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|10 Videos

  • CIRCLE

    CENGAGE|Exercise MATRIX MATCH TYPE|6 Videos

Similar Questions

Explore conceptually related problems

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

Find the coefficient of x^(6) in the expansion of (3+2x)^(10) .

The coefficient of x^(10) in the expansion of (1+x^2-x^3)^8 is 476 b. 496 c. 506 d. 528

The coefficient of x^5 in the expansion of (x^2-x-2)^5 is -83 b. -82 c. -86 d. -81

Coefficient of x^(11) in the expansion of (1+x^2)^4(1+x^3)^7(1+x^4)^(12) is 1051 b. 1106 c. 1113 d. 1120

The coefficient of x^2y^3 in the expansion of (1-x+y)^(20) is (20 !)/(213 !) b. -(20 !)/(213 !) c. (20 !)/(15!2!3!) d. none of these

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

Find the coefficient of a^3b^4c^5 in the expansion of (b c+c a+a b)^6dot

The sum of the coefficients of even power of x in the expansion of (1+x+x^2+x^3)^5 is a. 256 b. 128 c. 512 d. 64

Maximum sum of coefficient in the expansion of (1-xsintheta+x^2)^n is 1 b. 2^n c. 3^n d. 0

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. The coefficient of x^n in (1+x)^(101)(1-x+x^2)^(100) is nonzero, then ...

    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+x^2-x^3+...+x^(15)+x^(16)-x^(17) , then the coefficient of...

    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 coef...

    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...

    Text Solution

    |

  19. The value of ^20 C0+^(20)C1+^(20)C2+^(20)C3+^(20)C4+^(20)C 12+^(20)C 1...

    Text Solution

    |

  20. The sum of series ^(20)C0-^(20)C1+^(20)C2-^(20)C3++^(20)C 10 is

    Text Solution

    |