Home
Class 12
MATHS
The coefficient of x^(28) in the expansi...

The coefficient of `x^(28)` in the expansion of `(1+x^3-x^6)^(30)` is `1` b. `0` c. `^30 C_6` d. `^30 C_3`

A

1

B

0

C

`.^(30)C_(6)`

D

`.^(30)C_(3)`

Text Solution

Verified by Experts

The correct Answer is:
B
`(1+x^(3)-x^(6))^(30)`
`= {1+x^(3)(1-x^(3))}^(30)`
`=.^(30)C_(0) + .^(30)C_(1)x^(3)(1-x^(3))+.^(30)C_(2)x^(6)(1-x^(3))^(2) + "…."`
Obviously, each term will contain `x^(3m), m in N`. But 28 is not divisible by 3. Therefore ther will be no term containing `x^(28)`.
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise (Multiple)|27 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise (Comprehension)|20 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise 8.8|10 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|20 Videos

  • BINOMIAL THEORM

    CENGAGE|Exercise Question Bank|31 Videos

Similar Questions

Explore conceptually related problems

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

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

The coefficient x^(6) in the expansion (1+x^(2)-x^(3))^(8) is

The term with coefficient 6C_(2) in the expansion of (1+x)^(6)

The largest coefficient in the expansion of (1 + x)^(30) is.......

The A.M of the coefficient of the expansion (1+x)^(30) is

The A.M of the coefficient of the expansion (1+x)^(30) is

CENGAGE-BINOMIAL THEOREM-Exercise (Single)
  1. The coefficient of x^(10) in the expansion of (1+x^2-x^3)^8 is 476 b. ...

    Text Solution

    |

  2. If the coefficient of x^(n) in (1+x)^(101) (1+x^(3)-x^(6))^(30) is

    Text Solution

    |

  3. The coefficient of x^(28) in the expansion of (1+x^3-x^6)^(30) is 1 b....

    Text Solution

    |

  4. The coefficient of a^8b^4c^9d^9 in (a b c+a b d+a c d d+b c d)^(10) is...

    Text Solution

    |

  5. In the expansion of (1+ x + 7/x)^11find the term not containing x.

    Text Solution

    |

  6. The coefficient of x^(7) in the expansion of (1-x-x^(3)+x^(4))^(8) is ...

    Text Solution

    |

  7. Sum of the coefficients of terms of degree 13 in the expansion of(1+x)...

    Text Solution

    |

  8. The coefficient of x^2y^3 in the expansion of (1-x+y)^(20) is (20 !)/(...

    Text Solution

    |

  9. If coefficient of a^2b^3c^4in(a+b+c)^m(w h e r em in N)i sL(L!=0) , t...

    Text Solution

    |

  10. The coefficient of x^r[0lt=rlt=(n-1)] in lthe expansion of (x+3)^(n-1)...

    Text Solution

    |

  11. If (1+2x+3x^2)^(10)=a0+a1x+a2x^2++a(20)x^(20),t h e na1 equals 10 b. 2...

    Text Solution

    |

  12. If f(x)=1-x^2-x^3++^(15)+x^(16)-x^(17) , then the coefficient of x^2in...

    Text Solution

    |

  13. Let f(x0=a0+a1x+a2x^2++an x^n+ and (f(x))/(1-x)=b0+b1x+b2x^2++bn x^n+ ...

    Text Solution

    |

  14. Statement 1: The coefficient of x^n is (1+x+(x^2)/(2!)+(x^3)/(3!)++(x^...

    Text Solution

    |

  15. In the expansion of (3^(-x//4)+3^(5x//4))^n the sum of binomial coeffi...

    Text Solution

    |

  16. The sum of the coefficients of even power of x in the expansion of (1+...

    Text Solution

    |

  17. Maximum sum of coefficient in the expansion of (1-xsintheta+x^2)^n is ...

    Text Solution

    |

  18. If the sum of the coefficients in the expansion of (a+b)^n is 4096, th...

    Text Solution

    |

  19. The value of .^(20)C(10)+.^(20)C(1)+.^(20)C(2)+.^(20)C(3)+.^(20)C(4)+....

    Text Solution

    |

  20. The sum of the series C 20()0-C 20()1+C 20()2-C 20()3+...-...+C 20()(1...

    Text Solution

    |