Home
Class 12
MATHS
For r = 0, 1,"…..",10, let A(r),B(r), an...

For `r = 0, 1,"…..",10`, let `A_(r),B_(r)`, and `C_(r)` denote, respectively, the coefficient of `x^(r )` in the expansion of `(1+x)^(10), (1+x)^(20)` and `(1+x)^(30)`. Then `underset(r=1)overset(10)sum A_(r)(B_(10)B_(r ) - C_(10)A_(r ))` is equal to

A

`B_(10)-C_(10)`

B

`A_(10)(B_(10)^(2)-C_(10)A_(10))`

C

0

D

`C_(10)-B_(10)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    VMC MODULES ENGLISH|Exercise NUMERICAL VALUE TYPE FOR JEE MAIN|14 Videos

  • CIRCLES

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ( ARCHIVE )|68 Videos

Similar Questions

Explore conceptually related problems

For r = 0, 1,"…..",10 , let A_(r),B_(r) , and C_(r) denote, respectively, the coefficient of x^(r ) in the expansion of (1+x)^(10), (1+x)^(20) and (1+x)^(30) . Then sum_(r=1)^(10) A_(r)(B_(10)B_(r ) - C_(10)A_(r )) is equal to

Prove that the coefficient of x^r in the expansion of (1-2x)^(-1/2) is (2r!)/[(2^r)(r!)^2]

Find underset(r=0) overset(10)sumr^ (10)C_(r).3^(r).(-2)^(10-r)

underset(r=1)overset(n)(sum)r(.^(n)C_(r)-.^(n)C_(r-1)) is equal to

If A and B are coefficients of x^r and x^(n-r) respectively in the expansion of (1 + x)^n , then

If a_(r) is the coefficient of x^(r ) in the expansion of (1+x+x^(2))^(n)(n in N) . Then the value of (a_(1)+4a_(4)+7a_(7)+10a_(10)+……..) is equal to :

If C_(r) be the coefficients of x^(r) in (1 + x)^(n) , then the value of sum_(r=0)^(n) (r + 1)^(2) C_(r) , is

The value of ""^(40) C_(31) + sum _(r = 0)^(10) ""^(40 + r) C_(10 +r) is equal to

Let (1 + x)^(n) = sum_(r=0)^(n) a_(r) x^(r) . Then ( a+ (a_(1))/(a_(0))) (1 + (a_(2))/(a_(1)))…(1 + (a_(n))/(a_(n-1))) is equal to

If in the expansion of (1-x)^(2n-1) a_r denotes the coefficient of x^r then prove that a_(r-1) +a_(2n-r)=0

VMC MODULES ENGLISH-BINOMIAL THEOREM-JEE Archive
  1. Given, sn=1+q+q^2++q^n ,Sn=1+(q+1)/2+((q+1)/2)^2++((q+1)/2)^n ,q!=1 p...

    Text Solution

    |

  2. The coefficients of three consecutive terms of (1+x)^(n+5) are in the ...

    Text Solution

    |

  3. For r = 0, 1,"…..",10, let A(r),B(r), and C(r) denote, respectively, t...

    Text Solution

    |

  4. The value of ((30), (0))((30), (10))-((30), (1))((30),( 11)) +(30 2)(3...

    Text Solution

    |

  5. If ^n-1Cr=(k^2-3)^n C(r+1),t h e nk in (-oo,-2] b. [2,oo) c. [-sqrt...

    Text Solution

    |

  6. The sum sum(i=0)^m ((10)c,(i))((20),(m-1)), where ((p),(q))=0 if p ...

    Text Solution

    |

  7. ""^(n)C(r+1)+^(n)C(r-1)+2.""^(n)C(r)=

    Text Solution

    |

  8. If an=sum(r=0)^n1/(^n Cr) , then sum(r=0)^n r/(^n Cr) equals (n-1)an b...

    Text Solution

    |

  9. about to only mathematics

    Text Solution

    |

  10. Prove that the sum of the coefficients in the expansion of (1 + x ...

    Text Solution

    |

  11. If n and k are positive integers, show that 2^k(nC 0)(n k)-2^(k-1)(nC1...

    Text Solution

    |

  12. For any positive integer (m,n) (with ngeqm), Let ((n),(m)) =.^nCm Prov...

    Text Solution

    |

  13. Prove that (3!)/(2(n+3))=sum(r=0)^n(-1)^r((^n Cr)/(^(r+3)Cr))

    Text Solution

    |

  14. Let n be a positive integer and (1+x+x^2)^n=a0+a1x+ . . . . +a(2n)x^(2...

    Text Solution

    |

  15. Prove that C0-2^2C1+3^2C2-4^2C3++(-1)^n(n+1)^2xxCn=0w h e r eCr=^n Cr ...

    Text Solution

    |

  16. If (1 + x)^(n) = C(0) = C(1) x + C(2) x^(2) + …+ C(n) x^(n) , find...

    Text Solution

    |

  17. Prove that C(1)^(2)-2*C(2)^(2)+3*C(3)^(2)-…-2n*C(2n)^(2)=(-1)^(n)n*C(n...

    Text Solution

    |

  18. (.^(n)C(0))^(2)+(.^(n)C(1))^(2)+(.^(n)C(2))^(2)+ . . .+(.^(n)C(n))^(2)...

    Text Solution

    |

  19. The coefficient of x^(18) in the product (1+x)(1-x)^(10)(1+x+x^(2))^(9...

    Text Solution

    |

  20. The term independent of x in the expansion of (1/60-(x^(8))/81).(2x^(...

    Text Solution

    |