If (1012 + 25)² – (1012 – 25)² = 10n, then

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If (10¹² + 25)² – (10¹² – 25)² = 10ⁿ, then the value of n is

1. 20
2. 14
3. 10
4. 5

Correct Option: B

With the help of given below formula ,
(a + b)² - (a - b)² = 4ab
∴ (10¹² + 25)² - (10¹² - 25)² = 10ⁿ
Here , a = 10¹² , b = 25
⇒ 4 × 10¹² × 25 = 10ⁿ
⇒ 100 × 10¹² = 10ⁿ
⇒ 10² × 10¹² = 10ⁿ
⇒ 10¹⁴ = 10ⁿ
Equating powers on both sides ,
⇒ n = 14