JEE Mains Previous Year Questions (PYQ)

JEE Main 2023 11th April Evening Shift

The converse of $ ((\sim p)\wedge q) \Rightarrow r $ is:

7.

Consider the following statements :
$ P:$ I have fever $ \\ \\ Q:$ I will not take medicine $ \\ \\ R:$ I will take rest
The statement “If I have fever, then I will take medicine and I will take rest” is equivalent to :

8.

The statement $ \big(p \land (\sim q)\big) \lor \big((\sim p)\land q\big) \lor \big((\sim p)\land (\sim q)\big) $ is equivalent to ________.

9.

The statement $ (p \land (\sim q)) \Rightarrow (p \Rightarrow (\sim q)) $ is:

10.

The negation of the statement $ (p \vee q)\wedge(q \vee (\sim r)) $ is:

11.

The compound statement $ (\sim(P \land Q)) \lor ((\sim P) \land Q) \Rightarrow ((\sim P) \land (\sim Q)) $ is equivalent to:

12.

The number of values of $r \in \{p, q, \sim p, \sim q\}$ for which $((p \wedge q) \Rightarrow (r \vee q)) \wedge ((p \wedge r) \Rightarrow q)$ is a tautology, is:

13.

The statement $ B \Rightarrow ((\sim A) \lor B) $ is equivalent to:

14.

Among the two statements
$ (S1): (p \Rightarrow q) \land \left(p \land (\sim q)\right) $ is a contradiction and
$ (S2): (p \land q) \lor \left((\sim p) \land q\right) \lor \left(p \land (\sim q)\right) \lor \left((\sim p) \land (\sim q)\right) $ is a tautology.

15.

The negation of the statement $ ((A \wedge (B \vee C)) \Rightarrow (A \vee B)) \Rightarrow A $ is:

16.

For the system of linear equations
$ 2x - y + 3z = 5 $
$ 3x + 2y - z = 7 $
$ 4x + 5y + \alpha z = \beta $,
Which of the following is NOT correct?

17.

Negation of $ p \wedge (q \wedge \sim(p \wedge q)) $ is:

18.

Among the statements:
($ S1 $): $ (p \Rightarrow q) \vee ((\sim p) \wedge q) $ is a tautology.
($ S2 $): $ (q \Rightarrow p) \Rightarrow ((\sim p) \wedge q) $ is a contradiction.

19.

Negation of $ (p \Rightarrow q) \Rightarrow (q \Rightarrow p) $ is:

20.

The converse of $ ((\sim p)\wedge q) \Rightarrow r $ is:

21.

Among the statements:
$ (S1) \; ((p \lor q) \Rightarrow r) \Leftrightarrow (p \Rightarrow r) $
$ (S2) \; ((p \lor q) \Rightarrow r) \Leftrightarrow ((p \Rightarrow r) \lor (q \Rightarrow r)) $

22.

Let $ \Delta,\nabla \in \{\land,\lor\} $ be such that $ (p \to q)\,\Delta\,(p \nabla q) $ is a tautology. Then

23.

Which of the following statements is a tautology?

24.

The negation of $ \big(p\land(\sim q)\big)\lor(\sim p) $ is equivalent to:

25.

The negation of the expression $ q \vee \big((\sim q) \wedge p\big) $ is equivalent to:

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