Question : What is the simplified value of
$\left(1-\frac{1}{4-\frac{2}{1+\frac{1}{\frac{1}{3}+2}}}\right) \times \frac{15}{16} \div \frac{2}{3}$ of $2 \frac{1}{4}-\frac{3+4}{3^3+4^3}$

Option 1: $\frac{5}{13}$

Option 2: $\frac{4}{13}$

Option 3: $\frac{8}{13}$

Option 4: $\frac{6}{13}$

Question : What is the simplified value of $(3+1)(3^{2}+1)(3^{4}+1)(3^{8}+1)(3^{16}+1)$?

Option 1: $\frac{(3^{32}-1)}{2}$

Option 2: $\frac{(3^{16}-1)}{2}$

Option 3: $\frac{(3^{64}-1)}{2}$

Option 4: $\frac{(3^{128}-1)}{2}$

Question : The value of $6 \frac{8}{15}÷\frac{7}{9}$ of $\left(1 \frac{1}{10}+5 \frac{1}{5}\right)+\frac{2}{5}÷7 \frac{1}{5}$ is:

Option 1: $\frac{25}{16}$

Option 2: $\frac{5}{14}$

Option 3: $\frac{25}{18}$

Option 4: $\frac{5}{18}$

Question : What is the simplified value of:
$7 \frac{1}{3} \div 2 \frac{1}{2}$ of $1 \frac{3}{5}-\left(\frac{3}{8}+\frac{1}{7} \times 1 \frac{3}{4}\right)-\frac{5}{24}$

Option 1: $1$

Option 2: $2$

Option 3: $\frac{1}{24}$

Option 4: $\frac{1}{12}$

Question : Directions: In the following question a series is given, with one term missing. Choose the correct alternative from the given ones that will complete the series.
$7 \frac{1}{7}, 8 \frac{2}{6}, 9 \frac{5}{5}, 12 \frac{2}{4}, 16 \frac{2}{3},?$

Option 1: $35 \frac{3}{4}$

Option 2: $16 \frac{4}{4}$

Option 3: $\frac{50}{2}$

Option 4: $15 \frac{2}{4}$