Home
Class 12
MATHS
For let h(x)={1/q if x=p/q and 0 if x...

For let `h(x)={1/q if x=p/q and 0` if x is irrational where `p & q > 0` are relatively prime integers 0 then which one does not hold good?

A

h(x) is discontinuous for all x in `(0, oo)`

B

h(x) is continuous for each irrational in `(0, oo)`

C

h(x) is discontinuous for each rational in `(0, oo)`

D

h(x) is not derivable for all x in `(0, oo)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|26 Videos

  • CONTINUITY AND DIFFERENTIABILITY

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

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise For Session 7|10 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|43 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

For x >0,l e th(x)={1/q ,ifx=p/q0,ifxi si r r a t ion a l where p ,q >0 are relatively prime integers. Then prove that f(x) is continuous for all irrational values of xdot

If p,q in N and 0,12=(p)/(q) where p and q are relatively prime then identify which of the following is incorrect

Prove that sqrt(p)+sqrt(q) is an irrational,where p and q are primes.

If sum of all the solutions of the equation (4tan x+tan^(2)x+1)=2sqrt(2)sin(x+(pi)/(4))(1+tan^(2)x) in [0,pi] is (p, (pi)/(q)) where p,q are relatively prime number, then find the value of (p+q)

Express 0.123 as a rational number in the form of p/q, where p,p are integers,and q!=0

Let the maximum value of expression y= (x ^(4)-x ^(2))/(x ^(6) + 2x ^(3) -1) for x gt 1 is (p)/(q), where p and q are relatively prime natural numbers, then p+ q=

The reciprocal of any rational number (p)/(q) , where p and q are integers and q ne 0 , is

If the ratio of the coefficient of x^(10) in (1-x^(2))^(10) and term independent of x in (x-2/x)^(10) is p/q (where p and q are relative prime numbers) then q/8-p is

ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Single Option Correct Type Questions)
  1. If (d(f(x)))/(dx) = e^(-x) f(x) + e^(x) f(-x), then f(x) is, (given f(...

    Text Solution

    |

  2. Let f : (0, oo) rarr R be a continuous function such that f(x) = int(0...

    Text Solution

    |

  3. For let h(x)={1/q if x=p/q and 0 if x is irrational where p & q ...

    Text Solution

    |

  4. Let f(x) = (g(x))/(h(x)), where g and h are continuous functions on th...

    Text Solution

    |

  5. f(x)=(cosx-sin2x)/((pi-2x)^2);g(x)=(e^(-cosx)-1)/(8x-4pi)

    Text Solution

    |

  6. If f(x) = (x-e^(x) + cos 2x)/(x^(2)), x ne 0 is continuous at x = 0, t...

    Text Solution

    |

  7. Consider the function f(x) = [{:(x{x}+1",","if",0 le x lt 1),(2-{x}","...

    Text Solution

    |

  8. Let f(x) = [{:((2^(x)+2^(3-x) - 6)/(sqrt(2^(-x))-2^(1-x))",","if",x gt...

    Text Solution

    |

  9. Let [x] denote the integral part of x in R and g(x) = x- [x]. Let f(x...

    Text Solution

    |

  10. Let f be a differentiable function on the open interval(a, b). Which o...

    Text Solution

    |

  11. Number of points where the function f(x)=(x^2-1)|x^2-x-2| + sin(|x|) i...

    Text Solution

    |

  12. Consider function f: R - {-1,1}-> R. f(x)=x/[1-|x|] Then the incorrect...

    Text Solution

    |

  13. If the functions f : R -> R and g : R -> R are such that f(x) is conti...

    Text Solution

    |

  14. The total number of points of non-differentiability of f(x) = min[|sin...

    Text Solution

    |

  15. The function f(x)=[x]^2-[x^2] is discontinuous at (where [gamma] is t...

    Text Solution

    |

  16. The function f(x) = (x^(2) - 1)|x^(2)-6x + 5|+cos|x| is not differenti...

    Text Solution

    |

  17. If f(x) = {{:((1)/(e^(1//x))",",x ne 0),(0",",x = 0):} then

    Text Solution

    |

  18. Given f(x) = (e^(x)-cos 2x - x)/(x^(2)),"for x" in R-{0} g(x) = {{:(f(...

    Text Solution

    |

  19. The function g(x) = {{:(x+b",",x lt 0),(cos x",",x ge 0):} cannot be m...

    Text Solution

    |

  20. The graph of function f contains the point P(1, 2) and Q(s, r). The e...

    Text Solution

    |