Home
Class 11
MATHS
It is given that n is an odd integer gre...

It is given that n is an odd integer greater than 3 but n is not a multiple of 3 prove that `x^3+x^2+x` is a factor of `(x+1)^n-x^n-1:`

Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    PATHFINDER|Exercise QUESTION BANK|198 Videos

  • COMPLEX NUMBERS

    PATHFINDER|Exercise QUESTION BANK|67 Videos

Similar Questions

Explore conceptually related problems

It is given that n is an odd integer greater than 3 but n is not multiple of 3. prove that (x^(3)+x^(2)+x) is a factor of (1+x)^(n)-x^(n)-1 .

Show that if n be odd, x + 1 is a factor of x^n + 1 .

Determine whether n is an add or even positive integer, when (x + 1) is a factor of (x^(n)-1) .

If n be any positive integer (even or odd), prove that (x - y) is a factor of the polynomial x^(n)-y^(n) .

If n be an odd negative integer, then prove that (x + 1) is a polynomial of degree (x^(n)+1) .

If n be a positive integer greater than 1, prove that (frac(n+1)(2))^n > n

Show that, if n be any positive integer greater than 1, then (2^(3n) - 7n - 1) is divisible by 49.

If n is a positive integer then the coefficient of x ^(-1) in the expansion of (1+x) ^(n) (1+ (1)/(x)) ^(n) is-

'Prove that the co-efficient of x^n of the expansion of (1+x)^(2n) is the double of the coefficient of x^n of the expansion of '(1+x)^(2n-1)'

PATHFINDER-COMPLEX NUMBER-QUESTION BANK
  1. If abs(z-1)+abs(z+3)le8 then possible value of abs(z-4) is

    Text Solution

    |

  2. A complex number z is said to be unimodular if absz=1 suppose z1 and z...

    Text Solution

    |

  3. It is given that n is an odd integer greater than 3 but n is not a mul...

    Text Solution

    |

  4. Find the real values of x and y for which the following equation is sa...

    Text Solution

    |

  5. Let the complex numbers z1,z2 and z3 be the vertices of an equilateral...

    Text Solution

    |

  6. If in argand plane the vertices A,B,C of an isoceles triangle are rep...

    Text Solution

    |

  7. let z1=10+6i and z2=4+6i if z is nay complex number such that argument...

    Text Solution

    |

  8. if iz^3+z^2-z+i=0 then show that absz=1

    Text Solution

    |

  9. let z1 and z2 be roots of the equation z^2+pz+q=0 where the coefficien...

    Text Solution

    |

  10. For complex numbers z and w prove that absz^2w-abs(w)^2z=z-w if and on...

    Text Solution

    |

  11. if z1 and z2 are two complex numbers such that absz1lt1ltabsz2 then p...

    Text Solution

    |

  12. find the centre and radius of the circle formed by all the points repr...

    Text Solution

    |

  13. Let omega ne1 be a complex cube root of unity if (3-3omega+2omega^2)^(...

    Text Solution

    |

  14. For any integer k let alphak=cos((kpi)/7)+isin((kpi)/7) where i=sqrt(-...

    Text Solution

    |

  15. A complex number z is said to be unimodular if absz=1 suppose z1 and z...

    Text Solution

    |

  16. The value of ((1+sqrt3i)/(1-sqrt3i))^64+((1-sqrt3i)/(1+sqrt3i))^64

    Text Solution

    |

  17. Find the maximum value of absz when abs(z-3/z)=2 ,z being a complex nu...

    Text Solution

    |

  18. If z is a complex number such that abszge2 then the minimum value of a...

    Text Solution

    |

  19. Let z1,z2 be two fixed complex numbers in the Argand plane and z be an...

    Text Solution

    |

  20. In the Argand plane the distinct roots of 1+z+z^3+z^4=0 (z is a comple...

    Text Solution

    |