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NDA 2 2025 Maths, question 18

Topic: Algebra

Q18

How many 4-digit numbers that are divisible by 44 can be formed using the digits 1,2,31,2,3 and 44 (repetition of digits is not allowed)?

  1. (a) 33
  2. (b) 66Correct answer
  3. (c) 99
  4. (d) 1212

Solution.

Answer: (b) 66

  1. A number is divisible by 4 exactly when its last two digits form a multiple of 4.
  2. The possible distinct-digit endings are 12,24,32.
  3. Each leaves two digits for the first two positions, in 2! orders.
  4. Hence there are 3×2=6 numbers, giving option (b).