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 : A student was asked to find the value of $\left[(\frac{4}{9} \div \frac{3}{5} \div \frac{3}{2}) \times \frac{9}{25}\right] ×{\left[\frac{2}{3} \text { of } \frac{4}{9} \div\left(3 \times \frac{3}{5} \text { of } \frac{4}{5}\right)\right]}{\frac{2}{3} \div \frac{3}{4} \text { of } 6}$ His answer was $\frac{2}{9}$.
What is the difference between his answer and the correct answer?

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

Option 2: $\frac{1}{4}$

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

Option 4: $\frac{1}{6}$

Question : If $a-\frac{1}{a-5}=10$, then the value of $(a-5)^3-\frac{1}{(a-5)^3}$ is:

Option 1: 140

Option 2: 70

Option 3: 100

Option 4: 120

Question : The discount on a certain sum of money, due at the end of $2\frac{1}{4}$ years at $2\frac{2}{3}$% p.a. is Rs. 78 find the sum.

Option 1: Rs. 1,278

Option 2: Rs. 1,300

Option 3: Rs. 1,378

Option 4: Rs. 1,400

Question : The simple interest on a sum of money for 3 years is Rs. 240 and the compound interest on the same sum at the same rate for 2 years is Rs. 170. The rate of interest is:

Option 1: $8$%

Option 2: $29\frac{1}{6}$%

Option 3: $12\frac{1}{2}$%

Option 4: $5\frac{5}{17}$%