Question : If $A=\frac{\sqrt{0.0004} \times \sqrt[3]{0.000008}}{\sqrt[4]{16000} \times \sqrt[3]{125000} \times \sqrt[4]{810}}$ and $B=\frac{\sqrt[3]{0.729} \times \sqrt[4]{0.0016}}{\sqrt{0.16}}$, then what is $A \times B$?
Option 1: $6 \times 10^{–7}$
Option 2: $\frac{7}{4} \times 10^{–8}$
Option 3: $5 \times 10^{–8}$
Option 4: $\frac{7}{3} \times 10^{–7}$
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Correct Answer: $6 \times 10^{–7}$
Solution : Given: The values of $A=\frac{\sqrt{0.0004} \times \sqrt[3]{0.000008}}{\sqrt[4]{16000} \times \sqrt[3]{125000} \times \sqrt[4]{810}}$ and $B=\frac{\sqrt[3]{0.729} \times \sqrt[4]{0.0016}}{\sqrt{0.16}}$. $A=\frac{\sqrt{0.0004} \times \sqrt[3]{0.000008}}{\sqrt[4]{16000} \times \sqrt[3]{125000} \times \sqrt[4]{810}}=\frac{\sqrt{(0.02)^2}\times\sqrt[3]{(0.02)^3}}{\sqrt[4]{2^4\times10^3}\times\sqrt[3]{(50)^3}\times{\sqrt[4]{3^4\times10}}}$ $=\frac{{0.02} \times {0.02}}{(2\times50\times3)\times{\sqrt[4]{(10)^3}}\times{\sqrt[4]{10}}}=\frac{{0.02} \times {0.02}}{300\times{{\sqrt[4]{(10)^3\times10}}}}$ ⇒ $A=\frac{{0.02} \times {0.02}}{300\times10}=\frac{0.0004}{3000}$ $B=\frac{\sqrt[3]{0.729} \times \sqrt[4]{0.0016}}{\sqrt{0.16}}=\frac{\sqrt[3]{(0.9)^3} \times \sqrt[4]{(0.2)^4}}{\sqrt{(0.4)^2}}$ ⇒ $B= \frac{0.9\times 0.2}{0.4}=\frac{0.9}{0.2}$ The value of $A \times B=\frac{0.0004}{3000}\times\frac{0.9}{0.2}$ $=\frac{4}{30000000}\times\frac{9}{2}=6\times 10^{–7}$ Hence, the correct answer is $6 \times 10^{–7}$.
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Question : What is the value of $\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}–\sqrt{5}} \div \frac{\sqrt{14}+\sqrt{10}}{\sqrt{14}–\sqrt{10}}+\frac{\sqrt{10}}{\sqrt{5}}$?
Option 1: $\sqrt{2}+2$
Option 2: $2 \sqrt{2}+2$
Option 3: $\sqrt{2}+1$
Option 4: $2 \sqrt{2}+1$
Question : Directions: By interchanging the given two signs and numbers which of the following equations will be correct? – and +, 6 and 3
Option 1: 7 – 3 × 2 ÷ 6 + 4 = 17
Option 2: 8 × 3 – 6 + 4 ÷ 2 = 49
Option 3: 7 + 6 ÷ 3 × 8 – 5 = 35
Option 4: 9 – 6 ÷ 4 + 3 × 7 = 8
Question : Directions: By interchanging the given two signs which of the following equations will be correct? × and –
Option 1: 7 × 9 – 8 ÷ 2 + 6 = 25
Option 2: 8 × 6 – 9 ÷ 3 + 10 = 0
Option 3: 16 – 4 ÷ 2 + 8 × 1 = 36
Option 4: 5 + 7 × 3 – 4 ÷ 2 = 8
Question : The sum of the first 20 term of the series $\frac{1}{5×6}+\frac{1}{6×7}+\frac{1}{7×8}+....$ is:
Option 1: 0.16
Option 2: 1.6
Option 3: 16
Option 4: 0.016
Question : Directions: By interchanging the given two signs and numbers which of the following equations will be correct? × and +, 6 and 4
Option 1: 3 × 9 – 4 ÷ 2 + 6 = 8
Option 2: 8 × 6 + 4 ÷ 2 – 5 = –5
Option 3: 8 – 3 × 6 + 4 ÷ 1 = 18
Option 4: 7 × 6 – 4 + 9 ÷ 3 = –7
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