Basic Mathematics & Logarithm
Mathematical Induction
nta_abhyas_2025
Grade 11
Question:
If $(27)^{99}$ is divided by $7$, then the remainder is
Step-by-Step Solution
Key Concept: Use binomial expansion with a number close to a multiple of the divisor to find remainders efficiently
Express the given number $27^{99}$ as $(28-1)^{99}$. Now divide by 7 and apply the formula of binomial expansion. We get the remainder as $-1 \equiv 7 + (-1) = 6$.
Correct Answer: 4