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If 847 385 675 3025 = 3a 5b 7c 11d then...

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Surds and Indices
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If 847 × 385 × 675 × 3025 = 3a × 5b × 7c × 11d then the value of ab - cd is

Answer & Solution
Correct Answer: Option C
847 × 385 × 675 × 3025 = 3a × 5b × 7c × 11d
LHS ⇒ 847 × 385 × 675 × 3025
= (7 × 11 × 11) × (5 × 7 × 11) × (3 × 3 × 3 × 5 × 5) × (5 × 5 × 11 × 11)
= 33 × 55 × 72 × 115
= 3a × 5b × 7c × 11d
Compare value
a = 3; b = 5; c = 2; d = 5
⇒ ab - cd = 3 × 5 - 2 × 5 = 15 - 10 = 5
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