JEE MAIN - Mathematics (2019 - 9th January Evening Slot - No. 5)
The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1, 3, 7, 9 (repitition of digits allowed) is equal to :
374
372
375
250
Explanation
Total no 1 digit numbers possible = 4 (allowed digits 1, 3, 7, 9)
Total no 2 digit numbers possible = 4$$ \times $$5 = 20
Total no 3 digit numbers possible = 4$$ \times $$5$$ \times $$5 = 100
Total no 4 digit numbers possible = 2$$ \times $$5$$ \times $$5$$ \times $$5 = 250
So the number of natural numbers less than 7,000 possible are
= 4 + 20 + 100 + 250 = 374
Total no 2 digit numbers possible = 4$$ \times $$5 = 20
Total no 3 digit numbers possible = 4$$ \times $$5$$ \times $$5 = 100
Total no 4 digit numbers possible = 2$$ \times $$5$$ \times $$5$$ \times $$5 = 250
So the number of natural numbers less than 7,000 possible are
= 4 + 20 + 100 + 250 = 374
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