Question : The value of $\frac{0.7× 0.7× 0.7+0.3 × 0.3 × 0.3}{0.7 × 0.7-0.7× 0.3+0.3 × 0.3}$ is_____.
Option 1: 2
Option 2: 1
Option 3: 3
Option 4: – 1
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Correct Answer: 1
Solution : $\frac{0.7× 0.7× 0.7+0.3 × 0.3 × 0.3}{0.7 × 0.7-0.7× 0.3+0.3 × 0.3}$ = $\frac{(0.7)^3+(0.3)^3}{(0.7)^2-0.7× 0.3+(0.3)^2}$ = $\frac{(0.7+0.3)((0.7)^2-0.7× 0.3+(0.3)^2)}{(0.7)^2-0.7× 0.3+(0.3)^2}$ = $0.7+0.3$ = $1$ Hence, the correct answer is $1$.
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Question : What is the value of $\frac{(1.2)^{3} + (0.8)^{3} + (0.7)^{3} – 2.016}{(1.35)[(1.2)^{2} + (0.8)^{2} + (0.7)^{2} – 0.96 – 0.84 – 0.56]}?$
Option 1: $\frac{1}{4}$
Option 2: $\frac{1}{2}$
Option 3: $1$
Option 4: $2$
Question : If $\frac{b}{a}=0.7$, find the value of $\frac{a–b}{a+b}+\frac{11}{34}$.
Option 1: 0.2
Option 3: 0.5
Option 4: 0.3
Question : The value of $(0.3)^{[\frac {(200-146)}{(3 \times 3 \times 3)}-3]}$ is:
Option 1: $\frac{10}{3}$
Option 2: $\frac{5}{3}$
Option 3: $\frac{7}{3}$
Option 4: $\frac{8}{3}$
Question : The value of $\frac{(2.53)^3+(2.47)^3}{25.3 \times 25.3-624.91+24.7 \times 24.7}$ is 5 × 10k, where the value of k is:
Option 1: –2
Option 2: –1
Option 3: 1
Option 4: 2
Question : What is the value of $\frac{\frac{1}{3}+\frac{1}{3}\times\frac{1}{3}}{\frac{1}{3}\times\frac{1}{3}+\frac{1}{3}}$?
Option 1: 1
Option 2: 3
Option 3: $\frac{1}{3}$
Option 4: $\frac{1}{2}$
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