Home
Class 12
MATHS
Real root of the equation (x-1)^(20...

Real root of the equation
`(x-1)^(2013) +(x-2)^ (2013) +(x-3)^ (2013)+……….+(x-2013)^(2013) =0` is a four digit number. Then the sum of the digits is :

Text Solution

Verified by Experts

The correct Answer is:
8
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise Exersise-2 Part III|23 Videos

  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise Exersise-2 Part IV comprehension|11 Videos

  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise Exersise-2 Part I|26 Videos

  • COMBINATORICS

    RESONANCE|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|8 Videos

Similar Questions

Explore conceptually related problems

Real root of the equation (x-1)^(2013)+(x-2)^(2013)+(x-3)^(2013)+.......+(x-2013)^(2013)=0 digits is :

The numbr of real roots of the equation x ^(2013)+ e ^(20144x) =0 is

int_(1)^(2013)[(x-1)(x-2)...(x-2013)]dx

If x is the root of the equation x^(2) -ix -1 =0 , then x^(2013) - 1/x^(2013) may be

The number of value(s) of x satisfying the equation (2011)^(x)+(2012)^(x)+(2013)^(x)-(2014)^(x)=0

Find the remainder when 1^(2013)+2^(2013)+3^(2013)+...+2012^(2013) is divisible by 2013

The digit in the unit place of 17^(2013)+11^(2013)-7^(2013)

RESONANCE-APPLICATION OF DERIVATIVES-Exersise-2 Part II
  1. The sum of the ordinates of point of contacts of the common tangent to...

    Text Solution

    |

  2. if p in (0,1//e)then the number of the distinct roots of the equation...

    Text Solution

    |

  3. A light shines from the top of a pole 50 ft. high A ball is dropp...

    Text Solution

    |

  4. A variable Delta ABC in the xy plane has its orthocentre at vertex B ,...

    Text Solution

    |

  5. Function defined by f(x) =(e^(x^(2))-e^(-x^(2)))/(e^(x^(2))+e^(-x^(2))...

    Text Solution

    |

  6. Find lim( xto0) [(3x)/(2sinx + tanx)] where [ . ] denotes the GIF.

    Text Solution

    |

  7. if f(x) =2e^(x) -ae^(-x) +(2a +1) x-3 monotonically increases for AA x...

    Text Solution

    |

  8. if has set of all values of the parameter 'a' for which the function...

    Text Solution

    |

  9. If ln2pi ltlog2 (2+sqrt3)lt ln3pi, then number of roots the equation 4...

    Text Solution

    |

  10. For -1<=p<=1 , the equation 4x^3-3x-p = 0 has 'n' distinct real ro...

    Text Solution

    |

  11. Least value of the function , f(x)=2^(x^2)-1+2/(2^(x^2)+1) is :

    Text Solution

    |

  12. Real root of the equation (x-1)^(2013) +(x-2)^ (2013) +(x-3)^ (20...

    Text Solution

    |

  13. The exhaustive set of value of 'a' for which the function f(x)=a/3(x...

    Text Solution

    |

  14. if f(x) is a polynomial of degree 6. Which satisfies lim(h to 0) (1...

    Text Solution

    |

  15. Maximum value of (sqrt(-3+4x-x^2)+4)^2+(x-5)^2 (where 1 le x le 3) is

    Text Solution

    |

  16. The three sides of a trapezium are equal each being 6 cms long. Le...

    Text Solution

    |

  17. A sheet of poster has its area 18 m^(2). The margin at the top & ...

    Text Solution

    |

  18. The fuel charges for running a train are proportional to the square of...

    Text Solution

    |

  19. Let f(x) = Max. {x^2, (1 - x)^2, 2x(1 - x)} where x in [0, 1] If Rol...

    Text Solution

    |

  20. For every twice differentiable function f(x) the value of |f(x)| l...

    Text Solution

    |