Question : LCM of $ \frac{2}{3}, \frac{4}{9}, \frac{5}{6}$ is:

Option 1: $\frac{8}{27}$

Option 2: $\frac{20}{3}$

Option 3: $\frac{10}{3}$

Option 4: $\frac{20}{27}$

Question : Find the value of the given expression:
$\frac{(4\frac{1}{3}+3\frac{1}{3}\times 1\frac{4}{5}\div 3\frac{3}{4}\times (1\frac{1}{2}+1\frac{1}{3}))}{(\frac{2}{3}\div \frac{5}{6}\times \frac{2}{3})}$

Option 1: $11 \frac{3}{8}$

Option 2: $10\frac{1}{8}$

Option 3: $14\frac{3}{8}$

Option 4: $16\frac{5}{8}$

Question : If $\left(3 y+\frac{3}{y}\right)=8$, then find the value of $\left(y^2+\frac{1}{y^2}\right)$.

Option 1: $5\frac{1}{9}$

Option 2: $4\frac{5}{6}$

Option 3: $7\frac{1}{9}$

Option 4: $9\frac{1}{9}$

Question : If $A:B=3:4$ and $B:C=6:5$, then $C:A$ is

Option 1: $10:9$

Option 2: $9:10$

Option 3: $8:9$

Option 4: $9:8$

Question : The arrangement of the fractions $\frac{4}{3}, -\frac{2}{9}, -\frac{7}{8}, \frac{5}{12}$ in ascending order is _____.

Option 1: $–\frac{7}{8}, –\frac{2}{9}, \frac{5}{12}, \frac{4}{3}$

Option 2: $–\frac{7}{8}, –\frac{2}{9}, \frac{4}{3}, \frac{5}{12}$

Option 3: $–\frac{2}{9}, –\frac{7}{8}, \frac{5}{12}, \frac{4}{3}$

Option 4: $–\frac{2}{9}, –\frac{7}{8}, \frac{4}{3}, \frac{5}{12}$

Question : The simplified value of the following is:
$\left (\frac{3}{15}a^{5}b^{6}c^{3}\times \frac{5}{9}ab^{5}c^{4} \right )\div \frac{10}{27}a^{2}bc^{3}$.

Option 1: $\frac{9a^{2}bc^{4}}{10}$

Option 2: $\frac{3ab^{4}c^{3}}{10}$

Option 3: $\frac{3a^{4}b^{10}c^{4}}{10}$

Option 4: $\frac{1a^{4}b^{4}c^{10}}{10}$