Home
Class 12
MATHS
The period of f(x)=[x]+[2x]+[3x]+[4x]+[n...

The period of `f(x)=[x]+[2x]+[3x]+[4x]+[n x]-(n(n+1))/2x ,` where `n in N ,` is (where `[dot]` represents greatest integer function). `n` (b) 1 (c) `1/n` (d) none of these

A

n

B

1

C

`1//n`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) Level-II|20 Videos
  • FUNCTION

    FIITJEE|Exercise COMPREHENSIONS|8 Videos
  • FUNCTION

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (SUBJECTIVE) Level-II|17 Videos
  • ELLIPSE

    FIITJEE|Exercise NUMERICAL BASED|4 Videos
  • HEIGHTS & DISTANCE

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-II|20 Videos

Similar Questions

Explore conceptually related problems

The period of f(x)=[x]+[2x]+[3x]+[4x]+...[nx]-(n(n+1))/(2)x where n in N, is (where [.] represents greatest integer function).n (b) 1 (c) (1)/(n) (d) none of these

lim_(x->0) (lnx^n-[x])/[x], n in N where [x] denotes the greatest integer is

If n in N , the value of int_(0)^(n) [x] dx (where [x] is the greatest integer function) is

lim_(xrarr oo) (logx^n-[x])/([x]) where n in N and [.] denotes the greatest integer function, is

Evaluate lim{n-> oo) ([1.2x]+[2.3x]+.....+[n.(n+1)x])/(n^3)), where [.] denotes greatest integer function.

The value of int_0^x[cost]dt ,x in [(4n+1)pi/2,(4n+3)pi/2]a n dn in N , is equal to where [.] represents greatest integer function. pi/2(2n-1)-2x pi/2(2n-1)+x pi/2(2n+1)-x (d) pi/2(2n+1)+x

The function f(x)=lim_(nrarroo)cos^(2n)(pix)+[x] is (where, [.] denotes the greatest integer function and n in N )

f(x)=lim_(n rarr oo)sin^(2n)(pi x)+[x+(1)/(2)], where [.] denotes the greatest integer function,is

The range of f(x)=[1+sin x]+[2+sin((x)/(2))]+[3+sin((x)/(3))]+...+[n+sin((x)/(n))]AA x in[0,pi) ,where [.] denotes the greatest integer function,is,

FIITJEE-FUNCTION-ASSIGNMENT PROBLEMS (OBJECTIVE) Level-I
  1. lf domain of f(x) is [-1, 2] then domain of f([x]-x^2+4) where [.] den...

    Text Solution

    |

  2. Period of the function f(x) = [5x + 7] + cospix - 5x where [·] denotes...

    Text Solution

    |

  3. The period of f(x)=[x]+[2x]+[3x]+[4x]+[n x]-(n(n+1))/2x , where n in ...

    Text Solution

    |

  4. Let Sn=sum(r+1)^(n)r ! (n>6), then Sn-7[(Sn)/7] (where [.] denotes the...

    Text Solution

    |

  5. Period of the function f(x) =(1)/(3){sin 3x + |sin 3x | + [sin 3x]} is...

    Text Solution

    |

  6. The graph of y = f(x} is shown, then the number of solutions of f(f(x}...

    Text Solution

    |

  7. If f(x) = sin^(-1)(m^(2) -3m+ 1)sec (absx)/3-[e^(m-4)](sin{x}), where ...

    Text Solution

    |

  8. If f(x)=sinx+cosx and g(x)=x^2-1, then g(f (x)) is invertible in the ...

    Text Solution

    |

  9. If f(x)=abs(x-1)+abs(x-4)+abs(x-9)+…+abs(x-2500)AA x inR, where m and ...

    Text Solution

    |

  10. Domain of the function f(x) = sin^(-1) [1 + cos x]- sqrt(16-x^(2)) ([....

    Text Solution

    |

  11. The number of solutions of log(x)3. = 2x-3 is,

    Text Solution

    |

  12. Domain of f(x)=sqrt((x-1)/(x-2{x})), where {.} denotes the fractional ...

    Text Solution

    |

  13. Let f(x)=sqrt([sin 2x] -[cos 2x]) (where I I denotes the greatest inte...

    Text Solution

    |

  14. The region M consists of all the points (x, y) satisfying the inequali...

    Text Solution

    |

  15. The domain of the function f(x)=sqrt(((sinx-e^(x))(cosx-3)("In"x+2))/(...

    Text Solution

    |

  16. A function f: I to I, f(x + y) = f(x) + f(y) - 1/2 AAx, y in I, where ...

    Text Solution

    |

  17. Consider the function f: A -> A where A:{1,2,3,4,5} which satisfy the...

    Text Solution

    |

  18. If f(x+y)=f(x)-f(y)+2xy-1AAx,yinR. Also if f(x) is differentiable and ...

    Text Solution

    |

  19. If f(x) is a real-valued function discontinuous at all integral points...

    Text Solution

    |

  20. A function f from integers to integers is defined as f(x)={{:(n+3",",n...

    Text Solution

    |