Home
Class 12
MATHS
Let f:N rarr R be such that f(1)=1 and f...

Let `f:N rarr R` be such that f(1)=1 and f(1)+2f(2)+3f(3)+…+nf(n)=n(n+1)f(n), for `n ge 2, " then " `(2010f(2010))` is ……….. .

Text Solution

Verified by Experts

The correct Answer is:
2
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|12 Videos

  • FUNCTIONS

    ARIHANT MATHS|Exercise FUNCTION EXERCISE 7: Subjective Type Questions|1 Videos

  • FUNCTIONS

    ARIHANT MATHS|Exercise FUNCTION EXERCISE 5: Matching Type Questions|1 Videos

  • ESSENTIAL MATHEMATICAL TOOLS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|3 Videos

  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

Similar Questions

Explore conceptually related problems

Let f be a function from the set of positive integers to the set of real number such that f(1)=1 and sum_(r=1)^(n)rf(r)=n(n+1)f(n), forall n ge 2 the value of 2126 f(1063) is ………….. .

If f(x) =x^n and if f’ (1) = 10, find n.

Let f: Rrarr R be defined as f(x) = 2x for all x in N , then f is

Let f: (-1,1) rarr R be a differentiable function with f(0) = -1 and f'(0) = 1 let g(x) =[f(2f(x)+2)]^2 , then g'(0) =

Let f: N rarr N be defined by : f(n) = {:{((n+1)/2, if n is odd),(n/2, if n is even):} then f is

If n gt 0 is an odd integer and x = (sqrt(2) + 1)^(n), f = x - [x], " then" (1 - f^(2))/(f) is

Let f be defined on the natural numbers as follow: f(1)=1 and for n gt 1, f(n)=f[f(n-1)]+f[n-f(n-1)] , the value of 1/(30)sum_(r=1)^(20)f(r) is

Let f : WrarrW , be defined as f (n) = n – 1 , if n is odd and f (n) = n + 1 , if n is even. Show that f is invertible. Find the inverse of f . Here, W is the set of all whole numbers.

If f(x) is a polynomial of degree n such that f(0)=0 , f(x)=1/2,....,f(n)=n/(n+1) , ,then the value of f (n+ 1) is

ARIHANT MATHS-FUNCTIONS-Exercise (Single Integer Answer Type Questions)
  1. A wheel makes 720 revolutions in one minute. Through how many radians ...

    Text Solution

    |

  2. If f:R rarr R satisfying f(x-f(y))=f(f(y))+xf(y)+f(x)-1, for all x,y i...

    Text Solution

    |

  3. Let f:N rarr R be such that f(1)=1 and f(1)+2f(2)+3f(3)+…+nf(n)=n(n+1)...

    Text Solution

    |

  4. If f(x)=(2010x+165)/(165x-2010), x gt 0 " and " x ne (2010)/(165), the...

    Text Solution

    |

  5. If alpha,beta,gamma in R, alpha+beta+gamma=4 " and " alpha^(2)+beta^(2...

    Text Solution

    |

  6. The number or linear functions f satisfying f(x+f(x))=x+f(x) AA x in R...

    Text Solution

    |

  7. If A={1,2,3}, B={1,3,5,7,9}, the ratio of number of one-one functions ...

    Text Solution

    |

  8. If n(A)=4, n(B)=5 and number of functions from A to B such that range ...

    Text Solution

    |

  9. If a and b are constants, such that f(x)=asinx+bxcosx+2x^(2) and f(2...

    Text Solution

    |

  10. If the function f(x)=x^(3)+e^(x//2)andg(x)=f^(-1)(x), then the value ...

    Text Solution

    |

  11. If f(x)=x^(3)-12x+p,p in {1,2,3,…,15} and for each 'p', the number of ...

    Text Solution

    |

  12. The minimum value of the fuction f(x) given by f(x)=x^m/m+x^(−n)/n whe...

    Text Solution

    |

  13. If x^(2)+y^(2)=4 then find the maximum value of (x^(3)+y^(3))/(x+y)

    Text Solution

    |

  14. Let f(n) denotes the square of the sum of the digits of natural number...

    Text Solution

    |

  15. If [sinx]+[x/(2pi)]+[(2x)/(5pi)]=(9x)/(10pi), where [*] denotes the gr...

    Text Solution

    |

  16. The number of integral solutions of 1/x+1/y=1/6 " with " x le y " is "...

    Text Solution

    |

  17. If f(x) is a polynominal of degree 4 with leading coefficient '1' sati...

    Text Solution

    |

  18. If a+b = 3- cos 4 theta and a-b =4 sin 2theta, then ab is always less ...

    Text Solution

    |

  19. Let 'n' be the number of elements in the domain set of the function f(...

    Text Solution

    |

  20. Let f(x) be a function such that , f(x-1)+f(c+1)=sqrt(3)f(x), forall x...

    Text Solution

    |