Question : $\frac{3.25\times 3.25+1.75\times 1.75-2\times 3.25\times 1.75}{3.25\times 3.25-1.75\times 1.75}$ is simplified to:
Option 1: 0.5
Option 2: 0.4
Option 3: 0.3
Option 4: 0.2
Correct Answer: 0.3
Solution : Consider, $\frac{3.25\times 3.25+1.75\times 1.75-2\times 3.25\times 1.75}{3.25\times 3.25-1.75\times 1.75}$ $=\frac{(3.25)^2+(1.75)^2-2\times 3.25\times1.75}{(3.25)^2-(1.75)^2}$ Using $a^2+b^2-2ab = (a-b)^2$ and $a^2-b^2=(a-b)(a+b)$, we get, $=\frac{(3.25-1.75)^2}{(3.25-1.75)(3.25+1.75)}$ $=\frac{3.25-1.75}{3.25+1.75}$ $=\frac{1.5}{5}$ $= 0.3$ Hence, the correct answer is 0.3.
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Question : What is the value of $\small \frac{(0.7)^{3}-(0.4)^{3}}{(0.7)^{2}+0.7\times 0.4+(0.4)^{2}}$?
Option 1: 0.3
Option 2: 0.7
Option 3: 0.9
Option 4: 1.1
Question : What is the value of $\frac{(0.5)^{3}-(0.1)^{3}}{(0.5)^{2}+0.5\times 0.1+(0.1)^{2}}$?
Option 1: $0.1$
Option 2: $0.4$
Option 3: $0.5$
Option 4: $0.6$
Question : The simplified value of (0.2)3 × 400 ÷ 2000 of (0.2)2 is:
Option 1: $\frac{1}{25}$
Option 2: $\frac{3}{25}$
Option 3: $\frac{2}{25}$
Option 4: $\frac{1}{50}$
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 : The value of $\frac{0.325 \times 0.325+0.175 \times 0.175+25 \times 0.00455}{5 \times 0.0065 \times 3.25-7 \times 0.175 \times 0.025}+\frac{0.5}{1.5}$ is:
Option 1: $3$
Option 2: 0
Option 3: $\frac{7}{3}$
Option 4: $\frac{11}{3}$
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