JEE Main 2022 · 25 Jun · Shift 1, Mathematics question 22

Count by last digit $c\in\{1,3,5,7,9\}$ and first digit $a\in\{1,\dots,9\}$, middle $b\in\{0,\dots,9\}$, with $a+b+c\in\{7,14,21\}$.

Tally. For each $(a,c)$ the number of valid $b$ is 1 or 2; summing over the 45 pairs gives 63 (checked by direct enumeration).

Answer: 63