NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 1: Number System - Problems and Solutions
Question 165

Question. 165

Mobile number: first 4 digits = 9, 9, 8, 7; last 3 digits = 3, 5, 5. Find remaining distinct digits to make greatest possible number.

Answer:

Digits = 6, 4, 2

Detailed Answer with Explanation:

  1. All ten digits are:
    \(0,\;1,\;2,\;3,\;4,\;5,\;6,\;7,\;8,\;9\).
  2. Digits already used in the number are:
    \(9,\;9,\;8,\;7,\;3,\;5,\;5\).
  3. Remove these used digits from the list of all digits.
  4. Digits left are:
    \(\{0,\;1,\;2,\;4,\;6\}\).
  5. We need three more digits, all different (distinct).
  6. To make the number as large as possible, choose the biggest remaining digits.
  7. Order the remaining digits from greatest to least:
    \(6\;>\;4\;>\;2\;>\;1\;>\;0\).
  8. Pick the top three:
    \(6,\;4,\;2\).
  9. Therefore, the required digits are:
    \(\boxed{6,\;4,\;2}\).
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