Question : Find the value of $a$ in the following equation. (Given $a<10 $) $\frac{(187 \div 17 \times a-3 \times 3)}{\left(8^2-9 \times 7+a^2\right)}=1$
Option 1: 2
Option 2: 1
Option 3: 4
Option 4: 3
Correct Answer: 1
Solution : $\frac{(187 \div 17 \times a-3 \times 3)}{\left(8^2-9 \times 7+a^2\right)}=1$ $⇒\frac{(11a-9)}{\left(a^2+1\right)}=1$ $⇒11a - 9 = a^2 + 1$ $⇒a^2 - 11a + 10 = 0$ $⇒(a - 10)(a - 1) = 0$ $⇒a = 10$ and $a = 1$ Since $a<10$ So, $a = 1$ Hence, the correct answer is 1.
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Question : The value of $\left(5 \frac{1}{4} \div \frac{3}{7}\right.$ of $\left.\frac{1}{2}\right) \div\left(5 \frac{1}{9}-7 \frac{7}{8} \div 9 \frac{9}{20}\right) \times \frac{11}{21}+\left(2 \div 2\right.$ of $\left.\frac{1}{2}\right)$ is:
Option 1: $\frac{7}{2}$
Option 2: $3$
Option 3: $5$
Option 4: $\frac{9}{4}$
Question : The value of $8-3 \div 6$ of $2+\left(4 \div 4\right.$ of $\left.\frac{1}{4}\right) \div 8+\left(4 \times 8 \div \frac{1}{4}\right) \times \frac{1}{8}$ is:
Option 1: $\frac{7}{4}$
Option 2: $-\frac{97}{4}$
Option 3: $-\frac{7}{4}$
Option 4: $\frac{97}{4}$
Question : The value of $\left(5 \frac{1}{4} \div \frac{3}{7}\right.$ of $\left.\frac{1}{2}\right) \div\left(5 \frac{1}{9}-7 \frac{7}{8} \div 9 \frac{9}{20}\right) \times \frac{11}{21}-\left(5 \div 2\right.$ of $\left.\frac{1}{2}\right)$ is:
Option 1: $\frac{15}{28}$
Option 2: $-2$
Option 3: $\frac{35}{24}$
Option 4: $0$
Question : The value of $1-3 \div 6$ of $2+\left(4 \div 4\right.$ of $\left.\frac{1}{4}\right) \div 8+\left(4 \times 8 \div \frac{1}{4}\right) \times \frac{1}{8}$ is:
Option 1: $\frac{69}{4}$
Option 2: $-\frac{69}{4}$
Option 3: $\frac{7}{4}$
Option 4: $-\frac{7}{4}$
Question : The value of $\left[1 \frac{2}{7} \times\left\{3 \frac{1}{2} \div\left(\frac{1}{2}-\frac{1}{7}\right)\right\}\right] \div\left(4 \frac{1}{5} \times 1 \frac{1}{2}\right)$ is:
Option 1: $\frac{1}{3}$
Option 2: $\frac{3}{4}$
Option 3: $2$
Option 4: $1$
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