Question : If 91% of A is 39% of B, and B is x% of A, then the value of x is:
Option 1: $\frac{200}{3}$
Option 2: $\frac{700}{3}$
Option 3: $\frac{400}{3}$
Option 4: $\frac{500}{3}$
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Correct Answer: $\frac{700}{3}$
Solution : Given: 91% of A is 39% of B Now, $\Rightarrow \frac{91}{100}\times A = \frac{39}{100}\times B$ $\Rightarrow \frac{A}{B} = \frac{3}{7}$ According to the question, $\Rightarrow \frac{Ax}{100} = B$ $\Rightarrow \frac{B}{A}\times 100 = x$ $\Rightarrow x =\frac{7}{3}\times 100$ $\therefore x = \frac{700}{3}$ Hence, the correct answer is $\frac{700}{3}$.
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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: $\frac{1}{4}$
Question : If $(x+\frac{1}{x})$ = 5, then the value of $\frac{5x}{x^{2}+5x+1}$ is:
Option 1: $\frac{1}{3}$
Option 2: $\frac{1}{4}$
Option 3: $\frac{1}{2}$
Option 4: $\frac{1}{5}$
Question : If $x+\frac{1}{x}=6$, then find the value of $\frac{3 x}{2 x^2-5 x+2}$.
Option 1: $1$
Option 2: $\frac{3}{7}$
Option 3: $\frac{2}{3}$
Option 4: $0$
Question : If $\frac{1}{x^2+a^2}=x^2-a^2$, then the value of $x$ is:
Option 1: $\left(1-a^4\right)^\frac{1}{4}$
Option 2: $a$
Option 3: $\left(a^4-1\right)^\frac{1}{4}$
Option 4: $\left(a^4+1\right)^\frac{1}{4}$
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