Binomial Theorem
Remainder using Binomial Expansion
Grade None
Question:
<p>If <i>a</i> is the remainder when <i>540</i> is divided by 11 and <i>b</i> is the remainder when <i>2<sup>2011</sup></i> is divided by 17, the value of <i>a ⊕ b</i> is</p>
<p>(a) 7</p>
<p>(b) 8</p>
<p>(c) 9</p>
<p>(d) 10</p>
Step-by-Step Solution
Key Concept: Use Fermat's Little Theorem and modular arithmetic to find remainders, then combine them.
<p><strong>Solution:</strong></p><p>Find remainder when <i>540</i> is divided by 11.</p><p>Find remainder when <i>2<sup>2011</sup></i> is divided by 17.</p><p>Then compute <i>a ⊕ b</i>.</p>
Correct Answer: b