JEE Mains · Maths · STD 11 - 7. binomial theoram
The remainder on dividing \(5^{99}\) by \(11\) is
- A \(9\)
- B \(18\)
- C \(27\)
- D \(36\)
Answer & Solution
Correct Answer
(A) \(9\)
Step-by-step Solution
Detailed explanation
\(5^{99}=5^4 \cdot 5^{95}\) \(=625\left[5^5\right]^{19}\) \(=625[3125]^{19}\) \(=625[3124+1]^{19}\) \(=625[11 k \times 19+1]\) \(=625 \times 11\,k \times 19+625\) \(=11\,k _1+616+9\) \(=11\left( k _2\right)+9\) Remainder \(=9\)
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