AP EAMCET · Maths · Binomial Theorem
\(\frac{1}{81^{\mathrm{n}}}-{ }^{2 \mathrm{n}} \mathrm{C}_1 \frac{10}{81^{\mathrm{n}}}+{ }^{2 \mathrm{n}} \mathrm{C}_2 \frac{10^2}{81^{\mathrm{n}}}-\ldots+\frac{10^{2 \mathrm{n}}}{81^{\mathrm{n}}}=\)
- A \(0\)
- B \((-1)^{\mathrm{n}}\)
- C \(1\)
- D \(81\)
Answer & Solution
Correct Answer
(C) \(1\)
Step-by-step Solution
Detailed explanation
\( = \\frac{1}{81^{\\mathrm{n}}} \\left( { }^{2 \\mathrm{n}} \\mathrm{C}_0 (1)^{2 \\mathrm{n}} (10)^0 - { }^{2 \\mathrm{n}} \\mathrm{C}_1 (1)^{2 \\mathrm{n}-1} (10)^1 + \\ldots + { }^{2 \\mathrm{n}} \\mathrm{C}_{2 \\mathrm{n}} (1)^0 (10)^{2 \\mathrm{n}} \\right) \)…
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