Home
Class 12
MATHS
Let ast be a binary operation defined...

Let ` ast` be a binary operation defined on `Q^+` by the rule `a ast b=(a b)/3` for all `a ,\ b in Q^+` . The inverse of `4 ast 6` is

A

(a) `frac{9}{8}`

B

(b) `frac{2}{3}`

C

(c) `frac{3}{2}`

D

(d) none of these

Text Solution

Verified by Experts

The correct Answer is:
(a) `frac{9}{8}`
Given that,
`a ast b=(a b)/3`
`4 ast 6=(4 times 6)/3=8`
`a rightarrow a^-1`
`a^-1oa=aoa^-1=e`

Let `e=` identity
`aoe=eoa=a`
`a ast e=a`
...
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

Consider the binary operation * defined on Q-{1} by the rule a*b=a+b-a b for all a ,\ b in Q-{1} . The identity element in Q-{1} is (a) 0 (b) 1 (c) 1/2 (d) -1

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

Discuss the commutativity and associativity of binary operation* defined on Q by the rule a*b=a-b+ab for all a,b in Q

Let * be a binary operation defined by a*b=3a+4b-2. Find 4^(*)5

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

Q^(+) is the set of all positive rational numbers with the binary operation * defined by a*b=(ab)/(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)

For the binary operation * defined on R-{-1} by the rule a*b=a+b+ab for all a,b in R-{1}, the inverse of a is a (b) -(a)/(a+1)(c)(1)/(a) (d) a^(2)

If the binary operation * defined on Q, is defined as a*b=2a+b-ab, for all a*bQ, find the value of 3*4

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.

RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. Q^+ is the set of all positive rational numbers with the binary ope...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. Subtraction of integers is

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  12. A binary operation ast on Z defined by a ast b=3a+b for all a ,\ b i...

    Text Solution

    |

  13. Letastbe a binary operation on N defined by a ast b=a+b+10 for all a...

    Text Solution

    |

  14. Consider the binary operation ast defined on Q-{1} by the rule a ast...

    Text Solution

    |

  15. For the binary operation ast defined on R-{-1} by the rule a ast b=a...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. Let ast be a binary operation defined on Q^+ by the rule a ast b=(a...

    Text Solution

    |

  19. The number of binary operations that can be defined on a set of 2 el...

    Text Solution

    |

  20. The number of commutative binary operations that can be defined on a...

    Text Solution

    |