GATE Papers >> EEE >> 2019 >> Question No 6

Question No. 6 EEE | GATE 2019

How many integers are there between 100 and 1000 all of whose digits are even?


Answer : (C) 100


Solution of Question No 6 of GATE 2019 EEE Paper

Method-I:

Integers between 100 and 1000 all of the whose digits are even = 100; since

100 – 199 → No integers

200 – 300 → 25 integers

[200, 202, 204, 206, 208, 220, 222, 224, 226, 228, 240, 242, 246, 248, 260, 262, 264, 266, 268, 280, 282, 284, 286, 288].

Similarly;400 – 500 → 25 integers;600 – 700 → 25 integers;800 – 900 → 25 integers

$ \therefore $ Total number of integers=25+25+25+25=100

 

Method-II;

Required number of digits must be three.

$ \therefore $ Total number of integers $ =\frac4{\left(2,4,6,8\right)}\times\frac5{\left(0,2,4,6,8\right)}\times\frac5{\left(0,2,4,6,8\right)}=100 $

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