TS EAMCET · Maths · Binomial Theorem
When \(3^{2023}\) is divided by 16 , the remainder obtained is
- A 15
- B 11
- C 9
- D 7
Answer & Solution
Correct Answer
(B) 11
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text3^{2023}=3 \cdot\left(3^2\right)^{1011}=3(8+1)^{1011}=3(1+8)^{1011} \\ & =3\left[{ }^{1011} C_0+{ }^{1011} C_1 8+{ }^{1011} C_2 8^2+\ldots .+{ }^{1011} C_{1011} 8^{1011}\right] \\ & =3(1+1011 \times 8+16 k) \\ & \therefore \quad \text { Remainder when }…
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