JEE Novice - (8) (changed)

Number Theory Level 2

\[\Large N=7^{p+4}\times 5^q \times 2^3 \]

If \(N\) is a perfect cube where \(p,q \in \mathbb{N}\) , find the smallest possible value of \(p + q\).

This question is a part of JEE Novices.