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COMEDK · Maths · 17. Mathematical Reasoning

In the group \(Q-\{1\}\) under the binary operation * defined by \(a * b=a+b+a b\) the inverse of 10 is

  1. A \(\frac{1}{10}\)
  2. B \(\frac{11}{10}\)
  3. C \(\frac{-11}{10}\)
  4. D \(\frac{-10}{11}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{-10}{11}\)

Step-by-step Solution

Detailed explanation

Let the inverse element of 10 be \(e\), then \[ a * e=0 \] Therefore, \(10 \div e=10+e+10 e=0\) \[ \Rightarrow \quad 10+11 e=0 \] \(\begin{array}{rr}\Rightarrow & 11 e=-10 \\ \Rightarrow & e=\frac{-10}{11}\end{array}\)