Home
Class 12
MATHS
Product of any r consecutive natural num...

Product of any r consecutive natural numbers is always divisible by

A

`r!`

B

`(r+4)!`

C

`(r+1)!`

D

`(r+2)!`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • QUESTION PAPER 2008

    WB JEE PREVIOUS YEAR PAPER|Exercise MULTIPLE CHOICE QUESTIONS|80 Videos
  • QUESTION PAPER 2010

    WB JEE PREVIOUS YEAR PAPER|Exercise DESCRIPTIVE TYPE QEUSTIONS|10 Videos

Similar Questions

Explore conceptually related problems

Prove that the product of any r consecutive natural number is always divisible by r!.

Prove that the product of three consecutive natural numbers is always divisible by 6.

Statement - I : For every natural number ((n+4)!)/((n+1)!) is divisible by 6. Statement - II : Product of three consective natural numbers is divisible by 3 !

T_r is always

Prove using principle of mathematical induction that sum of the cube three consecutive natural number is divisible by 9.

Prove that the product of two consecutive natural numbers is even.

From a collection of 20 consecutive natural numbers, four are selected such that they are not consecutive. The number of such selections is

Prove by mathematical induction that for any positive integer n , 3^(2n)-1 is always divisible by 8 .

Find the sum of all three-digit natural numbers, which are divisible by 7.

WB JEE PREVIOUS YEAR PAPER-QUESTION PAPER 2009-MULTIPLE CHOICE QUESTIONS
  1. The general solution of the differential equation dy/dx = e^(y+x) + e^...

    Text Solution

    |

  2. Product of any r consecutive natural numbers is always divisible by

    Text Solution

    |

  3. The integrating factor of the differential equation xlogx(dy)/(dx)+y=2...

    Text Solution

    |

  4. If x^(2)-y^(2)=1 then

    Text Solution

    |

  5. If c(0),c(1),c(2)..........c(n) denote the co-efficients in the expans...

    Text Solution

    |

  6. A polygon has 44 diagonals. The number of its sides is

    Text Solution

    |

  7. If alpha,beta be the roots of x^(2)-a(x-1)+b=0 then the value of (1)/(...

    Text Solution

    |

  8. The angle between the lines joining the foci of an ellipse to one part...

    Text Solution

    |

  9. The order of the differential equation (d^(2)y)/(dx^(2))=sqrt(1+((dy)/...

    Text Solution

    |

  10. The sum of all real of the equation |x-2|^(2)+|x-2|-2=0 is

    Text Solution

    |

  11. If int(-1)^(4)f(x)dx=4 and int(2)^(4){3-f(x)}dx=7 then the value of in...

    Text Solution

    |

  12. For each ninN,2^(3n)-1 is divisible by

    Text Solution

    |

  13. The Rolle's theorem is applicable in the interval -1lexle1 for the fun...

    Text Solution

    |

  14. The distance covered by a particle in t seconds is given by x=3+8t-4t^...

    Text Solution

    |

  15. If agt0 and coefficients of x^5 and x^(15) in the expansion of (x^2+a/...

    Text Solution

    |

  16. The value of ((1)/(log(3)12)+(1)/(log(4)12)) is

    Text Solution

    |

  17. If x=log(a)bc,y=log(b)ca,z=log(c)ab, then the value of (1)/(1+x)+(1)/(...

    Text Solution

    |

  18. Find the approximate value of sin62^(@), correct to 3 places of decima...

    Text Solution

    |

  19. The rate of increase of a side of a square is 1 cm/sec. The rate of in...

    Text Solution

    |

  20. The quadratic equation whose roots are three times the roots of 3ax^(2...

    Text Solution

    |