Home
Class 12
MATHS
The expressions 1+x,1+x+x^2,1+x+x^2+x^3....

The expressions `1+x,1+x+x^2,1+x+x^2+x^3.............1+x+x^2+..............+x^a` are mutiplied together and the terms of the product thus obtained are arranged in increasing powers of `x` in the from of `a_0+a_1x+a_2x^2+.................,` then,

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    MOTION|Exercise Exercise -4 (Level - I) ( Previous Year )|12 Videos

  • BINOMIAL THEOREM

    MOTION|Exercise Exercise -4 (Level - II) ( Previous Year )|7 Videos

  • BINOMIAL THEOREM

    MOTION|Exercise Exercise - 2 (Level - II) (Multiple Correct ) (MIXED PROBLEMS )|3 Videos

  • BASIC MATHEMATIC & LOGARITHM

    MOTION|Exercise Exercise - 4|4 Videos

  • CIRCLE

    MOTION|Exercise Exercise - 4 | Level - II (Previous Year | JEE Advanced|22 Videos

Similar Questions

Explore conceptually related problems

If the expression in powers of x of the function 1/((1-ax)(1-bx)) is a_0+a_1 x+a_2 x^2+a_3 x^3+... then a_n is

Let (1+x^2)^2 (1+x)^n= A_0 +A_1 x+A_2 x^2 + ...... If A_0, A_1, A_2,........ are in A.P. then the value of n is

(1+x)(1+x+x^(2))(1+x+x^(2)+x^(3)).....(1+x+x^(2)+...+x^(100)) when written in the ascending power ofx then the highest exponent of x is

If cosx=a_0+a_1 x+a_2x^2+... then the value of a_2 is

Let (1 + x^2)^2 (1 + x)^n = A_0 +A_1 x+A_2 x^2 + ...... If A_0, A_1, A_2, are in A.P. then the value of n is

Let (1 + x^2)^2 (1 + x)^n = A_0 +A_1 x+A_2 x^2 + ...... If A_0, A_1, A_2, are in A.P. then the value of n is

If (1+x+2x^2)^20=a_0 + a_1x+a_2x^2+....................+a_40x^40 then a_0+a_2+a_4+.............+a_38 is

The expression ((x-1)(x-2)(x^(2) - 9x + 14))/((x-7)(x^(2) - 3x + 2)) in the lowest terms is:

MOTION-BINOMIAL THEOREM -Exercise -3 ( Subjective )
  1. Find the coefficient of x^(4) in the expansion of (1+x+x^(2)+x^(3))^(1...

    Text Solution

    |

  2. Find the coefficients of x^(4) in the expansions of (2 - x + 3x^(2...

    Text Solution

    |

  3. Let a = (72!)/(36!)^2-1 , then (A) a is odd (B) a is divisible by 7...

    Text Solution

    |

  4. find the sum of the series sum(r=0)^n(-1)^r *"^nCr[1/(2^r)+(3^r)/(2^(...

    Text Solution

    |

  5. Given that (1+x+x^2)^n=a0+a1x+a2x^2+........+a(2n)x^(2n) find the val...

    Text Solution

    |

  6. Given that (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+......+a(2n)x^(2n), f...

    Text Solution

    |

  7. Given that (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+......+a(2n)x^(2n), f...

    Text Solution

    |

  8. If n(j(r))=((1-xn)(1-x(n-1))(1-x^(n-2)).......(1-x^(n-r+1)))/((1-x)(1-...

    Text Solution

    |

  9. Prove that sum(k=0)^n ^nCk sinKx.cos(n-K)x=2^(n-1)sin nx

    Text Solution

    |

  10. The expressions 1+x,1+x+x^2,1+x+x^2+x^3.............1+x+x^2+.............

    Text Solution

    |

  11. Find the coefficients of x^(6) in the expansion of (ax^(2) + bx +...

    Text Solution

    |

  12. Find the coefficient of x^2 y^3 z^4 in the expansion of (ax-by+cz)^9

    Text Solution

    |

  13. Find the coefficient of x^2 y^3 z^4 in the expansion of (ax -by +cx...

    Text Solution

    |

  14. If sum(r=0)^(2n)ar(x-2)^r=sum(r=0)^(2n)br(x-3)^ra n dak=1 for all kgeq...

    Text Solution

    |

  15. Show that the integral part in each of the following is odd. n in N. ...

    Text Solution

    |

  16. Show that the integral part in each of the following is even. n in N....

    Text Solution

    |

  17. Show that the integer next above (sqrt(3)+1)^(2m) contains 2^(m+1) as ...

    Text Solution

    |

  18. The value of .^(n)C(0).^(n)C(n)+.^(n)C(1).^(n)C(n-1)+...+.^(n)C(n)....

    Text Solution

    |

  19. the value of r for which .^(30)Cr.^(20)C0+^(30)C(r-1).^(20)C1.....+^(...

    Text Solution

    |

  20. The value of r for which .^(20)C(r ), .^(20)C(r - 1) .^(20)C(1) + .^...

    Text Solution

    |