Question : A fraction is greater than its reciprocal by $\frac{9}{20}$. What is the fraction?

Option 1: $\frac{5}{4}$

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

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

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

Question : A fraction is greater than twice its reciprocal by $\frac{7}{15}$. What is the fraction?

Option 1: $\frac{3}{5}$

Option 2: $\frac{5}{3}$

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

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

Question : If $A=\frac{\sqrt{0.0004} \times \sqrt[3]{0.000008}}{\sqrt[4]{16000} \times \sqrt[3]{125000} \times \sqrt[4]{810}}$ and $B=\frac{\sqrt[3]{0.729} \times \sqrt[4]{0.0016}}{\sqrt{0.16}}$, then what is $A \times B$?

Option 1: $6 \times 10^{–7}$

Option 2: $\frac{7}{4} \times 10^{–8}$

Option 3: $5 \times 10^{–8}$

Option 4: $\frac{7}{3} \times 10^{–7}$

Question : Directions: By interchanging the given two signs and numbers, which of the following equations will be correct?
+ and ×, 1 and 2

Option 1: 8 × 3 – 4 ÷ 2 + 1 = 7

Option 2: 2 × 3 – 8 ÷ 1 + 9 = 18

Option 3: 8 × 3 – 4 ÷ 2 + 1 = 3

Option 4: 2 × 3 – 8 ÷ 1 + 2 = 5

Question : The average of $n$ numbers is $a$. The first number is increased by 2, the second one is increased by 4, the third one is increased by 8, and so on. The average of the new numbers is:

Option 1: $a+\frac{2^{n–1}–1}{n}$

Option 2: $a+\frac{2(2n–1)}{n}$

Option 3: $a+\frac{2^{n–1}}{n}$

Option 4: $a+\frac{2^{n}–1}{n}$