Number of points having position vector ai + bj + ck where a, b, c ∈ {1,2,3,4,5,} such that 2a + 3b + 5c is divisible by 4 is ​

Question

Number of points having position vector \(a\hat i + b\hat j + c\hat k\) where a, b, c ∈ {1,2,3,4,5,} such that 2^a + 3^b + 5^c is divisible by 4 is

(a) 70

(b) 140

(c) 210

(d) 280

Answer 1

Correct option is (a) 70