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NDA 1 2024 Maths, question 3

Topic: Algebra

Q3

What is the sum of all four digit numbers formed by using all digits 0,1,4,50,1,4,5 without repetition of digits ?

  1. (a) 4444044440
  2. (b) 4646046460
  3. (c) 4644046440
  4. (d) 6444064440Correct answer

Solution.

Answer: (d) 6444064440

  1. There are 3×3!=18 valid four-digit numbers.
  2. Each nonzero digit occurs six times in the thousands place, contributing 6(1+4+5)1000=60000.
  3. In each lower place each nonzero digit occurs four times, contributing 4(1+4+5)(100+10+1)=4440.
  4. The sum is 64440.