Home
Class 11
MATHS
The coefficient of x^m in (1+x)^r+ (1+x)...

The coefficient of `x^m` in `(1+x)^r+ (1+x)^(r+1)+(1+x)^(r+2)+………+(1+x)^n , rlemlen` is

A

`^(n+1)C_(m+1)`

B

`^(n-1)C_(m-1)`

C

`^nC_m`

D

`^nC_(m+1)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • BASIC MATHEMATICS

    PATHFINDER|Exercise QUESTION BANK |266 Videos

  • BINOMIAL THEOREM AND PRINCIPLE OF MATHEMATICAL INDUCTION

    PATHFINDER|Exercise QUESTION BANK|68 Videos

Similar Questions

Explore conceptually related problems

The coefficients of x^n in (1+x/(1!)+x^2/(2!)+……+x^n/(n!))^2 is

If the coefficient of x^(r)andx^(r+1) are equal in the expansion of (1+x)^(2n+1) , then find the value of r .

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

If a_(r) be the coefficient of x^(r) in the expression of (1+bx^(2)+cx^(3))^(n),"then prove that" , a_(3)=nc

The coefficient of x^r[0lt=rlt=(n-1)] in the expansion of (x+3)^(n-1)+(x+3)^(n-2)(x+2)+(x+3)^(n-3)(x+2)^2+.... +(x+2)^(n-1) is a.^n C_r(3^r-2^n) b.^n C_r(3^(n-r)-2^(n-r)) c.^n C_r(3^r+2^(n-r)) d. none of these

If a _(r) is the coefficient of x^r in the expansion of (1+ x+x^(2)) ^(n), then the value of a_(1)- 2a_(2) +3a_(3)-4a_(4)+…-2na_(2n) is -

If the coefficients of (r-5)^th and (2r - 1)^th terms in the expansion of (1 + x)^34 are equal, find r.

Find the coefficient of x^(r) in the following expression : (x+n)^(n)+(x+2)^(n-1)(x+1)+(x+2)^(n-2)(x+1)^(2)+.....+(x+1)^(n)

Find the coefficient of x^(r) in the expansion of (x+4)^(n)+(x+4)^(n-1)(x+3)+(x+4)^(n-2)(x+3)^(2)+.....+(x+3)^(n)

prove that the coefficient of the (r +1)th term in the expansion of (1+x)^(n) is equal to the sum of the coefficients of the rth and (r+1)th terms in the expansion of (1+x)^(n-1)

PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. The coefficients of x^n in (1+x/(1!)+x^2/(2!)+……+x^n/(n!))^2 is

    Text Solution

    |

  2. The sum of the coefficients of all the integral powers of x in the exp...

    Text Solution

    |

  3. The coefficient of x^m in (1+x)^r+ (1+x)^(r+1)+(1+x)^(r+2)+………+(1+x)^n...

    Text Solution

    |

  4. The coefficient of x^ny^n in the expansion of {(1+x)(1+y)(x+y)}^n is

    Text Solution

    |

  5. If log(1-x+x^2)=a1x+a2x^2+a3x^3+……… then a3+a6+a9+……… is equal to

    Text Solution

    |

  6. The greatest term in the expansion of (1+x)^(10) when x=2/3 is

    Text Solution

    |

  7. The number of integral terms in the expansion of (3^(1/2)+2^(1/2))^(50...

    Text Solution

    |

  8. The least (positive) remainder when 17^(30) is divided by 5 is

    Text Solution

    |

  9. The coefficient of x^(17) in the expansion of (x-1)(x-2)……..(x-18) is

    Text Solution

    |

  10. The number of terms in the expansion of (a+b+c)^n where ninN is

    Text Solution

    |

  11. The sum of the rational terms in the expansion of (sqrt2+3^(1/5))^(10)...

    Text Solution

    |

  12. The greatest coefficient iin the expansion of (x+y+z+t)^(15) is

    Text Solution

    |

  13. If (1+x)^n=sum(r=0)^n .^nCr x^r then sum(r=m)^n .^rCm is equal to

    Text Solution

    |

  14. Let n be a positive integer such that (1+x+x^2)^n=a0+a1x+a2x^2+…….+a(2...

    Text Solution

    |

  15. Give the integers rgt1 , ngt2 and c0-efficients of (3r)^th and (r+2)^(...

    Text Solution

    |

  16. If n in I^+ the value of sum(k=1)^n k^3 (^nCk)/(^nC(k-1))^2

    Text Solution

    |

  17. In a triangle ABC the value of sum(r=0)^(50) ^(50)Cr a^rb^(50-r) cos(R...

    Text Solution

    |

  18. The value of "^30C0.^30C10+^30C1.^30C11+^30C2.^30C(12)+……+^30C(20) . ^...

    Text Solution

    |

  19. The number of distinct terms in the expansion of (x^3+1+(1/x^3)): xinK...

    Text Solution

    |

  20. The number of integral of integral terms in the expansion of (17^(1/3)...

    Text Solution

    |