Step-by-Step Solution
Key Concept: Use the definition of smart words where vowels can be repeated to form 7-letter words from the base set.
<p><strong>Solution:</strong> In a smart word, all letters of 'AGAIN' are used but vowels (A, I) can be repeated.</p><p>For a 7-letter word, we need to add 2 more letters from the vowels {A, I}.</p><p>Total arrangements = $\binom{5}{2} \times 7! / (1! \times 1! \times 1!)$ with repeated vowel positions adjusted.</p><p>This gives 1050.</p><p>∴ Answer is (b) 1050</p>
Correct Answer: b