AP EAMCET · Maths · Binomial Theorem
If \(k\) is a positive integer and \(10^k\) is a divisor of the number \(9^{11}+11^9\), then the greatest value of \(k\) is
- A 1
- B 2
- C 3
- D 4
Answer & Solution
Correct Answer
(B) 2
Step-by-step Solution
Detailed explanation
\(9^{11} \pmod{100}\): \(9^1=9, 9^2=81, 9^5 \equiv 49 \pmod{100}\) \(9^{10} \equiv (9^5)^2 \equiv 49^2 = 2401 \equiv 1 \pmod{100}\) \(9^{11} \equiv 9^{10} \cdot 9 \equiv 1 \cdot 9 \equiv 9 \pmod{100}\) \(11^9 \pmod{100}\):…
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