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Jamb Mathematics Past QuestionsQuestions and Answers on Binary OperationsQuestion 21:The identity element with respect to the multiplication shown in the diagram below is \(\begin{array}{c|c} \otimes & p & p & r & s \\ \hline p & r & p & r & p \\ q & p & q & r & s\\ r & r & r & r & r\\ s & q & s & r & q\end{array}\) A. P B. Q C. R D. S Question 22:The binary operation \(\oplus\) is defined by x \(\ast\) y = xy - y - x for all real values x and y. If x \(\ast\) 3 = 2\(\ast\), find x A. -1 B. 4 C. 1 D. 5 Question 23:If \(m*n = (\frac{m}{n} - \frac{n}{m}\)) for m, n belong to R, evaluate -3*4 A. \(\frac{-25}{12}\) B. \(\frac{-7}{12}\) C. \(\frac{7}{12}\) D. \(\frac{25}{12}\) Question 24:A binary operation * is defined by a*b = ab+a+b for any real number a and b. if the identity element is zero, find the inverse of 2 under this operation. A. 2/3 B. 1/2 C. -1/2 D. -2/3 Question 25:A binary operation * is defined by a * b = a\(^b\). If a * 2 = 2 - a, find the possible values of a. A. 1, -1 B. 1, 2 C. 2, -2 D. 1, -2 |
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