Home
Class 11
MATHS
sum(r=0)^(300)arx^r=(1+x+x^2+x^3)^(100)....

`sum_(r=0)^(300)a_rx^r=(1+x+x^2+x^3)^(100)`. If `a=sum_(r=0)^(300)a_r`, then `sum_(r=0)^(300)ra_r` is equal to

A

300a

B

100a

C

150a

D

75a

Text Solution

Verified by Experts

The correct Answer is:
C
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

If (1+x)^n=sum_(r=0)^n .^nC_r x^r then sum_(r=m)^n .^rC_m is equal to

If (1+2x+x^(2))^(n) = sum_(r=0)^(2n)a_(r)x^(r) , then a_(r) =

If (1-x^2)^n=sum_(r=0)^na_rx^r(1-x)^(2n-r) , then a_r is equal to

The value of sum_(r=0)^(20)r(20-r)( ^(20)C_r)^2 is equal to ?

Let (1+x)^10=sum_(r=0)^(10)c_rx^r and (1+x)^7=sum_(r=0)^7d_rx^r . If P=sum_(r=0)^5c_(2r) and Q=sum_(r=0)^3d_(2r+1) , then P/Q is equal to

Let (1+x)^10= sum_(r=0)^(10)c_(r) x^(r), and (1+x)^(7)= sum_(r=o)^(7)d_(r)x^(r). If P= sum_(r=0)^5c_(2r) and Q= sum_(r=o)^(3) d_(2r+1) , then (p)/(Q) is equl to

If (1+x^(2))^(n) = underset(r=0)overset(n)suma_(r)x^(r )= (1+x+x^(2)+x^(3))^(100) . If a = underset(r=0)overset(300)suma_(r) , then underset(r=0)overset(300)sumra_(r) is

Find the sum sum_(r=0) .^(n+r)C_r .

If (x^(2)+x+1)/(1-x) = a_(0) + a_(1)x+a_(2)x^(2)+"…." , then sum_(r=1)^(50) a_(r) equal to

The value of sum_(r=0)^(20)(-1)^(r )(""^(50)C_(r))/(r+2) is equal to

PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. The value of sum(r=0)^(20)r(20-r)(^(20)Cr)^2 is equal to ?

    Text Solution

    |

  2. The value of sum(r=1)^(n+1)(sum(k=1)^n^kC(r-1)) (where r, k, n in N) i...

    Text Solution

    |

  3. sum(r=0)^(300)arx^r=(1+x+x^2+x^3)^(100). If a=sum(r=0)^(300)ar, then s...

    Text Solution

    |

  4. Coefficient of x^50 in (1+x)^(1000)+2x(1+x)^(999)+3x^2(1+x)^(998)+.......

    Text Solution

    |

  5. C0/2-C1/3+C2/4-C3/5+.... is equal to

    Text Solution

    |

  6. The coefficient of x^7 in the expansion of (1-x-x^2+x^3)^6 is

    Text Solution

    |

  7. Let (1+x^(2))^(2) (1+x)^(n) = underset(k = 0)overset(n+4)suma(k)x^(k)....

    Text Solution

    |

  8. Coefficient of x^n in the expansion of (1+x)^(2n) is

    Text Solution

    |

  9. If (1+x+x^2)^n=a0+a1x+...+a(2n)x^(2n) then

    Text Solution

    |

  10. The coefficients of x^7 in the expansion of (x^3+3x+3/x+1/x^3)^5 is

    Text Solution

    |

  11. 3^(2n+2)-8n-9 is divisible by

    Text Solution

    |

  12. If (x+1/x+x^2+1/x^2)^11=a0x^(-22)+a1x^(-21)+.....+a44x^(22), then a0+a...

    Text Solution

    |

  13. If (8+3sqrt7)^n=P+F, where P is an integer and F is a proper fraction,...

    Text Solution

    |

  14. Let n=3^(100), then for n

    Text Solution

    |

  15. Let an=(1000)^n/(n!) for n in N. Then an is greatest, when

    Text Solution

    |

  16. Which of the following is/are correct

    Text Solution

    |

  17. Answer the following question based on above passage: The coefficient...

    Text Solution

    |

  18. Answer the following question based on above passage: The coefficient...

    Text Solution

    |

  19. Let P=sum(r=1)^(50)(^(50+r)Cr(2r-1))/(^(50)Cr(50+r)), Q=sum(r=1)^(50)(...

    Text Solution

    |

  20. Let P=sum(r=1)^(50)((50+r)Cr(2r-1))/((50)Cr(50+r)), Q=sum(r=1)^(50)(50...

    Text Solution

    |