Question : What is the value of $x$? $\frac{3}{2}× \frac{7}{3} ÷ \frac{7}{6}+\frac{1}{4}=\frac{1}{x}$
Option 1: $\frac{7}{12}$
Option 2: $\frac{4}{13}$
Option 3: $\frac{13}{4}$
Option 4: $\frac{6}{7}$
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Correct Answer: $\frac{4}{13}$
Solution : $\frac{3}{2} \times \frac{7}{3} ÷ \frac{7}{6} + \frac{1}{4} = \frac{1}{x}$ $⇒\frac{3}{2} \times2 + \frac{1}{4} =\frac{1}{x}$ $⇒ 3 + \frac{1}{4} =\frac{1}{x}$ $⇒ \frac{13}{4}=\frac{1}{x}$ $\therefore x = \frac{4}{13}$ Hence, the correct answer is $ \frac{4}{13}$.
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Question : What is the value of $\frac{7 \text { of } 14 ÷ 4}{5 × 4 ÷ 2}+\frac{6 ÷ 12 × 3}{5 ÷ 25 × 2}+\frac{15 ÷ 5 × 6}{5× 15 ÷ 6}$?
Option 1: 7.44
Option 2: 7.64
Option 3: 7.62
Option 4: 7.22
Question : What is the value of $\frac{\frac{5}{6} \text { of } \frac{1}{3} \times \frac{12}{25}-\frac{1}{3} \text { of } \frac{5}{6} \times \frac{18}{25}}{\frac{25}{12} \text { of } \frac{1}{6} \times \frac{2}{5}+\frac{3}{8} \text { of } \frac{12}{25} \times \frac{5}{6}}$?
Option 1: $-\frac{3}{13}$
Option 2: $-\frac{5}{13}$
Option 3: $-\frac{8}{25}$
Option 4: $-\frac{3}{25}$
Question : If $x+\frac{2}{x}=1$, then the value of $\frac{x^2+7x+2}{x^2+13x+2}$ is:
Option 1: $\frac{5}{7}$
Option 2: $\frac{3}{7}$
Option 3: $\frac{4}{7}$
Option 4: $\frac{2}{7}$
Question : If $\frac{x}{y}=\frac{4}{5}$, then the value of $(\frac{4}{7}+\frac{2y–x}{2y+x})$ is:
Option 1: $\frac{3}{7}$
Option 2: $1\frac{1}{7}$
Option 3: $1$
Option 4: $2$
Question : What is the value of $\frac{4x^2+9y^2+12xy}{144}$?
Option 1: $(\frac{x}{3} + \frac{y}{4})^2$
Option 2: $(\frac{x}{3} + y)^2$
Option 3: $(\frac{x}{4} + \frac{y}{6})^2$
Option 4: $(\frac{x}{6} + \frac{y}{4})^2$
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