Question

Mathematical Reasoning JEE MAIN 2021 PYQ

Answer 1

Mathematical Reasoning JEE MAIN 2021 PYQ

Summary of the post :: According to our study jee main 2021 feb and march mostly Previous year questions are repeated , and In the chapter mathematical reasoning is Tautology is mostly asked

Q1) If P and Q are two statements, then which of the following compound statement is a tautology ?

(1) ((P ⇒ Q) ∧ ~ Q) ⇒ Q

(2) ((P ⇒ Q) ∧ ~ Q) ⇒ ~ P

(3) ((P ⇒ Q) ∧ ~ Q) ⇒ P

(4) ((P ⇒ Q) ∧ ~ Q) ⇒ (P ∧ Q)

Q2) If the Boolean expression

(p∧q)⊙(p⊗q)

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⊙

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⊗

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(1) →, →

(2) ∧, ∨

(3) ∨, →

(4) ∧, →

Q3) If the Boolean expression \((p \Rightarrow q)\Leftrightarrow (q\, *(\sim p))\) is a tautology, then the Boolean expression \(p\, *(\sim q)\) is equivalent to :

(1) \(q \Rightarrow p\)

(2) \(\sim q \Rightarrow p\)

(3) \(p \Rightarrow \sim q\)

(4) \(p \Rightarrow q\)

Q4)Which of the following Boolean expression is a tautology?

(1) (p ∧ q) \(\vee\) (p \(\vee\) q)

(2) (p ∧ q) \(\vee\) (p → q)

(3) (p ∧ q) ∧ (p → q)

(4) (p ∧ q) → (p → q)

Q5)Let F₁(A,B,C) = (A∧~B) ∨ [~C ∧ (A ∨ B)] ∨~A and F₂(A, B) = (A ∨ B) ∨ (B →~A) be two logical expressions. Then :

(1) F₁ and F₂ both are tautologies

(2) F₁ is a tautology but F₂ is not a tautology

(3) F₁ is not tautology but F₂ is a tautology

(4) Both F₁ and F₂ are not tautology

Q6) The contrapositive of the statement "If you will work, you will earn money" is :

(1) You will earn money, if you will not work

(2) If you will earn money, you will work

(3) If you will not earn money, you will not work

(4) To earn money, you need to work

Q7) The statement A → (B → A) is equivalent to :

(1) A → (A ∧ B)

(2) A →(A → B)

(3) A → (A \(\leftrightarrow\)B)

(4) A → (A V B)

Q8) The negation of the statement ∼p∧(p∨q) is :

A ) p∨∼qB) ∼p∨qC) ∼ p ∧ q D) p ∧ ∼ q

Q9) The statement among the following that is a tautology is :

(1) A ∧ (A ∧ B)

(2) A ∧(A ∧ B)

(3) B → [A ∧(A → B)]

(4) [A ∧ (A → B)] → B