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`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`

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Using `a*e=e=>frac{ae}{2}=a=>frac{ae}{2}-a=0 `
`a/2 (e-2)=0`
`e=2`
`ab/2=2=>b(4/a)=>a^(-1)=4/a`
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. Q^+ denote the set of all positive rational numbers. If the binary ope...

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

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

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

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

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

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

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

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

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  10. Subtraction of integers is

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

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

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

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

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

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

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

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

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

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

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