Home
Class 12
MATHS
Consider the function f defined by f(x)...

Consider the function f defined by `f(x)=(0,x=0` or x is irrational `1/n`, where x is a non – zero rational number `m/n, n > 0 and m/n` is in lowest term which of the following statements is true?

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP|Exercise All Questions|15 Videos
  • MATRICES

    RESONANCE DPP|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

x^(m)xx x^(n)=x^(m+n) , where x is a non zero rational number and m,n are positive integers.

The function f(x)={0,x is irrational and 1,x is rational,is

If f (x) = lim _( n to oo) (n (x ^(1//n)-1)) for x gt 0, then which of the following is/are true?

The function f:N rarr N defined by f(x)=x-5[(x)/(5)] where N is a set of natural numbers,then

Let f : R - {n} rarr R be a function defined by f(x)=(x-m)/(x-n) , where m ne n . Then,

Let f:R rarr R be defined as f(x)={0,x is irrational sin|x|,x is rational Then which of the following is true?

Let f(x)={x^(n),x is rational and -x^(n),x is irrational then f(x) is discontinuous at x=0 if n

RESONANCE DPP-JEE MAINS-All Questions
  1. The value of ("lim")(xvec0)(e^(2x)-cos x-"ln"(1+2x))/(xtanx-sinx)i s ...

    Text Solution

    |

  2. alpha,beta,gammaa n ddelta are the smallest positive angle in ascendin...

    Text Solution

    |

  3. Consider the function f defined by f(x)=(0,x=0 or x is irrational 1/...

    Text Solution

    |

  4. if m belongs to [-1,0], then prove that the equation sin^4 x+ (m+1) si...

    Text Solution

    |

  5. Prove the trigonometric identities: (1-sintheta)/(1+sintheta)=(secthet...

    Text Solution

    |

  6. Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in ...

    Text Solution

    |

  7. ("lim")(nvecoo)[sum(r=1)^n1/(2^r)],"where "[dot]" denotes G I F is equ...

    Text Solution

    |

  8. Consider the equation x ^(3) -ax ^(2) +bx-c=0, where a,b,c are ration...

    Text Solution

    |

  9. The lines x+y-1=0,(m-1)x+(m^2-7)y-5=0, and (m-2)x+(2m-5)y=0 are concur...

    Text Solution

    |

  10. If m1 and m2 are the roots of the equation x^2-a x-a-1=0 , then the ar...

    Text Solution

    |

  11. The sides of a rhombus are parallel to the lines x+y-1=0 and 7x-y-5=0...

    Text Solution

    |

  12. Consider lim(x->0)(a x+b e^(-x)+sinx+1)/(a x-bsinx)=l(l is finite) the...

    Text Solution

    |

  13. Let C be a circle with two diameters intersecting at an angle of 30^0d...

    Text Solution

    |

  14. The roots of the equation x^(5)-40x^(4)+ax^

    Text Solution

    |

  15. The equatio of a circel touching the coordinate axes and the line 3x -...

    Text Solution

    |

  16. Let f(x)=x^(3)+ax^(2)+bx+c be the given cubic polynomial and f(x)=0 be...

    Text Solution

    |

  17. |(2x-1)/(x-1)|>2

    Text Solution

    |

  18. If f(x)a n dg(x) are continuous functions in [a , b] and are different...

    Text Solution

    |

  19. |x-1|+|x-2|+|x-3|geq6

    Text Solution

    |

  20. If sum(r=1)^n r(r+1)(2r+3)=a n^4+b n^3+c n^2+d n+e , then a-b=d-c ...

    Text Solution

    |