Home
Class 12
MATHS
The coefficient of x^(301 ub the expansi...

The coefficient of `x^(301` ub the expansion of `(1+x)^(500)+x(1+x)^(499)+x^(2)(1+x)^(498)+…+x^(500)` is

A

`"^(501)C_(301)`

B

`"^(500)C_(301)`

C

`"^(501)C_(300)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` The given series
`S=(1+x)^(500)[1+(x)/(1+x)+((x)/(1+x))^(2)+....+((x)/(1+x))^(500)]`
`=(1+x)^(500)xx(1-((x)/(1+x))^(501))/(1-(x)/(1+x))`
`=(1+x)^(501)-x^(501)`
Hence, the coefficient of `x^(301)` in `S=^(501)C_(301)`.
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|10 Videos

  • CIRCLE

    CENGAGE|Exercise MATRIX MATCH TYPE|6 Videos

Similar Questions

Explore conceptually related problems

The coefficient of x^(4) in the expansion of (1 + x + x^(2) + x^3)^(11) is

The expansion of (1-x)^-2 is?

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

Find the coefficient of x^5 in the expansion of (1+x^2)^5 (1+x)^4

The coefficient of x^(-9) in the expansion of (x^(2)/2 - 2/x)^(9) is

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

Find the coefficient of x^(8) in the expansion of (1-2x)^(- 1/2) .

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

The coefficient of x^(4) in the expansion of (x/2-3/x^(2))^(10) is

CENGAGE-BINOMIAL THEOREM-Single correct Answer
  1. In the expansion of ((x)/(costheta)+(1)/(xsintheta))^(16), if l(1) is ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  12. The number of distinct terms in the expansion of is (x^(3)+(1)/(x^(3))...

    Text Solution

    |

  13. If r^[th] and (r+1)^[th] term in the expansion of (p+q)^n are equal, ...

    Text Solution

    |

  14. If (3+asqrt2)^100+(3+bsqrt2)^100=7+5sqrt2 number of pairs (a, b) for...

    Text Solution

    |

  15. The coefficient of the middle term in the expansion of (x + 2y)^(6) is

    Text Solution

    |

  16. The algebraically second largest term in the expansion of (3-2x)^(15) ...

    Text Solution

    |

  17. If 6^(th) term in the expansion of ((3)/(2)+(x)/(3))^(n) is numericall...

    Text Solution

    |

  18. Let (5 + 2sqrt6)^n= p+ f, where n in N and p in N and 0<f<1, then the ...

    Text Solution

    |

  19. The sum of last 3 digits of 3^100 is

    Text Solution

    |

  20. The remainder when 27^(10)+7^(51) is divided by 10

    Text Solution

    |