JEE Main202429 Jan 2024Evening ShiftMathematicsBinomial TheoremActual

Remainder when 64 32 32 is divided by 9 is equal to _____.

Correct answer

Step-by-step solution

Given, 64 32 32 = 63 + 1 32 × 32 × 32 . . . . 32 times ⇒ 64 32 32 = 63 + 1 32 λ Now we know that by binomial theorem, 1 + 63 32 λ = C 0 32 λ · 1 + C 1 32 λ · 1 · 63 + C 2 32 λ · 1 · 63 2 + . . . . . . . ⇒ 1 + 63 32 λ = 1 + 9 α So, when 64 32 32 is divided by 9 we get 1 as remainder.

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