Home
Class 11
MATHS
(1+x)(1+x+x^2)(1+x+x^2+x^3)…….(1+x+x^2+…...

`(1+x)(1+x+x^2)(1+x+x^2+x^3)…….(1+x+x^2+…….+x^(100))` when written in the ascending power of x then the highest exponent of x is `lambda(1010)` then `lambda` is____

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 line y=x+lambda is tangent to the ellips 2x^2+3y^2=1 Then lambda is

The coefficient of x^9 in the expansion of (1+x)(16 x^2)(1+x^3)(1+x^(100)) is

Given, f(x)=(x-1)/(2x^2-7x+5) when xne1 Find the derivative of f(x) at x=1

The line y=x+lambda is tangent to the ellipse 2x^(2)+3y^(2)=1 , then lambda is-

The coefficient of x^9 in the expansion of (1+x)(1+x^2)(1+x^3)....(1+x^100) is

The number of terms in the expansion of (1+x)^(101) (1+x^2-x)^(100) in powers of x is

The coefficient of x^4 in the expansion of (1+x+x^2+x^3)^11 is lamda . Then the number of divisors of lambda of the form 9k _____

Given, f (x) =(x-1)/(2x^(2)-7x+5)' when x ne 1 =-(1)/(3) when x = 1 Find the derivative of f (x) at x = 1 .

The highest power of the variable of the equation x-(1)/(x)=a^(2) (a=constant) is

If (x^(3))/((2x-1) (x+2) (x-3))=A+ (B)/(2x-1) +(C )/(x+2) + (D)/(x-3), then the value of A is-

PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. Match List-I with List-II

    Text Solution

    |

  2. If the second term of the expansion [a^(1/13)+(a/sqrt(a^(-1))] is 14a^...

    Text Solution

    |

  3. (1+x)(1+x+x^2)(1+x+x^2+x^3)…….(1+x+x^2+…….+x^(100)) when written in th...

    Text Solution

    |

  4. The value of {3^(2003)/28}=a/b where {} denotes the fractional part th...

    Text Solution

    |

  5. The coefficient of x^4 in the expansion of (1+x+x^2+x^3)^11 is lamda ....

    Text Solution

    |

  6. The fractional part of the sum of all the rational terms in the expans...

    Text Solution

    |

  7. Find the last three digits of (17)^256

    Text Solution

    |

  8. Find the term independent of x in the expansion of [(t^(-1)-1)x+(t^(-1...

    Text Solution

    |

  9. If ak=1/(k(k+1)) for k=1 ,2……..,n then prove that (sum(k=1)^n ak)^2 =n...

    Text Solution

    |

  10. Find the unit digit in the number 17^(1995)+11^(1995)-7^(1995)

    Text Solution

    |

  11. If ((1+x)/(1-x))^n=1+a1x+a2x^2+…….+arx^r+…….. then prove that a1+a2+a3...

    Text Solution

    |

  12. Prove that ^nC0 "^(2n)Cn-^nC1 ^(2n-2)Cn +^nC2 ^(2n-4)Cn =2^n

    Text Solution

    |

  13. If (1+x)^n=a0+a1x+a2x^2+…….+anx^n then prove that (1+(a/a0))(1+(a2)/(a...

    Text Solution

    |

  14. Prove that the following identity about binomial coefficients ((n),(0)...

    Text Solution

    |

  15. The terms independent of x in (3/2(x^2)-1/(3x))^9 is

    Text Solution

    |

  16. The 10^(th) term in the expansion of (2x^2+1/x)^(12) is

    Text Solution

    |

  17. If the 6th term in the expansion of (1/x^(8//3)+x^2log(10)x)^8 is 5600...

    Text Solution

    |

  18. The coefficient of x^5 in the expansion of (x^2-x-2)^5 is

    Text Solution

    |

  19. The sum of series ,^20C0-^20C1+^20C2-^20C3+.....+ ^20C10 is

    Text Solution

    |

  20. ^8C2+^8C3+^8C4+....^8C7 is equal to

    Text Solution

    |