Home
Class 11
MATHS
The coefficient x^5 in the expansion of ...

The coefficient `x^5` in the expansion of `(1+x)^(21)+(1+x)^(22)+.........+(1+x)^(30)` is

A

`"^51 C_5`

B

`"^9C_5`

C

`"^31 C_6``-"^(21)C_6`

D

`"^30 C_5`+`"^(20)C_5`

Text Solution

Verified by Experts

The correct Answer is:
C
We have `(1+x)^{21}+(1+x)^{22}+ldots(1+x)^{30}`
`=(1+x)^{21}[frac{(1+x)^{10}-1}{(1+x)-1}] `
`=frac{1}{x}[(1+x)^{31}-(1+x)^{21}]`
Coefficient of `x^{5}` in the given expansion `=` Coefficient of `x^{5}` in `frac{1}{x}[(1+x)^{31}-(1+x)^{21}]`
`=` Coefficient of `x^{6}` in `[(1+x)^{31}-(1+x)^{21}]`
`\ ^{31} C_{6}-\ ^{21} C_{6}`
Promotional Banner

Topper's Solved these Questions

  • ARITHMETIC PROGRESSIONS

    RD SHARMA|Exercise Solved Examples And Exercises|248 Videos

  • BRIEF REVIEW OF CARTESIAN SYSTEM OF RECTANGULAR COORDINATES

    RD SHARMA|Exercise Solved Examples And Exercises|75 Videos

Similar Questions

Explore conceptually related problems

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

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

The coefficient of x^(r) in the expansion of (1-x)^(-2) is

The coefficient of x^(7) in the expansion of (1+x)^(9) is

Find the coefficient of x^(5) in the expansion of (1+x)^(21)+(1+x)^(22)+...+(1+x)^(30)

The coefficient of x^(r) in the expansion of (1-2x)^(-(1)/(2)) is

If coefficient of x^(21) in the expansion of (1 + x)^(21) + (1 + x)^(22) + ... + (1 + x)^(30) is ""^(31)C_(r) , where r ge 20 , then r= ___

RD SHARMA-BINOMIAL THEOREM-Solved Examples And Exercises
  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 (x^2 +k/x)^5 is 270, then k=

    Text Solution

    |

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

    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)+...........

    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+x...

    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)^9are ...

    Text Solution

    |