JEE Main Mathematical Reasoning Practice Questions With Solutions

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JEE Main Mathematical Reasoning Practice Questions with Solutions

Mathematical Reasoning refers to analysing mathematical concepts and making conclusions from them. This part assesses the logical thinking abilities and analysis skills of the JEE Main aspirant. It is an important part of the Mathematics section, and usually helps students yield scores. Practising the JEE Main Mathematical Reasoning Practice Questions with Solutions will provide students with an understanding of the types of questions asked and how to solve them. Regular practice will also strengthen their reasoning skills and improve their logical thinking. In the JEE Main question paper, you may expect about 1 to 2 questions from the mathematical reasoning part. The questions asked in the JEE Main paper from the Mathematical Reasoning part will be in the form of multiple-choice questions and assertion-reason types of questions. Attempting the JEE Main Mathematical Reasoning Practice Test regularly will give you an edge in answering these questions accurately during the exam.

The important topics included in the Mathematical Reasoning section, from which students can expect questions in the question paper, are- Truth Tables, Statements and Logical Operations, General Logical Equivalence, Negation, Converse, and Contrapositive, Tautology and Contradiction, General Logical Equivalence, and Practical Reasoning Questions. The JEE Main Mathematical Reasoning Practice Questions with Solutions consist of a variety of questions from all these topics mentioned above for students to practise. These practice test consists of 15 to 20 questions on Mathematical Reasoning along with their solutions and explanations. Practising these tests on a frequent basis will enhance the students' speed and accuracy while drawing conclusions from mathematical concepts. It is recommended that students they must practise at least 5 to 10 questions on Mathematical Reasoning every week to develop a strong grasp of the subject. Regular practice will also develop critical thinking skills in the students, which is necessary for achieving success in any highly competitive exams.

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

JEE Main Mathematical Reasoning Practice Questions With Solutions

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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