Home
Class 12
MATHS
The 13^(th) term in the expanion of (x^(...

The `13^(th)` term in the expanion of `(x^(2)+2//x)^(n)` is independent of `x` then the sum of the divisiors of `n` is

A

`36`

B

`37`

C

`38`

D

`51`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` `13^(th)` term in expansion `(x^(2)//2x)^(n)` is
`.^(n)C_(12)(x^(2))^(n-12)(2//x)^(12)=^(n)C_(12)x^(2n-36)`
Given `13^(th)` term is independent of `x`
`:.n=18`
`:. ` Divisors of `18` are `1,2,3,6,9,12,18` sum of which is `51`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE|Exercise Multiple Correct Answer|4 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Comprehension|11 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise JEE Previous Year|16 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|20 Videos

  • BINOMIAL THEORM

    CENGAGE|Exercise Question Bank|31 Videos

Similar Questions

Explore conceptually related problems

n th term in the expansion of (x+(1)/(x))^(2n)

The fourth term in the binomial expansion of (x^2 - (1)/(x^3) )^n is independent of x , when n is equal to

I the expansinof (x^2+2/x)6n for positive integer n has 13th term independent of x, then the sum of divisors of n is (A) 36 (B) 38 (C) 39 (D) 32

Find the (r+1) th term in the expansion of ((x)/(a)-(a)/(x))^(2n)

If the expansion of (x - (1)/(x^(2)))^(2n) contains a term independent of x, then n is a multiple of 2.

If 6^(th) term in the expansion of ((3)/(2)+(x)/(3))^(n) is numerically greatest, when x=3 , then the sum of possible integral values of 'n' is

CENGAGE-BINOMIAL THEOREM-Single correct Answer
  1. Coefficient of x^(6) in (1+x)(1+x^(2))^(2)(1+x^(3))^(3)…(1+x^(n))^(n) ...

    Text Solution

    |

  2. The term independent of x in the product (4 + x + 7x^2)(x-3/x)^11 is

    Text Solution

    |

  3. The 13^(th) term in the expanion of (x^(2)+2//x)^(n) is independent of...

    Text Solution

    |

  4. Coefficient of x^(2009) in (1+x+x^(2)+x^(3)+x^(4))^(1001) (1-x)^(1002)...

    Text Solution

    |

  5. If the constant term in the binomial expansion of (x^2-1/x)^n ,n in N...

    Text Solution

    |

  6. If p^(4)+q^(3)=2(p gt 0, q gt 0), then the maximum value of term indep...

    Text Solution

    |

  7. In the expansion of (x^3-1/(x^2))^n ,n in N , if the sum of the coeff...

    Text Solution

    |

  8. Find the coefficient of t^8 in the expansion of (1+2t^2-t^3)^9.

    Text Solution

    |

  9. The term independent of 'x' in the expansion of (9x-(1)/(3sqrt(x)))^(1...

    Text Solution

    |

  10. In the expansion of ((x)/(costheta)+(1)/(xsintheta))^(16), if l(1) is ...

    Text Solution

    |

  11. If A(i,j) be the coefficient of a^i b^j c^(2010-i-j) in the expansion ...

    Text Solution

    |

  12. The coefficient of x^(301 ub the expansion of (1+x)^(500)+x(1+x)^(499)...

    Text Solution

    |

  13. The coefficient of x^70 in the product (x-1)(x^2-2)(x^3-3)....(x^12-12...

    Text Solution

    |

  14. Given (1-x^(3))^(n)=sum(k=0)^(n)a(k)x^(k)(1-x)^(3n-2k) then the value ...

    Text Solution

    |

  15. Find the sum of the roots (real or complex) of the equation x^2001 + (...

    Text Solution

    |

  16. If the 4^(th) term of {sqrt(x^((1)/(1+log(10)x)))+root(12)(x)}^(6) is ...

    Text Solution

    |

  17. The number of distinct terms in the expansion of (x+y^(2))^(13)+(x^(2)...

    Text Solution

    |

  18. The value of sum(r=1)^n(sum(p=0)^(r-1) ^nCr ^rCp 2^p) is equal to

    Text Solution

    |

  19. If in the expansion of (x^(3)-(2)/(sqrt(x)))^(n) a term like x^(2) exi...

    Text Solution

    |

  20. In (3 3+1/(3 3))^n if the ratio of 7th term from the beginning to the ...

    Text Solution

    |