Home
Class 12
MATHS
The range of function f (x) =[1+sin x] +...

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

A

`{(n ^(2) +n-2)/(2), (n(n+1))/(2)}`

B

`{(n (n+1))/(2)}`

C

`{(n(n +1))/(2), (n ^(2) +n+2)/(2), (n ^(2)+ n+4)/(2)}`

D

`{(n (n+1))/(2), (n ^(2) +n-2)/(2)}`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise ONE OR MORE THAN ONE ANSWE IS/ARE CORRECT|23 Videos

  • FUNCTION

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise COMPREHENSION TYPE PROBLEMS|13 Videos

  • ELLIPSE

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-4 : Subjective Type Problems|2 Videos

  • HYPERBOLA

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-4 : Subjective Type Problems|3 Videos

Similar Questions

Explore conceptually related problems

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

If f(x)=[sin^(2) x] ([.] denotes the greatest integer function), then

Draw the graph of [y] = sin x, x in [0,2pi] where [*] denotes the greatest integer function

If [sin x]+[sqrt(2) cos x]=-3 , x in [0,2pi] , (where ,[.] denotes th greatest integer function ), then

lim _(x to (pi)/(2))(sin x )/(cos ^(-1)[(1)/(4 ) (3 sin x- sin 3x)]), (where [.] denotes greatest integer function) is :

If f(x) =[ sin ^(-1)(sin 2x )] (where, [] denotes the greatest integer function ), then

Range of f(x) =[1+sinx]+[cosx-1]+[tan^(- 1)x] AA x in [0,2pi] where [] denotes the greatest integer function is

f(x)=sin^(-1)((2-3[x])/4) , which [*] denotes the greatest integer function.

Range of f(x)=sin^(-1)[x-1]+2cos^(-1)[x-2] ([.] denotes greatest integer function)

The value of int_(-20pi)^(20 pi) |sin x| [ sin x] dx is (where [.] denotes greatest integer function)

VIKAS GUPTA (BLACK BOOK) ENGLISH-FUNCTION -SUBJECTIVE TYPE PROBLEMS
  1. The range of function f (x) =[1+sin x] + [2+sin ""(x)/(2)]+[3+ sin ""(...

    Text Solution

    |

  2. Let f (x) be a polynomial of degree 6 with leading coefficient 2009, S...

    Text Solution

    |

  3. Let f(x)=x^(3)-3x+1. Then number of different real solutions of f(f(x)...

    Text Solution

    |

  4. If f(x+y+1)={sqrt(f(x))+sqrt(f(y))}^2 and f(0)=1AAx ,y in R ,d e t e ...

    Text Solution

    |

  5. If the domain of f(x) = sqrt (12-3^(x)-3^(3-x))+ sin ^(-1) ((2x)/(3 ...

    Text Solution

    |

  6. The number of elements in the range of the function : y =sin ^(-1) [...

    Text Solution

    |

  7. The number of integers in the range of function f(x)= [sinx] + [cosx] ...

    Text Solution

    |

  8. If P (x) is polynomial of degree 4 such than P (-1)=P (1) =5 and P (-2...

    Text Solution

    |

  9. The number of integral vlaue (s) of k for which the curve y = sqrt ( ...

    Text Solution

    |

  10. Let the solution set of the equation sqrt([x+[x/2]])+[sqrt({x})+[x/3]]...

    Text Solution

    |

  11. For the real number x, let f (x)=(1)/( ""^(2011sqrt(1-x^(2011)))). Fi...

    Text Solution

    |

  12. Find the number of elements contained in the range of the function f (...

    Text Solution

    |

  13. Let f (x,y)= x^(2) - y^(2) and g (x,y)=2xy. such that (f ( x,y))^(2) -...

    Text Solution

    |

  14. Let f (x) = (x+5)/(sqrt(x^(2) +1) ) , then the smallest integral va...

    Text Solution

    |

  15. The number of roots of equation (((x-1)(x-3))/((x-2)(x-4))-e^(x)) (((x...

    Text Solution

    |

  16. Let f (x) =x ^(2)-bx+c,b is an odd positive integer. Given that f (x)=...

    Text Solution

    |

  17. Let f(x) be a continuous function such that f(0) = 1 and f(x)=f(x/7)=x...

    Text Solution

    |

  18. If x=10 sum(r=3) ^(100) (1)/((r ^(2) -4)), then [x]= (where [.] deno...

    Text Solution

    |

  19. Let f(x)= cx+d/ax+b ​ . Then fof(x) = x provided that.

    Text Solution

    |

  20. Let A = {x|x ^(2) -4x+ 3 lt 0 , x in R} B={x|2^(1-x)+p le 0;x^2-2(p+7...

    Text Solution

    |

  21. Let the maximum value of expression y= (x ^(4)-x ^(2))/(x ^(6) + 2x ^(...

    Text Solution

    |