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3. Binary Operations
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Q8 of 123 Page 3

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

The given binary operation is a*b =

We have to find the value of x so that 2*(x*5) = 10


Firstly, x*5 = = x


Now 2*(x*5) = 2*x =


As per the question, it is equal to 10


∴ = 10


∴ x = 25


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Write the total number of binary operations on a set consisting of two elements.

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Write the identity element for the binary operation * defined on the set R of all real numbers by the rule for all a, b ∈ R.

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Write the inverse of 5 under multiplication modulo 11 on the set {1, 2, …, 10}.

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Questions · 123
3. Binary Operations
1 1 1 1 1 1 1 2 2 2 2 2 2 3 4 5 6 7 8 9 10 1 1 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
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