Home
Class 12
MATHS
The sum of all the coefficients of the ...

The sum of all the coefficients of the expansion of `(a+b+c+d)^(8)` which contains b but not c is (a) 729 (b) 6305 (c) 665 (d) 1024

A

729

B

3367

C

665

D

1024

Text Solution

Verified by Experts

The correct Answer is:
C
Sum of coefficient which contains a but not b
`=` Number of ways of distributing six distinct object in three boxes (a,c,d)
- Number of ways of distributing siz distinct objects in to boxes `(c,d)`
`= 3^(6) - 2^(6) = 665`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Matrix|4 Videos

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Numerical|25 Videos

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|27 Videos

  • AREA

    CENGAGE PUBLICATION|Exercise Comprehension Type|2 Videos

  • CIRCLE

    CENGAGE PUBLICATION|Exercise For problems 3 and 4|2 Videos

Similar Questions

Explore conceptually related problems

The sum of all the coefficients of the terms in the expansion of (x+y+z+w)^(6) which contain x but not y , is (a) 3^(6) (b) 2^(6) (c) 3^(6)-2^(6) (d) none of these

The coefficient of a^3b^4c in the expansion of (1+a-b+c)^9 is equal to

If the sum of the coefficients in the expansion of (a+b)^n is 4096, then the greatest coefficient in the expansion is a. 924 b. 792 c. 1594 d. none of these

If the sum of the coefficients in the expansion of (a+b)^(n) is 4096, then the greatest coefficient in the expansion is-

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 a^8b^4c^9d^9 in (a b c+a b d+a c d +b c d)^(10) is

If the sum of the coefficients in the expansion of (1-3x+10 x^2)^ni sa and if the sum of the coefficients in the expansion of (1+x^2)^n is b , then a. a=3b b. a=b^3 c. b=a^3 d. none of these

If a,b,c,d be four consecutive coefficients in the binomial expansion of (1+x)^(n) , then value of the expression (((b)/(b+c))^(2)-(ac)/((a+b)(c+d))) (where x gt 0 and n in N ) is

Consider the expansion of (a+b+c+d)^(6) . Then the sum of all the coefficients of the term Which contains both a and b is

If the coefficients of three successive terms in the expansion of (1+x)^(n) be a ,b and c respectively , then show that , n=(2ac+b(a+c))/(b^(2)-ac)and(a(b+c))/(b^(2)-ac)= no. of the terms has coefficients a .

CENGAGE PUBLICATION-BINOMIAL THEOREM-Linked Comphrension
  1. The sixth term in the expansion of [sqrt({2^(log(10-3^(x)))})+5sqrt(...

    Text Solution

    |

  2. The sixth term in the expansion of ( sqrt(2^(log(10-3^x))) + (2^((x-2)...

    Text Solution

    |

  3. The sixth term in the expansion of [sqrt({2^(log(10-3^(x)))})+5sqrt(...

    Text Solution

    |

  4. If the 2nd, 3rd and 4th terms in the expansion of (x+a)^n are 240, 7...

    Text Solution

    |

  5. If the 2nd, 3rd and 4th terms in the expansion of (x+a)^n are 240, 7...

    Text Solution

    |

  6. If the 2nd, 3rd and 4th terms in the expansion of (x+a)^n are 240, 7...

    Text Solution

    |

  7. An equation a(0) + a(2)x^(2) + "……" + a(99)x^(99) + x^(100) = 0 has ro...

    Text Solution

    |

  8. An equation a0+a1x+a2x^2+...............+a99x^99+x^100=0 has roots .^(...

    Text Solution

    |

  9. An equation a(0) + a(2)x^(2) + "……" + a(99)x^(99) + x^(100) = 0 has ro...

    Text Solution

    |

  10. If a= .^(20)C(0) + .^(20)C(3) + .^(20)C(6) + .^(20)C(9) + "…..", b = ....

    Text Solution

    |

  11. If a= ^(20)C(0) + ^(20)C(3) + ^(20)C(6) + ^(20)C(9) + "…..", b = ^(20)...

    Text Solution

    |

  12. Consider the expansion of (a+b+c+d)^(6). Then the sum of all the coef...

    Text Solution

    |

  13. The sum of all the coefficients of the expansion of (a+b+c+d)^(8) whi...

    Text Solution

    |

  14. Consider the expansion of (a+b+c+d)^(6). Then the sum of all the coef...

    Text Solution

    |

  15. Let P = sum(r=1)^(50) (""^(50+r)C(r)(2r-1))/(""^(50)C(r)(50+r)), Q = s...

    Text Solution

    |

  16. Let P =sum(r=1)^(50)(""^(50+r)C(r)(2r-1))/(""^(50)C(r)(50+r)), R = su...

    Text Solution

    |

  17. Let Q = sum(r=0)^(50)(""^(50)C(r))^(2), R = sum(r=0)^(100)(-1)^(r) (""...

    Text Solution

    |

  18. If (1+x-2x^(2))^(6) = 1 + a(1)x+a(2)x^(2) + "……" + a(12)x^(12), then f...

    Text Solution

    |

  19. If (1+x+2x^(2))^(20) = a(0) + a(1)x^() "……" + a(40)x^(40), then follow...

    Text Solution

    |

  20. If (1+x+2x^(2))^(20) = a(0) + a(1)x^(2) "……" + a(40)x^(40), then follo...

    Text Solution

    |