Home
Class 12
MATHS
^404C4-^303C4.^4C1+^202C4.^4C2-^101C4.^4...

`^404C_4-^303C_4.^4C_1+^202C_4.^4C_2-^101C_4.^4C_3=`

A

`(401)^(4)`

B

`(101)^(4)`

C

`0`

D

`(201)^(4)`

Text Solution

Verified by Experts

The correct Answer is:
B
The given expression is the coefficient of `x^(4)` in
`.^(4)C_(0)(1+x)^(404)-.^(4)C_(1)(1+x)^(303)+.^(4)C_(2)(1+x)^(202)-.^(4)C_(3)(1+x)^(101)+.^(4)C_(4)`
= Coefficient of`x^(4)` in `[(1+x)^(101)-1]^(4)`
`=` Coefficient of `x^(4)` in `(.^(101)C_(1)x+.^(101)C_(2)x^(2)+".....")^(4)`
`= (101)^(4)`
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

404C_(4)-^(303)C_(4)*^(4)C_(1)+^(202)C_(4)*^(4)C_(2)-^(101)C_(4)*^(4)C_(3)=

The coefficient of x^3y^4z in the expansion of (1+x+y-z)^9 is (A) 2.^9C_7.^7C_4 (B) -2.^9C_2 . ^7C_4 (C) ^9C_7.^7C_4 (D) none of these

Prove that: .^2C_1+^3C_1+^4C_1=^5C_3-1

Find the value of .^(7)C_(4)-.^(6)C_(4)-.^(5)C_(3)-.^(4)C_(2) .

8C_(4)+^(8)C_(3)=^(9)C_(4)

Prove that : ""^(2)C_(1)+ ""^(3)C_(1)+""^(4)C_(1)=""^(3)C_(2)+""^(4)C_(2) .

C_(2)H_(4),C_(4)H_(10), C_(3)H_(8),CH_(4)

Evaluate: .^(20)C_(5)+^(20)C_(4)+^(21)C_(4)+^(22)C_(4)

If alpha=mC_(2), then ^(alpha)C_(2) is equal to a.m+1C_(4) b.^(m-1)C_(4) c.3^(m+2)C_(4) d.3^(m+1)C_(4)

CENGAGE-BINOMIAL THEOREM-Exercise (Single)
  1. The value of .^(15)C(0)^(2)-.^(15)C(1)^(2)+.^(15)C(2)^(2)-"...."-.^(15...

    Text Solution

    |

  2. If (1+x)^n=C0+C1x+C2x^2++Cn x^n ,t h e nC0C2+C1C3+C2C4++C(n-2)Cn= ((2...

    Text Solution

    |

  3. ^404C4-^303C4.^4C1+^202C4.^4C2-^101C4.^4C3=

    Text Solution

    |

  4. The value of sum(r=0)^(40) r""^(40)C(r)""^(30)C(r) is

    Text Solution

    |

  5. The value of sum(r=1)^(15) (r2^(r))/((r+2)!) is equal to

    Text Solution

    |

  6. (n+2)^n C0 2^(n+1)-(n+1)^n C1 2^n^n C2 2^(n-1)- is equal to 4 b. 4n c....

    Text Solution

    |

  7. The value of sum(r=0)^(20)(-1)^(r )(""^(50)C(r))/(r+2) is equal to

    Text Solution

    |

  8. If (1+x^(2))^(n) =sum(r=0)^(n) a(r)x^(r )= (1+x+x^(2)+x^(3))^(100). If...

    Text Solution

    |

  9. sum(r=0)^(300) a(r)x^(r)=(1+x+x^(2)+x^(3))^(100). if a=sum(r=0)^(300)a...

    Text Solution

    |

  10. The value of sum(r=0)^(20) r(20-r)(""^(20)C(r))^(2) is equal to

    Text Solution

    |

  11. If f(x) = .^(40)C(1).x(1-x)^(39) + 2..^(40)C(2)x^(2)(1-x)^(38)+3..^(40...

    Text Solution

    |

  12. If a(n) = sum(r=0)^(n) (1)/(""^(n)C(r)), then the value of (sumsum)(0l...

    Text Solution

    |

  13. In the expansion of [(1+x)//(1-x)]^2, the coefficient of x^n will be 4...

    Text Solution

    |

  14. The sum of 1+n(1-1/x)+(n(n+1))/(2!)(1-1/x)^2+oo will be x^n b. x^(-n) ...

    Text Solution

    |

  15. sum(k=1)^(oo) k(1-1/n)^(k-1) =

    Text Solution

    |

  16. Find the coefficient of x in the expansion of [sqrt(1+x^2) - x]^-1 in...

    Text Solution

    |

  17. 1+1/3x+(1xx4)/(3xx6)x^2+(1xx4xx7)/(3xx6xx9)x^3+ is equal to x b. (1+x)...

    Text Solution

    |

  18. 1+1/4 + (1xx3)/(4xx8) + (1xx3xx5)/(4xx8xx12) x^(3) + "….." is equal to

    Text Solution

    |

  19. If |x|<1,t h e n1+n((2x)/(1+x))+(n(n+1))/(2!)((2x)/(1+x))^2+ is equal ...

    Text Solution

    |

  20. Find the coefficient of x^5 in (1+2x+3x^2...........)^(-3/2)

    Text Solution

    |