Step-by-Step Solution
Key Concept: Multiples of a number form an arithmetic progression (AP) with common difference equal to that number. Use the AP formula for the number of terms: \( n = \frac{l - a}{d} + 1 \), where \(a\) is the first term, \(l\) the last term and \(d\) the common difference.
1. Identify the AP formed by multiples of 4: \(4, 8, 12, 16, \dots\) with common difference \(d = 4\).
2. Find the smallest multiple of 4 greater than 10. Since \(4 \times 2 = 8 < 10\) and \(4 \times 3 = 12 > 10\), the first term \(a = 12\).
3. Find the largest multiple of 4 less than 250. Since \(4 \times 62 = 248 < 250\) and \(4 \times 63 = 252 > 250\), the last term \(l = 248\).
4. Use the formula for the number of terms in an AP:
$$ n = \frac{l - a}{d} + 1 $$
Substituting the values:
$$ n = \frac{248 - 12}{4} + 1 = \frac{236}{4} + 1 = 59 + 1 = 60 $$
5. Hence, there are 60 multiples of 4 lying between 10 and 250.
Correct Answer: 60