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\(\frac{0.01 \times 0.01 \times 0.01 +0.003 \times 0.003 \times 0.003}{0.05 \times 0.05 - 0.015 \times 0.05+0.015 \times 0.015}\)

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SSC CGL 2023 Tier-I Official Paper (Held On: 24 Jul 2023 Shift 3)
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  1. \(\frac{13}{25} \times 10^3 \)
  2. \(\frac{13}{15} \times \) 10-3
  3. \(\frac{13}{15} \times 10^3 \)
  4. \(\frac{13}{25} \times \) 10-3

Answer (Detailed Solution Below)

Option 4 : \(\frac{13}{25} \times \) 10-3
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Detailed Solution

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প্রদত্ত:

\(\frac{0.01 × 0.01 × 0.01 +0.003 × 0.003 × 0.003}{0.05 × 0.05 - 0.015 × 0.05+0.015 × 0.015}\)

অনুসৃত সূত্র:

a3 + b3 = (a + b)(a2 - ab + b2)

গণনা:

\(\frac{0.01 × 0.01 × 0.01 +0.003 × 0.003 × 0.003}{0.05 × 0.05 - 0.015 × 0.05+0.015 × 0.015}\)

⇒ (0.013 + 0.0033)/(5 × 0.01 × 5 × 0.01 - 5 × 0.01 × 5 × 0.003 + 5 × 0.003 × 5 × 0.003)

(0.013 + 0.0033)/(25 × 0.01 × 0.01 - 25 × 0.01 × 0.003 + 25 × 0.003 × 0.003)

(0.013 + 0.0033)/25(0.012 - 0.01 × 0.003 + 0.0032)

⇒ (0.01 + 0.003)/25

⇒ 13/25 × 10- 3

∴ মানটি হল 13/25 × 10-3

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