Question 12 of 44intermediate🔧 ApplyShort Answer3 marks

How many multiples of 4 lie between 10 and 250?

Correct Answer

60 multiples of 4 lie between 10 and 250.

Exercise: EXERCISE 5.2 | Q: 14 | (Chapter: Page 14)
For More Understanding

Explanation

This question requires finding the count of multiples of 4 in a given range. The multiples of 4 form an Arithmetic Progression. We identify the first and last multiples within the range, then use the nth term formula to find the number of terms.

Solution Steps

  1. Step 1: Identify the first multiple of 4 greater than 10. Since 10 ÷ 4 = 2.5, the next integer is 3. So, first term a = 4×34 \times 3 = 12.

  2. Step 2: Identify the last multiple of 4 less than 250. Since 250 ÷ 4 = 62.5, the integer part is 62. So, last term l = 4×624 \times 62 = 248.

  3. Step 3: The multiples of 4 form an AP: 12, 16, 20, ..., 248 with first term a = 12, common difference d = 4, and last term l = 248.

  4. Step 4: Apply the formula l = a + (n - 1)d

  5. 248 = 12 + (n - 1) × 4

  6. 236 = (n - 1) × 4

  7. n - 1 = 59

  8. n = 60

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