Home
Class 12
MATHS
Q^+ is the set of all positive rationa...

`Q^+` is the set of all positive rational numbers with the binary operation * defined by a*b= `(a b)/2` for all `a ,\ b in Q^+` . The inverse of an element `a in Q^+` is `a` (b) `1/a` (c) `2/a` (d) `4/a`

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF INTEGRALS

    RD SHARMA ENGLISH|Exercise All Questions|163 Videos

  • BINOMIAL DISTRIBUTION

    RD SHARMA ENGLISH|Exercise All Questions|149 Videos

Similar Questions

Explore conceptually related problems

On the set Q^+ of all positive rational numbers a binary operation * is defined by a * b=(a b)/2 for all a ,\ b in Q^+ . The inverse of 8 is (a) 1/8 (b) 1/2 (c) 2 (d) 4

Find the identity element in set Q^+ of all positive rational numbers for the operation * defined by a*b=(a b)/2 for all a , b in Q^+dot

Find the identity element in set Q^+ of all positive rational numbers for the operation * defined by a*b= (a b)/2 for all a , b in Q^+dot

Q^+ denote the set of all positive rational numbers. If the binary operation o. on Q^+ is defined as a o.b=(a b)/2, then the inverse of 3 is

On the set Z of all integers a binary operation ** is defined by a**b=a+b+2 for all a ,\ b in Z . Write the inverse of 4.

Check the commutativity of * on Q defined by a*b=(a-b)^2 for all a ,\ b in Q .

On the set Q of all rational numbers if a binary operation * is defined by a*b= (a b)/5 , prove that * is associative on Qdot

Check the commutativity of * on Q defined by a*b=a b^2 for all a ,\ b in Q .

For the binary operation * defined on R-{1} by the rule a * b=a+b+a b for all a ,\ b in R-{1} , the inverse of a is

On Q , the set of all rational numbers a binary operation * is defined by a*b= (a+b)/2 . Show that * is not associative on Qdot

RD SHARMA ENGLISH-BINARY OPERATIONS-All Questions
  1. Q^+ denote the set of all positive rational numbers. If the binary ope...

    Text Solution

    |

  2. If G is the set of all matrices of the form [xxxx] , where x in R-...

    Text Solution

    |

  3. Q^+ is the set of all positive rational numbers with the binary oper...

    Text Solution

    |

  4. If the binary operation o. is defined on the set Q^+ of all positive r...

    Text Solution

    |

  5. Let * be a binary operation defined on set Q-{1} by the rule a*b=a+b...

    Text Solution

    |

  6. Which of the following is true? * defined by (a)a*b=(a+b)/2 is a bin...

    Text Solution

    |

  7. The binary operation * defined on N by a*b=a+b+a b for all a ,\ b in...

    Text Solution

    |

  8. If a binary operation * is defined by a*b=a^2+b^2+a b+1 ,then (2*3)*...

    Text Solution

    |

  9. Let * be a binary operation on R defined by a*b= a b+1 . Then, * is ...

    Text Solution

    |

  10. Subtraction of integers is (a)commutative but not associative (b)c...

    Text Solution

    |

  11. The law a+b=b+a is called

    Text Solution

    |

  12. An operation * is defined on the set Z of non-zero integers by a*b...

    Text Solution

    |

  13. On Z an operation * is defined by a*b=a^2+b^2 for all a ,\ b in Z ....

    Text Solution

    |

  14. A binary operation * on Z defined by a*b= 3a+b for all a ,\ b in Z ...

    Text Solution

    |

  15. Let * be a binary operation on N defined by a*b=a+b+10 for all a ,\ ...

    Text Solution

    |

  16. Consider the binary operation * defined on Q-{1} by the rule a*b= a+...

    Text Solution

    |

  17. For the binary operation * defined on R-{1} by the rule a*b=a+b+a b ...

    Text Solution

    |

  18. For the multiplication of matrices as a binary operation on the set...

    Text Solution

    |

  19. On the set Q^+ of all positive rational numbers a binary operation *...

    Text Solution

    |

  20. Let * be a binary operation defined on Q^+ by the rule a*b=(a b)/3 f...

    Text Solution

    |