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 × 10^k, where the value of k is:
Option 1: –2
Option 2: –1
Option 3: 1
Option 4: 2

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Question : What is the value of S $= \frac{1}{1 \times 3 \times 5} + \frac{1}{1 \times 4} + \frac{1}{3 \times 5 \times 7} + \frac{1}{4 \times 7} + \frac{1}{5 \times 7 \times 9} + \frac{1}{7 \times 10} + . . . .$ Up to 20 terms, then what is the value of S?

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Answer 1

Correct Answer: –2

Solution : $\frac{(2.53)^{3} + (2.47)^{3}}{25.3 \times 25.3 - 624.91 + 24.7 \times 24.7}$
$\Rightarrow \frac{(2.53)^{3} + (2.47)^{3}}{25.3 \times 25.3 - 624.91 + 24.7 \times 24.7} = 5 \times 10^{k}$
$\Rightarrow \frac{(2.53 + 2.47) ({2.53}^{2} + {2.47}^{2} - 2.53 \times 2.47)}{100 \times 2.53 \times 2.53 - 100 \times 6.2491 + 100 \times 2.47 \times 2.47} = 5 \times 10^{k}$
$\Rightarrow \frac{(2.53 + 2.47) ({2.53}^{2} - 6.2491 + {2.47}^{2})}{10^{2} (2.53 \times 2.53 - 6.2491 + 2.47 \times 2.47)} = 5 \times 10^{k}$
$\Rightarrow (2.53 + 2.47) \times 10^{- 2} = 5 \times 10^{k}$
$\Rightarrow 5 \times 10^{- 2} = 5 \times 10^{k}$
$∴ k = - 2$
Hence, the correct answer is –2.

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Question : The value of (2.53)3+(2.47)325.3×25.3−624.91+24.7×24.7 is 5 × 10k, where the value of k is:Option 1: –2Option 2: –1Option 3: 1Option 4: 2

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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 × 10^k, where the value of k is:
Option 1: –2
Option 2: –1
Option 3: 1
Option 4: 2