Home
Class 12
MATHS
If n is a positive integer then the coef...

If n is a positive integer then the coefficient of `x ^(-1)` in the expansion of `(1+x) ^(n) (1+ (1)/(x)) ^(n)` is-

A

`((2n)!)/((n!)^(2))`

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • MCQ's

    CHHAYA PUBLICATION|Exercise QUESTION PAPER 6|90 Videos

  • MCQ's

    CHHAYA PUBLICATION|Exercise QUESTION PAPER 9|66 Videos

  • MCQ's

    CHHAYA PUBLICATION|Exercise QUESTION PAPER 7|90 Videos

  • MCQ ZONE 3

    CHHAYA PUBLICATION|Exercise Question Paper 8|30 Videos

  • Measures of Central Tendency

    CHHAYA PUBLICATION|Exercise Exercise 2 C Very short answer type question|18 Videos

Similar Questions

Explore conceptually related problems

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

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

Coefficient of x^n in the expansion of (1+x)^(2n) is

Coefficient of x^n in the expansion of (a+x)^(2n)

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

Find the coefficient of x^n in the expansion of (1-9x+20 x^2)^(-1)dot

Let m be the smallest positive integer such that the coefficient of x^2 in the expansion of (1+x)^2 + (1 +x)^3 + (1 + x)^4 +........+ (1+x)^49 + (1 + mx)^50 is (3n + 1) .^51C_3 for some positive integer n. Then find the value of n.

Let , m be the the smallest positive interger such that the coefficient of x^(2) in the expansion of (1+x)^(2)+(1+x)^(3)+....+(1+x)^(49)+(1+mx)^(50) " is " (3n+1)^(51)C_(3) for some positive integer n . Then the value of n is ,

The coefficient of x^ny^n in the expansion of {(1+x)(1+y)(x+y)}^n is

The coefficient of the middle term in the expansion of (1+x)^(2n) is

CHHAYA PUBLICATION-MCQ's-QUESTION PAPER 8
  1. If x = sum (n =0) ^(oo) a^(n) , y = sum (n=0) ^(oo) b ^(n), z= sum (n=...

    Text Solution

    |

  2. If n is a natural number, then [7 ^(2n)+2^(3(n-1)), 3 ^(n=-1)] is alwa...

    Text Solution

    |

  3. If n is a positive integer then the coefficient of x ^(-1) in the expa...

    Text Solution

    |

  4. The number of numbers that can be formed using the digits 3,4,5,6,7 (r...

    Text Solution

    |

  5. A point P which represents a complex number z, moves such that |z-z(1)...

    Text Solution

    |

  6. Solution set of the inequation |(2)/(x-4)| gt 1 (x ne 4) is-

    Text Solution

    |

  7. If the 5th term of a G.P. is x, then the product of its first nine ter...

    Text Solution

    |

  8. The sum of first n terms of the series 1^(2)+ 2 . 2^(2) + 3^(2) + 2. 4...

    Text Solution

    |

  9. If ""^(-3) ^(n)C(r+1) then-

    Text Solution

    |

  10. omega is an imaginary cube root of unity. If (1+ omega ^(2)) ^(m)=(1+o...

    Text Solution

    |

  11. Locus of mid-point of the portionof the line x cos alpha + y sin alpha...

    Text Solution

    |

  12. A ray of light is sent along the lie x-2y+5=0, upon reaching the line ...

    Text Solution

    |

  13. The coordinates of O , A and B are (0,0) , (x,y) and (y,x) respectivel...

    Text Solution

    |

  14. If t is a variable parameter, then the equation to the locus defined b...

    Text Solution

    |

  15. A circel cuts intercepts of lenghts 2a and 2b from the x-axis and the ...

    Text Solution

    |

  16. The ordinate of the centre of the circle passing through (0,0) and (1,...

    Text Solution

    |

  17. The sides of a triangle are 3x+4y, 4x +3y and 5x +5y where, x, y gt 0,...

    Text Solution

    |

  18. The triangle formed by joining the points (x,y,z), (y,z,x) and (z,x,y)...

    Text Solution

    |

  19. The sum of the focal distances of any point on the conic 16x^(2) + 25 ...

    Text Solution

    |

  20. Without rotation of axes if the origin is shifted to the point ((ab)/(...

    Text Solution

    |