JEE Main Mathematical Reasoning Practice Questions With Solutions

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JEE Main Mathematics Mathematical Reasoning Practice Questions

Chemistry Physics

Question 1.

Negation of

p \land (q \land \sim (p \land q))

is :

(\sim (p \land q)) \land q

(\sim (p \land q)) \lor p

p \lor q

\sim (p \lor q)

Question 2.

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

(\sim p) \lor (\sim q)

p \lor (\sim q)

p \lor q

(\sim p) \lor q

Question 3.

The negation of the statement $((A \land (B \lor C)) \Rightarrow (A \lor B)) \Rightarrow A$ is

equivalent to

B \lor \sim C

equivalent to

\sim A

equivalent to

\sim C

a fallacy

Question 4.

Among the two statements

$(S 1) : (p \Rightarrow q) \land (p \land (\sim q))$ is a contradiction and

$(S 2) : (p \land q) \lor ((\sim p) \land q) \lor (p \land (\sim q)) \lor ((\sim p) \land (\sim q))$ is a tautology

both are false.

only (S1) is true.

both are true.

only (S2) is true.

Question 5.

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

((\sim p) \lor q) \Rightarrow r

(\sim r) \Rightarrow p \land q

(p \lor (\sim q)) \Rightarrow (\sim r)

(\sim r) \Rightarrow ((\sim p) \land q)

Question 6.

The statement $\sim [p \lor (\sim (p \land q))]$ is equivalent to :

(\sim (p \land q)) \land q

\sim (p \lor q)

(p \land q) \land (\sim p)

\sim (p \land q)

Question 7.

The negation of the statement $(p \lor q) \land (q \lor (\sim r))$ is :

((\sim p) \lor r)) \land (\sim q)

(p \lor r) \land (\sim q)

((\sim p) \lor (\sim q)) \lor (\sim r)

((\sim p) \lor (\sim q)) \land (\sim r)

Question 8.

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

p \land q

p \land (\sim q)

p \land (q \land (\sim p))

p \lor (q \lor (\sim p))

Question 9.

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

(\sim q) \land p

q \land (\sim p)

p \lor (\sim q)

(\sim p) \lor q

Question 10.

Among the statements

(S1) : $(p \Rightarrow q) \lor ((\sim p) \land q)$ is a tautology

(S2) : $(q \Rightarrow p) \Rightarrow ((\sim p) \land q)$ is a contradiction

neither (S1) and (S2) is True

only (S2) is True

both

(S 1)

and

(S 2)

are True

only (S1) is True

Question 1.

Statement $(P \Rightarrow Q) \land (R \Rightarrow Q)$ is logically equivalent to :

(P \Rightarrow R) \land (Q \Rightarrow R)

(P \Rightarrow R) \lor (Q \Rightarrow R)

(P \land R) \Rightarrow Q

(P \lor R) \Rightarrow Q

Question 2.

Which of the following statements is a tautology?

p \lor (p \land q)

(p \land (p \to q)) \to \sim q

p \to (p \land (p \to q))

(p \land q) \to (\sim (p) \to q)

Question 3.

The negation of the expression $q \lor ((\sim q) \land p)$ is equivalent to

(\sim p) \land (\sim q)

(\sim p) \lor q

p \land (\sim q)

(\sim p) \lor (\sim q)

Question 4.

The number of values of

r \in {p, q, \sim p, \sim q}

for which

((p \land q) \Rightarrow (r \lor q)) \land ((p \land r) \Rightarrow q)

is a tautology, is :

Question 5.

$(S 1) (p \Rightarrow q) \lor (p \land (\sim q))$ is a tautology

$(S 2) ((\sim p) \Rightarrow (\sim q)) \land ((\sim p) \lor q)$ is a contradiction.

Then

only (S2) is correct

both (S1) and (S2) are correct

only (S1) is correct

both (S1) and (S2) are wrong

Question 6.

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 :

((\sim P) \lor \sim Q) \land ((\sim P) \lor \sim R)

(P \lor \sim Q) \land (P \lor \sim R)

((\sim P) \lor \sim Q) \land ((\sim P) \lor R)

(P \lor Q) \land ((\sim P) \lor R)

Question 7.

Among the statements :

$(S 1) ((p \lor q) \Rightarrow r) \Leftrightarrow (p \Rightarrow r)$

$(S 2) ((p \lor q) \Rightarrow r) \Leftrightarrow ((p \Rightarrow r) \lor (q \Rightarrow r))$

only (S1) is a tautology

neither (S1) nor (S2) is a tautology

both (S1) and (S2) are tautologies

only (S2) is a tautology

Question 8.

If $p, q$ and $r$ are three propositions, then which of the following combination of truth values of $p, q$ and $r$ makes the logical expression ${(p \lor q) \land ((\sim p) \lor r)} \to ((\sim q) \lor r)$ false?

p = F, q = T, r = F

p = T, q = T, r = F

p = T, q = F, r = T

p = T, q = F, r = F

Question 9.

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

Δ = \lor, \nabla = \lor

Δ = \lor, \nabla = \land

Δ = \land, \nabla = \land

Δ = \land, \nabla = \lor

Question 10.

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

a tautology

equivalent to

(\sim p) \lor (\sim q)

a contradiction

p \lor q

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JEE Main Mathematical Reasoning Practice Questions With Solutions

JEE Main Mathematics Mathematical Reasoning Practice Questions

Question 1.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.

Question 7.

Question 8.

Question 9.

Question 10.

Question 1.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.

Question 7.

Question 8.

Question 9.

Question 10.

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