Home
Class 12
MATHS
For a fixed positive integer n , if =|n ...

For a fixed positive integer `n ,` if `=|n !(n+1)!(n+2)!(n+1)!(n+2)!(n+3)!(n+2)!(n+3)!(n+4)!|` , then show that `[/((n !)^3)-4]` is divisible by `ndot`

Promotional Banner

Topper's Solved these Questions

  • COMPOUND ANGLES

    ALLEN|Exercise EX -JA|8 Videos
  • INVERSE TRIGONOMETRIC FUNCTIONS

    ALLEN|Exercise All Questions|147 Videos

Similar Questions

Explore conceptually related problems

If n is a positive integer, show that 4^n -3n -1 is divisible by 9

If n is an odd positive integer, show that (n^2-1) is divisible by 8.

If n is an odd positive integer, show that (n^2-1) is divisible by 8.

If n is a positive integer, show that: 4^n-3n-1 is divisible by 9

For all n in N , 4^(n)-3n-1 is divisible by

For all positive integers n , show that \ ^(2n)C_n+\ ^(2n)C_(n-1)=1/2(\ ^(2n+2)C_(n+1)) .

For all positive integers n , show that \ ^(2n)C_n+\ ^(2n)C_(n-1)=1/2(\ ^(2n+2)C_(n+1)) .

If n is a positive integer, then show tha 3^(2n+1)+2^(n+2) is divisible by 7 .

10^n+3(4^(n+2))+5 is divisible by (n in N)

If n is any positive integer , show that 2^(3n +3) -7n - 8 is divisible by 49 .

ALLEN-DETERMINANTS-All Questions
  1. Prove that |b+c a a b c...

    Text Solution

    |

  2. about to only mathematics

    Text Solution

    |

  3. For a fixed positive integer n , if =|n !(n+1)!(n+2)!(n+1)!(n+2)!(n+3)...

    Text Solution

    |

  4. If "Delta"r=|[2^(r-1),2. 3^(r-1),4. 5^(r-1)],[x, y ,z],[2^n-1, 3^n-1, ...

    Text Solution

    |

  5. If D=|[1/z,1/z,-(x+y)/(z^2)],[-(y+z)/(x^2),1/x,1/x],[-(y(y+z)/(x^2z))...

    Text Solution

    |

  6. about to only mathematics

    Text Solution

    |

  7. Solve the following sets of equation using Cramer’s rule and remark...

    Text Solution

    |

  8. Solve the following sets of equation using Cramers rule and remark a...

    Text Solution

    |

  9. Determine for that values of lambda and mu the following system of eq...

    Text Solution

    |

  10. Find those values of c for which the equations: 2x+3y=3,(c+ 2)x + (c +...

    Text Solution

    |

  11. Let alpha1,alpha2 and beta1, beta2 be the roots of the equation ax^2+b...

    Text Solution

    |

  12. Let a, b, c, d be real numbers in G.P. If u, v, w satisfy the system...

    Text Solution

    |

  13. If a^2+b^2+c^2=1 then show that value of the determinant |a^2+(b^2+c^2...

    Text Solution

    |

  14. Using the properties of determinants, find the value of | 0 a -b ...

    Text Solution

    |

  15. Find the value of the determinant |"cos"(x-y)"cos"(y-z)"cos"(z-x)"cos"...

    Text Solution

    |

  16. If SS(r)=alpha^(r)+beta^(r)+gamma^(r)"then show that "=[{:(,S(0),S(1),...

    Text Solution

    |

  17. If a x1 2+b y1 2+c z1 2=a x1 2+b y2 2+c z2 2=a x3 2+b y3 2+c z3 2=d\ a...

    Text Solution

    |

  18. If ∣ x - 2 -3 3x 2x ∣ =3, find the negative of integer va...

    Text Solution

    |

  19. If x,y and y are not all zero and if ax+by+cz=0,bx+cy+az=0 and cx...

    Text Solution

    |

  20. Prove that the system of equations in xa +y+z=0 , x +by +z=0 ,...

    Text Solution

    |