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Q.

On the set of positive rational, a binary operation * is defined by Question Image. If Question Image then find the value of Question Image.


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a

Question Image

b

Question Image

c

Question Image

d

Question Image 

answer is A.

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Detailed Solution

Concept- Under the binary operation, we have a set of positive rational numbers. Then it is defined by some condition. We apply this condition, and then we obtain the value.
Here, set of all positive rational number and is denoted by Question Image.
It is form Question Image is always positive, Question ImageAlso given that binary operation is ' * ' is defined by Question Image, where Question ImageAgain, it is given that Question Image, where Question ImageAlso, 2 belongs to Question ImageBecause 2 can be written as Question Image, where Question ImageHence, Question ImageHere Question Image can be written by using Question ImageAlso, it is defined by Question ImageHere Question Image and Question Image, we get
Question ImageWhen substituting Question Image, we get
Question ImageQuestion ImageMultiply 2 by Question Image, we get,
Question ImageQuestion ImageQuestion ImageTherefore, Question Image belongs to a set of positive rational numbers.
That is, Question ImageHence, the correct answer is option 1) Question Image.
 
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