Home
Class 12
MATHS
On the set R of real numbers, the relati...

On the set R of real numbers, the relation `rho` is defined by `x rho y, (x, y) in R`.

A

If `|x-y|lt 2` then `rho` is reflexive but neither symmetric nor transitive

B

If `x-y lt 2` then `rho` is reflexive and symmetric but not transitive

C

If `|x | ge y` then `rho` is reflexive and transitive but not symmetric

D

If `x gt |y|` then `rho` is transitive but neither reflexive nor symmetric.

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • QUESTION PAPER 2017

    WB JEE PREVIOUS YEAR PAPER|Exercise Multiple Choice Questions|75 Videos
  • QUESTION PAPER 2019

    WB JEE PREVIOUS YEAR PAPER|Exercise MULTIPLE CHOICE QUESTIONS|73 Videos

Similar Questions

Explore conceptually related problems

If R denotes the set of all real numbers then the mapping f:R to R defined by f(x)=|x| is -

RR is a set of real numbers .If the relation R over a set A is defined such that R={(a,b): a-blt 3, a,b in RR}. then relation R is -

IR is a set of real number. If the realtion R over a set A is defined such that R= {(a,b):a-b< 3, a,b,inIR }, then relation R is

Let ZZ be the set of integers and let R be the relation on ZZ defined as R={(x,y)|x,y in ZZ and x^2+y^2=100} Find R as the set of ordered pairs. Also find its domain and range.

On the set R of real numbers we define xPy if and only if xy ge0 . Then the relation P is

Let a relation R_1 on the set R of real numbers be defined as (a , b) in R_1 1+a b >0 for all a , b in Rdot Show that R_1 is reflexive and symmetric but not transitive.

A relation R on the set of natural number N N is defined as follows : (x,y) in R to (x-y) is divisible by 5 for all x,y in N N Prove that R is an equivalence relation on N N .

Let R be the set of real numbers. If f:R->R is a function defined by f(x)=x^2, then f is (a) injective but not surjective (b) surjective but not injective (c) bijective (d) non of these

Let R be the set of real numbers and the mappings f:R toR" and "g:RtoR be defined by f(x)=5-x^2" and " g(x)=3x-5 , then the value of (f@g)(-1) is

WB JEE PREVIOUS YEAR PAPER-QUESTION PAPER 2018-MULTIPLE CHOICE QUESTIONS
  1. If the following three linear equations have a non-trivial solution, t...

    Text Solution

    |

  2. On In a relation rho is defined by x rho y if and only if x-y is zero ...

    Text Solution

    |

  3. On the set R of real numbers, the relation rho is defined by x rho y, ...

    Text Solution

    |

  4. If f: R rarr R be defined by f(x)= e^(x) and g: R rarr R be defined by...

    Text Solution

    |

  5. In order to get a head at least once with probility ge 0.9. The minimu...

    Text Solution

    |

  6. A student appears for test I, II and III. The student is successful if...

    Text Solution

    |

  7. If sin 6 theta + sin 4theta + sin 2theta= 0, then general value of the...

    Text Solution

    |

  8. If 0 le A le (pi)/(4), then tan^(-1) ((1)/(2) tan 2A) + tan^(-1) (cot ...

    Text Solution

    |

  9. Without changing the direction of the axes, the origin is transferred ...

    Text Solution

    |

  10. The angle between a pair of tangents drawn from a point P to the circl...

    Text Solution

    |

  11. The point Q is the image of the point P(1,5) about the line y=x and R ...

    Text Solution

    |

  12. The angular points of a triangle are A(-1, -7), B(5, 1) and C(1, 4). T...

    Text Solution

    |

  13. If one of the diameters f the circle, given by the equation x^(2)+y^(2...

    Text Solution

    |

  14. A chord AB is drawn from the point A(0, 3) on the circle x^(2)+4x+(y-3...

    Text Solution

    |

  15. Let the occentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=...

    Text Solution

    |

  16. Let A. B be two distinct points on the parabola y^(2)=4x. If the axis ...

    Text Solution

    |

  17. Let P(a t^(2), 2 a t), Q, R (a r^(2).2 ar) be three points on a parabo...

    Text Solution

    |

  18. Let P be a point on the ellipse (x^(2))/(9) + (y^(2))/(4)=1 and the li...

    Text Solution

    |

  19. A point P lies on a line through Q(1, -2, 3) and is parallel to the li...

    Text Solution

    |

  20. The foot of the perpendicular drawn from the point (1, 8,4) on the lin...

    Text Solution

    |