JEE Maths PYQ Practice, chapter-wise

JEE Main 2021 (Online) 18th March Evening ShiftQuestion 1

If $P$ and $Q$ are two statements, then which of the following compound statement is a tautology ?

Mathematical Reasoning

$((P\Rightarrow Q)\wedge\sim Q)\Rightarrow P$$((P\Rightarrow Q)\wedge\sim Q)\Rightarrow Q$$((P\Rightarrow Q)\wedge\sim Q)\Rightarrow\sim P$$((P\Rightarrow Q)\wedge\sim Q)\Rightarrow(P\wedge Q)$

JEE Main 2021 (Online) 27th August Evening ShiftQuestion 2

The Boolean expression $(p\wedge q)\Rightarrow((r\wedge q)\wedge p)$ is equivalent to :

Mathematical Reasoning

$(q\wedge r)\Rightarrow(p\wedge q)$$(p\wedge q)\Rightarrow(r\wedge q)$$(p\wedge q)\Rightarrow(r\vee q)$$(p\wedge r)\Rightarrow(p\wedge q)$

JEE Main 2021 (Online) 24th February Morning ShiftQuestion 3

The statement among the following that is a tautology is :

Mathematical Reasoning

$A\wedge(A\vee B)$$A\vee(A\wedge B)$$[A\wedge(A\to B)]\to B$$B\to[A\wedge(A\to B)]$

JEE Main 2021 (Online) 22nd July Evening ShiftQuestion 4

Which of the following Boolean expressions is not a tautology ?

Mathematical Reasoning

$(p\Rightarrow q)\vee(\sim q\Rightarrow p)$$(p\Rightarrow\sim q)\vee(\sim q\Rightarrow p)$$(\sim p\Rightarrow q)\vee(\sim q\Rightarrow p)$$(q\Rightarrow p)\vee(\sim q\Rightarrow p)$

JEE Main 2021 (Online) 3rd August Morning ShiftQuestion 5

If $\square,\lozenge\in\{\wedge,\vee\}$ such that $(\sim q\wedge p)\ \square\ (q\ \lozenge\ \sim p)$ is a tautology, then

Mathematical Reasoning

$\square=\wedge$ and $\lozenge=\wedge$$\square=\wedge$ and $\lozenge=\vee$$\square=\vee$ and $\lozenge=\wedge$$\square=\vee$ and $\lozenge=\vee$