial coefficients of [2x+1/x]^n is equal to 256. Th...

    Text Solution

    |

  9. If the fifth term of the expansion (a^(2//3)+a^(-1))^n does not contai...

    Text Solution

    |

  10. The coefficient of x^(-3) in the expansion of (x-m/x)^(11) is a. -924 ...

    Text Solution

    |

  11. The coefficient of the term independent of x in the expansion of (a x+...

    Text Solution

    |

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

    Text Solution

    |

  13. The coefficient of x^8y^(10) in the expansion of (x+y)^(18) is a. \ ^(...

    Text Solution

    |

  14. If the coefficients of the (n+1)^(t h) term and the (n+3)^(t h) term i...

    Text Solution

    |

  15. If the coefficients of 2nd, 3rd and 4th terms in the expansion of (1...

    Text Solution

    |

  16. The middle term in the expansion of ((2x)/3-3/(2x^2))^(2n) is a. \ ^(2...

    Text Solution

    |

  17. If r^(th) term is the middle term in the expansion of (x^2-1/(2x))^...

    Text Solution

    |

  18. The number of terms with integral coefficients in the expansion of (...

    Text Solution

    |

  19. Constant term in the expansion of (x-1/x)^(10) is a. 152 b. -152 c. -2...

    Text Solution

    |

  20. If the coefficients of x^2a n d\ x^3 in the expansion of (3+a x)^9 are...

    Text Solution

    |