Question : The value of $\frac{4.669 \times 4.669–9 \times(0.777)^2}{(4.669)^2+(2.331)^2+14(0.667)(2.331)}$ is $(1-k)$, where $k = $?
Option 1: 0.666
Option 2: 0.647
Option 3: 0.467
Option 4: 0.768
Correct Answer: 0.666
Solution : Given: The expression is $\frac{4.669 \times 4.669–9 \times(0.777)^2}{(4.669)^2+(2.331)^2+14(0.667)(2.331)}=(1 - k)$ Use the algebraic identities, $(a+b)^2=a^2+b^2+2ab$ and $a^2-b^2=(a+b)(a-b)$ ⇒ $\frac{4669 \times 4669–9 \times(777)^2}{(4669)^2+(2331)^2+14(0667)(2331)}=(1 - k)$ ⇒ $\frac{(4669)^2–(2331)^2}{(4669)^2+(2331)^2+2(4669)(2331)}=(1 - k)$ ⇒ $\frac{(4669)^2–(2331)^2}{(4669+2331)^2}=(1 - k)$ ⇒ $\frac{(4669–2331)(4669+2331)}{(4669+2331)^2}=(1 - k)$ ⇒ $\frac{(4669–2331)}{(4669+2331)}=(1 - k)$ ⇒ $\frac{2338}{7000}=(1 - k)$ ⇒ $0.334=1 - k$ ⇒ $k=1 - 0.334$ ⇒ $k= 0.666$ Hence, the correct answer is 0.666.
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Question : The value of $\frac{(0.321)^3+(0.456)^3-(0.777)^3}{0.9 \times(0.107)(0.76)(0.777)}$ is:
Option 1: 60
Option 2: –6
Option 3: –3
Option 4: 30
Question : The value of $\frac{2}{3} \div \frac{3}{10}$ of $\frac{4}{9}-\frac{4}{5} \times 1 \frac{1}{9} \div \frac{8}{15}+\frac{3}{4} \div \frac{1}{2}$ is:
Option 1: $\frac{29}{6}$
Option 2: $\frac{17}{9}$
Option 3: $\frac{14}{3}$
Option 4: $\frac{49}{12}$
Question : The value of $\frac{2}{3} \div \frac{3}{10}$ of $\frac{4}{9}-\frac{4}{5} \times 1 \frac{1}{9} \div \frac{8}{15}-\frac{3}{4}+\frac{3}{4} \div \frac{1}{2}$ is:
Option 1: $\frac{25}{6}$
Option 2: $\frac{14}{3}$
Option 3: $\frac{17}{9}$
Question : The value of $\frac{1 \frac{1}{2} \div 3 \frac{1}{4}+\frac{1}{2} \div \frac{13}{14}+\frac{1}{5}}{\frac{1}{5} \times 3 \frac{1}{2}-\frac{1}{3} \div 1 \frac{3}{4} \times 3 \frac{1}{2}}$ is:
Option 1: 33
Option 2: 36
Option 3: 38
Option 4: 40
Question : The value of $\frac{5-2 \div 4 \times[5-(3-4)]+5 \times 4 \div 2 \text { of } 4}{4+4 \div 8 \text { of } 2 \times(8-5) \times 2 \div 3-8 \div 2 \text { of } 8}$ is:
Option 1: $\frac{9}{8}$
Option 2: $\frac{9}{4}$
Option 3: $\frac{15}{32}$
Option 4: $\frac{89}{4}$
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