Question : If $\sqrt {0.05\times 0.5 \times a } = 0.5 \times 0.05 \times \sqrt b$, then $\frac{a}{b}$ is equal to:
Option 1: 0.0025
Option 2: 0.025
Option 3: 0.25
Option 4: 0.00025
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Correct Answer: 0.025
Solution : $\sqrt {0.05\times 0.5 \times a } = 0.5 \times 0.05 \times \sqrt b$ On squaring both sides, ⇒ $ 0.05\times 0.5 \times a = 0.5 \times 0.05 \times 0.5 \times 0.05 \times b$ ⇒ $a = 0.5 \times 0.05 \times b$ ⇒ $\frac{a}{b} = 0.5 \times 0.05 = 0.025$ Hence, the correct answer is 0.025.
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Question : If $\sin A-\cos A=\frac{\sqrt{3}-1}{2}$, then the value of $\sin A\cdot \cos A$ is:
Option 1: $\frac{\sqrt{3}}{2}$
Option 2: $\frac{3}{2}$
Option 3: $\frac{\sqrt{3}}{4}$
Option 4: $\frac{1}{\sqrt{3}}$
Question : 1% of 1% of 25% of 1000 is:
Option 1: 0.025
Option 2: 0.0025
Option 4: 0.000025
Question : If $a^2+\frac{1}{a^2}=\frac{7}{3}$, then what is the value of $\left(a^3-\frac{1}{a^3}\right)?$
Option 1: $\frac{5}{3 \sqrt{3}}$
Option 2: $\frac{10}{3 \sqrt{3}}$
Option 3: $\frac{7}{3 \sqrt{3}}$
Option 4: $\frac{8}{3 \sqrt{3}}$
Question : If $x=\sqrt{3}-\frac{1}{\sqrt{3}}, y=\sqrt{3}+\frac{1}{\sqrt{3}}$, then the value of $\frac{x^2}{y}+\frac{y^2}{x}$ is:
Option 1: $\sqrt{3}$
Option 2: $3\sqrt{3}$
Option 3: $16\sqrt{3}$
Option 4: $2\sqrt{3}$
Question : If $\sec \theta+\tan \theta=\frac{1}{\sqrt{3}}$, then the positive value of $\cot \theta+\cos \theta$ is:
Option 1: $\frac{3 \sqrt{3}}{2}$
Option 2: $\frac{\sqrt{3}}{2}$
Option 3: $\frac{2}{3 \sqrt{3}}$
Option 4: $\frac{2}{\sqrt{3}}$
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