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) then which of the following is correct a. `n` (b) 1 (c) `1/n` (d) none of these

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP ENGLISH|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP ENGLISH|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

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

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,

Evaluate: int_0^x[cost]dt where x in (2npi,(4n+1pi/2),n in N ,a n d[dot] denotes the greatest integer function.

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

The integral int_(-1/2)^(1/2) ([x]+1n((1+x)/(1-x)))dx is equal to (where [.] represents the greatest integer function)

If [dot] denotes the greatest integer function, then find the value of lim_(x->0) ([x]+[2x]++[n x])/(n^2)

f(x) = (x^n + (pi/3)^n)/(x^(n-1) + (pi/3)^(n-1)) ,(n is an even number, then which of the following is correct

The number of terms in the expansion of (x+1/x+1)^n is (A) 2n (B) 2n+1 (C) 2n-1 (D) none of these

Prove that for n=1, 2, 3... [(n+1)/2]+[(n+2)/4]+[(n+4)/8]+[(n+8)/16]+...=n where [x] represents Greatest Integer Function

If phi(x)=lim_(n->oo)(x^(2n)(f(x)+g(x)))/(1+x^(2n)) then which of the following is correct

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. If m and n are positive integers satisfying 1+cos2theta+cos4theta+cos6...

    Text Solution

    |

  2. Find logarithm of the following values: 500

    Text Solution

    |

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

    Text Solution

    |

  4. Find logarithm of the following values: 500

    Text Solution

    |

  5. Total number of ordered pairs (x, y) satisfying |y| = cos x and y = si...

    Text Solution

    |

  6. The smallest natural number of the form 123x43y, which is exactly divi...

    Text Solution

    |

  7. Circle with centre C (1, 1) passes through the origin and intersects t...

    Text Solution

    |

  8. Number of integers whose characteristic of logarithms to the base 10 i...

    Text Solution

    |

  9. If f(x+y)=2f(x) f(y) for all x,y where f'(0)=3 and f(4)=2, then f'(4) ...

    Text Solution

    |

  10. If mantissa of lagarithm of 719.3 to the base 10 is 0.8569 then mantis...

    Text Solution

    |

  11. If f(x)=x^(n), then the value of f(1)-(f'(1))/(1!)+(f''(1))/(2!)-(f''...

    Text Solution

    |

  12. Number of digits in integral part of 60^(12)+60^(-12)-60^(-15)is ("giv...

    Text Solution

    |

  13. The extremities of the diagonal of a rectangle are (-4, 4) and (6,-1)....

    Text Solution

    |

  14. In the adjoining figure, find the value of tan B.

    Text Solution

    |

  15. The number of ways in which 4 different red balls and 8 similar green ...

    Text Solution

    |

  16. A rhombus is formed by two radii and two chords of a circle whose r...

    Text Solution

    |

  17. The number of ways of seven digit number with distinct digits of the f...

    Text Solution

    |

  18. Given log 2 =0.3010, log 3=0.4771, find thevalue of ((16)^(1/5) *5^2)/...

    Text Solution

    |

  19. If the terms sqrt(a-x),sqrtx,sqrt(a+x) are in A.P and all are integers...

    Text Solution

    |

  20. The value of expression, log4((x^2)/4)-2log4(4x^4) when x=-2 is (a)-6...

    Text Solution

    |