Home
Class 12
MATHS
Let '*' be a binary operation on Q0 (set...

Let `'*'` be a binary operation on `Q_0` (set of all non-zero rational numbers) defined by `a*b=(a b)/4` for all `a , b in Q_0dot` Then, find the identity element in `Q_0` inverse of an element in `Q_0dot`

Text Solution

Verified by Experts

For `a,b in Q∗` is a binary operation on `Q` as `a∗b= frac{ 3ab}{5}` ​
Now `b∗a= frac{ 3ba}{5}` ...
Promotional Banner

Topper's Solved these Questions

  • ARITHMETIC PROGRESSION

    RD SHARMA|Exercise EXAMPLE|5 Videos

  • BINOMIAL DISTRIBUTION

    RD SHARMA|Exercise Solved Examples And Exercises|141 Videos

Similar Questions

Explore conceptually related problems

Let t be a binary operation on Q_(0)( set of non- zero rational numbers) defined by a*b=(3ab)/(5) for all a,b in Q_(0) Find the identity element.

Let * be a binary operation o Q defined by a^(*)b=(ab)/(4) for all a,b in Q,find identity element in Q

Let 'o' be a binary operation on the set Q_0 of all non-zero rational numbers defined by a\ o\ b=(a b)/2 , for all a ,\ b in Q_0 . Show that 'o' is both commutative and associate (ii) Find the identity element in Q_0 (iii) Find the invertible elements of Q_0 .

Let t be a binary operation on Q_(0)( set of non- zero rational numbers) defined by a*b=(3ab)/(5) for all a,b in Q_(0). Show that * is commutative as well as associative.Also,find the identity element,if it exists.

Let t be a binary operation,on the set of all non-zero real numbers,given by a*b=(ab)/(5) for all a,b in R-{0}. Write the value of x given by 2*(x*5)=10

Let * be a binary operation,on the set of all- zero real numbers,given by a a^(*)b=(ab)/(5) for all a,b in R-{0}. Find the value of x given that 2*(x*5)=10

Let * be a binary operation on N, the set of natural numbers, defined by a*b= a^b for all a , b in Ndot Is '*' associative or commutative on N ?

Let * be a binary operation on the set Q of all rational number given as a*b= (2a-b)^(2) for all a,b in Q find 3*5 and 5*3 Is 3*5=5*3?

Let S be the set of all rational numbers except 1 and * be defined on S by a*b=a+b-ab, for alla ,b in S. Find its identity element

RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. Let * be a binary operation on set Q-[1] defined by a*b=a+b-a b for al...

    Text Solution

    |

  2. Show that the binary operation * on A=R-{-1} defined as a*b=a+b+a b fo...

    Text Solution

    |

  3. Let '*' be a binary operation on Q0 (set of all non-zero rational numb...

    Text Solution

    |

  4. Let '*' be a binary operation on Q0 (set of all non-zero rational numb...

    Text Solution

    |

  5. Let * be a binary operation on N given by a*b=LdotCdotM(a ,\ b) for...

    Text Solution

    |

  6. Let '*' be a binary operation on N given by a*b=LdotCdotMdot(a , b) fo...

    Text Solution

    |

  7. Define a binary operation * on the set A={0,1,2,3,4,5} given by a*b=a ...

    Text Solution

    |

  8. On the set M=A(x)={[xxxx]: x in R}of2x2 matrices, find the identity ...

    Text Solution

    |

  9. Let X be a non-empty set and let * be a binary operation on P(X) (t...

    Text Solution

    |

  10. Let X be a nonempty set and *be a binary operation on P(X), the power ...

    Text Solution

    |

  11. Let X be a non-empty set and let * be a binary operation on P\ (X) ...

    Text Solution

    |

  12. Let X be a non-empty set and let * be a binary operation on P\ (X) ...

    Text Solution

    |

  13. Let A=QxxQ and let ** be a binary operation on A defined by (a ,\ b)...

    Text Solution

    |

  14. Let A=QxxQ and let * be a binary operation on A defined by (a ,\ b)...

    Text Solution

    |

  15. Let A=Nuu{0}xxNuu{0} and let * be a binary operation on A defined b...

    Text Solution

    |

  16. Let A=Nuu{0}xxNuu{0} and let * be a binary operation on A defined b...

    Text Solution

    |

  17. Let A=NxxN , and let * be a binary operation on A defined by (a ,\ ...

    Text Solution

    |

  18. Let A=NxxN , and let * be a binary operation on A defined by (a ,\ ...

    Text Solution

    |

  19. Show that the number of binary operations on {1," "2} having 1 as iden...

    Text Solution

    |

  20. Determine the total number of binary operations on the set S={1,\ 2...

    Text Solution

    |