Use the binomial theorem to compute $(101)^4$.

1. Write $(101)^4 = (100 + 1)^4$ and expand using the binomial theorem. 2. $(100+1)^4 = \binom{4}{0}\,100^4 + \binom{4}{1}\,100^3 + \binom{4}{2}\,100^2 + \binom{4}{3}\,100 + \binom{4}{4}$. 3. Plug in binomial coefficients $1, 4, 6, 4, 1$: - $1 \cdot 100\,000\,000 = 100{,}000{,}000$ - $4 \cdot 1\,000\,000 = 4{,}000{,}000$ - $6 \cdot 10\,000 = 60{,}000$ - $4 \cdot 100 = 400$ - $1 \cdot 1 = 1$ 4. Sum: $100{,}000{,}000 + 4{,}000{,}000 + 60{,}000 + 400 + 1 = 104{,}060{,}401$. 5. Other options are arithmetic slips (option B swaps two digits, C drops a millions slot, D wrong coefficients). _Source: NCERT Class 11 Mathematics, Ch 7, Example 3 (Similar method), p. 7._