Question : Study the given graph and answer the question that follows. The total production of computers in 2013, 2015, and 2018 is x% of the total exports of computers by the company during the six years. The value of x is:
Option 1: $46 \frac{1}{3}$
Option 2: $52 \frac{1}{3}$
Option 3: $53 \frac{1}{3}$
Option 4: $49 \frac{2}{3}$
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Correct Answer: $53 \frac{1}{3}$
Solution : Production of computers in 2013 = 180, in 2015 = 300, in 2018 = 320 Exports of computers in 2013 = 140, in 2014 = 240, in 2015 = 200, in 2016= 350, in 2017 = 300, in 2018 = 270 Calculation: The production of computers in 2013, 2015, and 2018 = 180 + 300 + 320 = 800 The exports of computers in 2013, 2014, 2015, 2016, 2017, and 2018 = 140 + 240 + 200 + 350 + 300 + 270 = 1500 Production in above years as x% of total exports = $\frac{800}{1500} \times 100$ = $53\frac{1}{3}\%$ Hence, the correct answer is $53\frac{1}{3}$.
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Question : Study the given graph and answer the question that follows. In which year was the production of computers by the company 16% more than the average exports of computers in the six years (2013 to 2018)?
Option 1: 2015
Option 2: 2018
Option 3: 2014
Option 4: 2016
Question : The value of $(x^{\frac{1}{3}}+x^{-\frac{1}{3}})(x^{\frac{2}{3}}-1+x^{-\frac{2}{3}})$ is:
Option 1: $x^{-1}+x^{\frac{2}{3}}$
Option 2: $x+x^{-\frac{1}{3}}$
Option 3: $x^{\frac{1}{3}}+x^{–1}$
Option 4: $x+x^{–1}$
Question : Study the given graph and answer the question that follows.
By what percent were the total exports of computers, by the company, in 2013, 2014, and 2018 less than the total production of computers from 2015 to 2017 (correct to one decimal place)?
Option 1: 28.8
Option 2: 32.6
Option 3: 43.1
Option 4: 30.1
Question : If $x=2+\sqrt3$, then the value of $\frac{x^{2}-x+1}{x^{2}+x+1}$ is:
Option 1: $\frac{2}{3}$
Option 2: $\frac{3}{4}$
Option 3: $\frac{4}{5}$
Option 4: $\frac{3}{5}$
Question : If $x+\frac{1}{x}=1$, then the value of $\frac{x^2+7x+1}{x^2+11x+1}$:
Option 1: $\frac{3}{4}$
Option 2: $\frac{2}{3}$
Option 3: $\frac{1}{3}$
Option 4: $\frac{1}{4}$
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