JEE Main · 2021 · 26 Aug 2021 · Shift 1 · Mathematical Reasoning *

An implication is false only when its antecedent is true and its consequent is false, so $(p\vee q)\wedge (q\to r)\wedge (\sim r)$ must be true while $p\wedge q$ is false.
Truth of $\sim r$ forces $r$ to be false. With $r$ false, $q\to r$ is true only if $q$ is false. With $q$ false, $p\vee q$ is true only if $p$ is true.
These values give $p\wedge q$ false, so the whole implication is indeed false, and the truth values are $p$ true, $q$ false, $r$ false.