Home
Class 12
MATHS
If sum(r=0)^(2n) a(r)(x-1)^(r) = sum(r=0...

If `sum_(r=0)^(2n) a_(r)(x-1)^(r) = sum_(r=0)^(2n) b_(r)(x-2)^(r)` and `b_(r) = (-1)^(r-n)` for all `r ge n`, then `a_(n)`=

A

`.^(2n+1)C_(n-1)`

B

`.^(3n)C_(n)`

C

`.^(2n+1)C_(n)`

D

0

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise High Level Problem|37 Videos
  • EQUATIONS

    RESONANCE|Exercise EXERCISE-2 (PART-II: PREVIOUSLY ASKED QUESTION OF RMO) |7 Videos

Similar Questions

Explore conceptually related problems

sum_(i=0i0)^(2n)a_(r)(x-1)^(r)=sum_(r=0)^(2n)b_(r)(x-2)^(r) and b_(r)=(-1)^(r-n) for all r<=n, then a_(n)=

sum_(r=0)^(2n)a_(r)(x-2)^(r)=sum_(r=0)^(2n)b_(r)(x-3)^(r) and a_(k)=1 for all k>=n, then show that b_(n)=2n+1C_(n+1)

If sum_(r=0)^(2n)a_(r)(x-100)^(r)=sum_(r=0)^(2n)br(x-101)^(r) and a_(k)=(2^(k))/(kC_(n))AA k>=n then b_(-) n equals ( A )2^(n)(2^(n+1)-1)(B)2^(n)(2^(n)-1)(C)2^(n)(2^(n)+1)(D)2^(n+1)(2^(n)-1)

If sum_(r=1)^(n)I(r)=2^(n)-1 then sum_(r=1)^(n)(1)/(I_(r)) is

lim_(x rarr2)(sum_(r=1)^(n)x^(r)-sum_(r=1)^(n)2^(r))/(x-2)

If a_(n)=sum_(r=0)^(n)(1)/(nC_(r)), then sum_(r=0)^(n)(r)/(nC_(r)) equals

RESONANCE-DPP-QUESTION
  1. Find the degree of the polynomial 1/(sqrt(4x+1)){((1+sqrt(4x+1))/2)^7-...

    Text Solution

    |

  2. The figure shows a rectangle ABCD with a semi-circle and a circle insc...

    Text Solution

    |

  3. If sum(r=0)^(2n) a(r)(x-1)^(r) = sum(r=0)^(2n) b(r)(x-2)^(r) and b(r) ...

    Text Solution

    |

  4. p is a prime number and n<p<2ndot If N=^(2n)Cn , then p dividesN b. p...

    Text Solution

    |

  5. The sum of the greatest and the smallest term in (x+12)^(21) is zero t...

    Text Solution

    |

  6. the continued product 2.6.10.14.... to n factors is equal to ^2n pn ...

    Text Solution

    |

  7. The solution of |x^2+3x|+x^2-2>=0 is

    Text Solution

    |

  8. Which of the following equations have no real solutions ?

    Text Solution

    |

  9. The solution set satisfying the inequality,sqrt(21-4a-a^2)/(a+1)<=1

    Text Solution

    |

  10. The co-efficient of x in the expansion of (1-x+2x^2)^11 is

    Text Solution

    |

  11. If (1+x)^(n) = c(0) + C(1)x+C(2)x^(2)+"….."+X(n)x^(n), m ge 2 C(0) -...

    Text Solution

    |

  12. Solve the equation: |x+1|-|x|+3|x-1|-2|x-2|=x+2

    Text Solution

    |

  13. Solve the following |(x^2+2x+2)+(3x+7)|<|x^2+2x+2|+|3x+7|

    Text Solution

    |

  14. |x^(2) -1|+|x^(2) - 4|le 3

    Text Solution

    |

  15. Number of non-empty subsets {1,2,3,4,5,6,7,8} having exactly k element...

    Text Solution

    |

  16. If the expansion in powers of x of the function 1//[(1-a x)(1-b x)] is...

    Text Solution

    |

  17. If x is so small that x^3 and higher powers of x may be neglectd, then...

    Text Solution

    |

  18. The sum of the series sum(r=1)^(n) (-1)^(r-1).""^(n)C(r)(a-r), n gt 1 ...

    Text Solution

    |

  19. sum(k=1)^(360)((1)/(ksqrt(k+1)+(k+1)sqrt(k))) is the ratio of two rela...

    Text Solution

    |

  20. Number of ways in which 3 tickets can be selected from a set of 500 ...

    Text Solution

    |