Question : The greatest among the following numbers $(3)^{\frac{1}{3}}, (2)^{\frac{1}{2}}, 1, (6)^{\frac{1}{6}}$ is:

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

Option 2: 1

Option 3: $(6)^{\frac{1}{6}}$

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

Question : If $\cos ^4 \alpha-\sin ^4 \alpha=\frac{5}{6}$, then the value of $2 \cos ^2 \alpha-1$ is:

Option 1: $\frac{11}{6}$

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

Option 3: $\frac{6}{11}$

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

Question : A student was asked to find the value of $\frac{\left(2 \frac{1}{3}+2 \frac{1}{2}-\frac{1}{6}\right) \div 2 \frac{1}{3} \times 5 \frac{2}{3} \div 1 \frac{2}{3} \text { of } 4 \frac{1}{4}}{3 \frac{1}{5} \div 4 \frac{1}{2} \text { of } 5 \frac{1}{3}+5 \frac{1}{3} \times \frac{3}{4} \div 2 \frac{2}{3}}$. His answer was $\frac{6}{7}$. What is the difference between the correct answer and his answer?

Option 1: $\frac{9}{14}$

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

Option 3: $\frac{11}{49}$

Option 4: $\frac{6}{49}$

Question : The value of $\frac{\frac{5}{2}-\frac{3}{7} \times 1 \frac{4}{5} \div 3 \frac{6}{7}}{\frac{3}{2}+1 \frac{2}{5} \div 3 \frac{1}{2} \times 1 \frac{1}{4}}$ is:

Option 1: $2 \frac{3}{20}$

Option 2: $1\frac{2}{20}$

Option 3: $1 \frac{3}{20}$

Option 4: $1 \frac{7}{20}$

Question : What is the value of $999 \frac{1}{2} + 999 \frac{1}{6} + 999\frac{1}{12}+999 \frac{1}{20} + 999\frac{1}{30}?$

Option 1: $999\frac{1}6$

Option 2: $999\frac{5}6$

Option 3: $4995\frac{1}6$

Option 4: $4995\frac{5}6$