JEE Main 2020 (Online) 6th September Morning ShiftQuestion 1
Set $A$ has $m$ elements and Set $B$ has $n$ elements. If the total number of subsets of $A$ is $112$ more than the total number of subsets of $B$, then the value of $m\cdot n$ is $\_\_\_\_\_\_\_\_$ .
Sets, Relations and Function
Answer$28$
Solution
$2^m-2^n=112=2^4(2^3-1)$ gives $n=4$, $m=7$, so $mn=28$.