117153
Let * be a binary operation on the set \(Q^{+}\)of all +ve rational numbers defined by \(a * b=\frac{a b}{100}\) for all \(a, b \in Q^{+}\). The inverse of 0.1 under operation * is
1 \(10^5\)
2 \(10^6\)
3 \(10^4\)
4 None of these
Explanation:
Exp: (A) : We have \(\mathrm{a} * \mathrm{~b}=\frac{\mathrm{ab}}{100}\) Let e be the identify element. Then, \(\quad \mathrm{e} * \mathrm{a}=\mathrm{a} * \mathrm{e}=\mathrm{a} \forall \mathrm{a} \in \mathrm{Q}^{+}\) \(\mathrm{a}=\frac{\mathrm{ea}}{100} \Rightarrow \mathrm{e}=100\) Now, let inverse of 0.1 be \(\mathrm{x}\), then \(0.1 * \mathrm{x}=\mathrm{e}\) \(\Rightarrow \quad \frac{0.1 \mathrm{x}}{100}=100 \quad \mathrm{x} \in \mathrm{Q}^{+}\) \(\\ \mathrm{x}=\frac{10^4}{0.1}=10^5\)
117153
Let * be a binary operation on the set \(Q^{+}\)of all +ve rational numbers defined by \(a * b=\frac{a b}{100}\) for all \(a, b \in Q^{+}\). The inverse of 0.1 under operation * is
1 \(10^5\)
2 \(10^6\)
3 \(10^4\)
4 None of these
Explanation:
Exp: (A) : We have \(\mathrm{a} * \mathrm{~b}=\frac{\mathrm{ab}}{100}\) Let e be the identify element. Then, \(\quad \mathrm{e} * \mathrm{a}=\mathrm{a} * \mathrm{e}=\mathrm{a} \forall \mathrm{a} \in \mathrm{Q}^{+}\) \(\mathrm{a}=\frac{\mathrm{ea}}{100} \Rightarrow \mathrm{e}=100\) Now, let inverse of 0.1 be \(\mathrm{x}\), then \(0.1 * \mathrm{x}=\mathrm{e}\) \(\Rightarrow \quad \frac{0.1 \mathrm{x}}{100}=100 \quad \mathrm{x} \in \mathrm{Q}^{+}\) \(\\ \mathrm{x}=\frac{10^4}{0.1}=10^5\)
117153
Let * be a binary operation on the set \(Q^{+}\)of all +ve rational numbers defined by \(a * b=\frac{a b}{100}\) for all \(a, b \in Q^{+}\). The inverse of 0.1 under operation * is
1 \(10^5\)
2 \(10^6\)
3 \(10^4\)
4 None of these
Explanation:
Exp: (A) : We have \(\mathrm{a} * \mathrm{~b}=\frac{\mathrm{ab}}{100}\) Let e be the identify element. Then, \(\quad \mathrm{e} * \mathrm{a}=\mathrm{a} * \mathrm{e}=\mathrm{a} \forall \mathrm{a} \in \mathrm{Q}^{+}\) \(\mathrm{a}=\frac{\mathrm{ea}}{100} \Rightarrow \mathrm{e}=100\) Now, let inverse of 0.1 be \(\mathrm{x}\), then \(0.1 * \mathrm{x}=\mathrm{e}\) \(\Rightarrow \quad \frac{0.1 \mathrm{x}}{100}=100 \quad \mathrm{x} \in \mathrm{Q}^{+}\) \(\\ \mathrm{x}=\frac{10^4}{0.1}=10^5\)
117153
Let * be a binary operation on the set \(Q^{+}\)of all +ve rational numbers defined by \(a * b=\frac{a b}{100}\) for all \(a, b \in Q^{+}\). The inverse of 0.1 under operation * is
1 \(10^5\)
2 \(10^6\)
3 \(10^4\)
4 None of these
Explanation:
Exp: (A) : We have \(\mathrm{a} * \mathrm{~b}=\frac{\mathrm{ab}}{100}\) Let e be the identify element. Then, \(\quad \mathrm{e} * \mathrm{a}=\mathrm{a} * \mathrm{e}=\mathrm{a} \forall \mathrm{a} \in \mathrm{Q}^{+}\) \(\mathrm{a}=\frac{\mathrm{ea}}{100} \Rightarrow \mathrm{e}=100\) Now, let inverse of 0.1 be \(\mathrm{x}\), then \(0.1 * \mathrm{x}=\mathrm{e}\) \(\Rightarrow \quad \frac{0.1 \mathrm{x}}{100}=100 \quad \mathrm{x} \in \mathrm{Q}^{+}\) \(\\ \mathrm{x}=\frac{10^4}{0.1}=10^5\)