JEE Mains · Maths · STD 11 - 7. binomial theoram
The remainder, when \(7^{103}\) is divided by \(17\) is \(..........\).
- A \(11\)
- B \(12\)
- C \(13\)
- D \(14\)
Answer & Solution
Correct Answer
(B) \(12\)
Step-by-step Solution
Detailed explanation
\(7^{103}=7 \times 7^{102}\) \(=7 \times(49)^{51}\) \(=7 \times(51-2)^{51}\) Remainder :- \(7 \times(-2)^{51}\) \(\Rightarrow-7\left(2^3 \cdot(16)^{12}\right)\) \(\Rightarrow-56(17-1)^{12}\) \(\text { Remainder }=-56 \times(-1)^{12}=-56+68=12\)
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