Question : If $\sqrt{0.04\times 0.4\times a}=0.004\times 0.4\times \sqrt{b},$ then the value of $\frac{a}{b}$ is:
Option 1: $16\times 10^{-3}$
Option 2: $16\times 10^{-4}$
Option 3: $16\times 10^{-5}$
Option 4: $16 \times 10^{-6}$
Correct Answer: $16\times 10^{-5}$
Solution : $\sqrt{0.04\times 0.4\times a}=0.004\times 0.4\times \sqrt{b}$ Squaring both sides, we get, $⇒0.04\times 0.4\times a=0.004^2\times 0.4^2\times {b}$ $⇒\frac{a}{b} = \frac{0.004 \times 0.004 \times 0.4 \times \times0.4}{0.04 \times 0.4}$ $⇒\frac{a}{b} = \frac{16}{10^{5}}$ $\therefore$ $\frac{a}{b} = 16 \times 10^{-5}$ Hence, the correct answer is $16 \times 10^{-5}$.
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Question : The value of the following expression $\frac{0.2×0.02×0.002×32}{0.4×0.04×0.004×16}$ is:
Option 1: 0.20
Option 2: 0.50
Option 3: 0.4
Option 4: 0.25
Question : If $\sin A=\frac{1}{2}$, then the value of $(\tan A+\cos A)$ is:
Option 1: $\frac{2}{3 \sqrt{3}}$
Option 2: $\frac{3}{2 \sqrt{3}}$
Option 3: $\frac{5}{2 \sqrt{3}}$
Option 4: $\frac{5}{3 \sqrt{3}}$
Question : If $a-\frac{1}{a}=4$, then the value of $a+\frac{1}{a}$ is:
Option 1: $5 \sqrt{5}$
Option 2: $4 \sqrt{5}$
Option 3: $2 \sqrt{5}$
Option 4: $3 \sqrt{5}$
Question : $\frac{1}{3-\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{6}}-\frac{1}{\sqrt{6}-\sqrt{5}}+\frac{1}{\sqrt{5}-2}=?$
Option 1: 5
Option 2: 4
Option 3: 3
Option 4: 2
Question : If $x^2+\frac{1}{x^2}=\frac{7}{4}$ for $x>0$, what is the value of $(x^3+\frac{1}{x^3})$?
Option 1: $\frac{3\sqrt{3}}{5}$
Option 2: $\frac{3\sqrt{15}}{5}$
Option 3: $\frac{3\sqrt{15}}{8}$
Option 4: $\frac{3\sqrt{5}}{8}$
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