Question : The value of $11. \overline{4}+22.5 \overline{67}-33.5 \overline{9}$ is:
Option 1: $40. \overline{12}$
Option 2: $4. \overline{12}$
Option 3: $0.4\overline{12}$
Option 4: $0.04\overline{12}$
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Correct Answer: $0.4\overline{12}$
Solution : $11 . \overline{4}+22.5 \overline{67}-33.5 \overline{9}$ $= 11 + .\overline{4} + 22 + .5 \overline{67} - 33 - .5 \overline{9}$ $= .\overline{4} + .5 \overline{67} - .5 \overline{9}$ $= \frac{4}{9} + \frac{567-5}{990} - \frac{59-5}{90}$ $= \frac{440}{990} + \frac{562}{990} - \frac{594}{990}$ $= \frac{440 + 562 - 594}{990}$ $= \frac{408}{990}$ $= 0 .41212121212$ $= 0.4 \overline{12}$ Hence, the correct answer is $0.4 \overline{12}$.
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Question : The value of $0. \overline{57}-0.4 \overline{32}+0.3 \overline{5}$ is:
Option 1: $0.4 \overline{98}$
Option 2: $0.4 \overline{94}$
Option 3: $0. \overline{498}$
Option 4: $0. \overline{495}$
Question : The value of $0.4 \overline{6}+0.7 \overline{23}-0.3 \overline{9} \times 0. \overline{7}$ is:
Option 1: $0.\overline{97}$
Option 2: $0.\overline{57}$
Option 3: $0.\overline{77}$
Option 4: $0.\overline{87}$
Question : If $\mathrm{A}=0.3 \overline{12}, \mathrm{~B}=0.4 \overline{15}$ and $\mathrm{C}=0.30 \overline{9}$, then what is the value of $A + B + C$?
Option 1: $\frac{1141}{1100}$
Option 2: $\frac{1097}{1100}$
Option 3: $\frac{1211}{1100}$
Option 4: $\frac{1043}{1100}$
Question : If $A =(\frac{1}{0.4})+(\frac{1}{0.04})+(\frac{1}{0.004})+....$ upto 8 terms, then what is the value of $A$?
Option 1: 27272727.5
Option 2: 25252525.5
Option 3: 27777777.5
Option 4: 25555555.5
Question : If $(4 y-\frac{4}{y})=13$, find the value of $(y^2+\frac{1}{y^2})$.
Option 1: $12 \frac{11}{16}$
Option 2: $10 \frac{9}{16}$
Option 3: $12 \frac{9}{16}$
Option 4: $8 \frac{9}{16}$
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