Home
Class 12
MATHS
Which of the following are true?...

Which of the following are true?

A

`f(x)={{:(1",", "if x is rational"),(0",", "if x is irrational"):}`

B

`f(x)={{:(x-[x]",", 2n le x lt 2n+1),(1/2",", 2n+1 le x lt 2n+2):}` where `[*]` denotes the greatest integer function

C

`f(x)=(-1)^([(2x)/pi])`, where `[*]` denotes the greatest integer function

D

`f(x)=ax-[ax+a]+tan((pix)/2)," where " [*]` denotes the greatest integer function

Text Solution

Verified by Experts

The correct Answer is:
B, C, D
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|25 Videos

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|76 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

An aluminium sphere is dipped into water. Which of the following is true?

Which of the following is true ?

Which of the following is a true statement?

Which of the following is a true fruit?

Which of the following is true?

Which of the following is true?

If f : X to Y is an invertible function, then which of the following is true?

If y+log(1+x)=0 which of the following is true?

Which of the following is true :

DeltaABC~=DeltaQPR then which of the following is true ?

ARIHANT MATHS-FUNCTIONS-Exercise (More Than One Correct Option Type Questions)
  1. f(x)=x^2-2a x+a(a+1),f:[a ,oo)⟶[a ,oo)dot If one of the solution of th...

    Text Solution

    |

  2. The function 'g' defined by g(x)=sin(sin^(-1){sqrt(x)}+cos (sin^(-1){s...

    Text Solution

    |

  3. The graph of f:R rarr R defined by y=f(x) is symmetric with respect to...

    Text Solution

    |

  4. Let y=f(x) be a differentiable function such that f(−1)=2,f(2)=−1 and ...

    Text Solution

    |

  5. Let f(x)=abs(x-1)+abs(x-2)+abs(x-3)+abs(x-4), then a. least value of ...

    Text Solution

    |

  6. Let A={1,2,3,4,5}, B={1,2,3,4} and f:A rarr B is a function, then

    Text Solution

    |

  7. In a function 2f(x)+ xf(1/x)-2f(|sqrt2sin(pi(x+1/4))|)=4cos^2[(pix)/2]...

    Text Solution

    |

  8. If f(x) is a differntiable function satisfying the condition f(100x)=x...

    Text Solution

    |

  9. If [x] denotes the greatest integer function then the extreme values o...

    Text Solution

    |

  10. Which of the following are true?

    Text Solution

    |

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

    Text Solution

    |

  12. Let f: R->R be a function defined by f(x+1)=(f(x)-5)/(f(x)-3)AAx in R...

    Text Solution

    |

  13. Let f(x)=1-x-x^3.Find all real values of x satisfying the inequality,...

    Text Solution

    |

  14. If a function satisfies (x-y)f(x+y)-(x+y)f(x-y)=2(x^2 y-y^3) AA x, y i...

    Text Solution

    |

  15. If the fundamental period of function f(x)=sinx+cos(sqrt(4-a^(2)))x "...

    Text Solution

    |

  16. Let f (x) be a real vaued continuous function such that f (0) =1/2 a...

    Text Solution

    |

  17. if f(g(x)) is one-one function, then

    Text Solution

    |

  18. Which of the following functions have their range equal to R(the set o...

    Text Solution

    |

  19. Which of the following pairs of function are identical? a. f(x)=e^(In ...

    Text Solution

    |

  20. Let f:R rarr R defined by f(x)=cos^(-1)(-{-x}), where {x} denotes fra...

    Text Solution

    |