If the 6 digit number $7002\ast 4$ is completely divisible by 8, then the smallest integer in place of $\ast$ will be:

According to the divisibility rule of 8, a number is divisible by 8 if its last three digits form a number that is divisible by 8.Here, the last three digits are $2\ast 4$. Let the digit $\ast$ be $d$. So the three-digit number is $200+10d+4=204+10d$.Let's check the options for the smallest integer value of $d$:If $d=0$: the number is 204. $\frac{204}{8}=25.5$ (not perfectly divisible).If $d=2$: the number is 224. $\frac{224}{8}=28$ (perfectly divisible).Thus, the smallest integer in place of $\ast$ is 2.