Mathematical Reasoning & Induction · JEE Main previous year questions

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2020 12 questions

Q162020 · 6 Sept 2020 · Shift 1
The negation of the Boolean expression $p \lor (\sim p \land q)$ is equivalent to :
1. A. $p \land \sim q$
2. B. $\sim p \lor \sim q$
3. C. $\sim p \land q$
4. D. $\sim p \land \sim q$
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Answer: D
Q182020 · 6 Sept 2020 · Shift 2
Consider the statement : “For an integer n, if $n^{3} - 1$ is even, then n is odd.” The contrapositive statement of this statement is :
1. A.For an integer n, if n is even, then $n^{3} - 1$ is even.
2. B.For an integer n, if $n^{3} - 1$ is not even, then n is not odd.
3. C.For an integer n, if n is odd, then $n^{3} - 1$ is even.
4. D.For an integer n, if n is even, then $n^{3} - 1$ is odd.
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Answer: D
Q172020 · 3 Sept 2020 · Shift 2
Let p, q, r be three statements such that the truth value of $(p \land q) \to (\sim q \lor r)$ is F. Then the truth values of p, q, r are respectively :
1. A.T, F, T
2. B.F, T, F
3. C.T, T, T
4. D.T, T, F
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Answer: D
Q162020 · 2 Sept 2020 · Shift 1
The contrapositive of the statement "If I reach the station in time, then I will catch the train" is :
1. A.If I will catch the train, then I reach the station in time.
2. B.If I do not reach the station in time, then I will not catch the train.
3. C.If I will not catch the train, then I do not reach the station in time.
4. D.If I do not reach the station in time, then I will catch the train.
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Answer: C
Q182020 · 2 Sept 2020 · Shift 2
Which of the following is a tautology ?
1. A. $(\sim p) \land (p \lor q) \to q$
2. B. $(q \to p) \lor \sim (p \to q)$
3. C. $(p \to q) \land (q \to p)$
4. D. $(\sim q) \lor (p \land q) \to q$
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Answer: A
Q182020 · 9 Jan 2020 · Shift 1
Negation of the statement : $5$ is an integer or 5 is irrational is :
1. A. $5$ is not an integer and 5 is not irrational.
2. B. $5$ is irrational or 5 is an integer.
3. C. $5$ is an integer and 5 is irrational.
4. D. $5$ is not an integer or 5 is not irrational.
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Answer: A
Q192020 · 9 Jan 2020 · Shift 2
If $p \to (p \land \sim q)$ is false, then the truth values of p and q are respectively :
1. A.T, T
2. B.T, F
3. C.F, T
4. D.F, F
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Answer: A
Q192020 · 8 Jan 2020 · Shift 1
Which one of the following is a tautology?
1. A. $P \land (P \lor Q)$
2. B. $P \lor (P \land Q)$
3. C. $Q \to (P \land (P \to Q))$
4. D. $(P \land (P \to Q)) \to Q$
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Answer: D
Q172020 · 8 Jan 2020 · Shift 2
Which of the following statements is a tautology?
1. A. $\sim (p \land \sim q) \to p \lor q$
2. B. $\sim (p \lor \sim q) \to p \lor q$
3. C. $\sim (p \lor \sim q) \to p \land q$
4. D. $p \lor (\sim q) \to p \land q$
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Answer: B
Q202020 · 7 Jan 2020 · Shift 1
The logical statement $(p \Rightarrow q) \land (q \Rightarrow\sim p)$ is equivalent to :
1. A.q
2. B. $\sim p$
3. C.p
4. D. $\sim q$
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Answer: B
Q72020 · 7 Jan 2020 · Shift 2
Let $α$ and $β$ be the roots of the equation $x^{2} - x - 1 = 0$ . If $p_{k} = (α)^{k} + (β)^{k}$ , $k \geq 1$ , then which one of the following statements is not true?
1. A. $(p_{1} + p_{2} + p_{3} + p_{4} + p_{5}) = 26$
2. B. $p_{5} = 11$
3. C. $p_{3} = p_{5} - p_{4}$
4. D. $p_{5} = p_{2} \cdot p_{3}$
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Answer: D
Q172020 · 7 Jan 2020 · Shift 2
Let A, B, C and D be four non-empty sets. The contrapositive statement of "If $A \subseteq B$ and $B \subseteq D$ , then $A \subseteq C$ " is :
1. A.If $A ⊈ C$ , then $A ⊈ B$ or $B ⊈ D$
2. B.If $A ⊈ C$ , then $A ⊈ B$ and $B \subseteq D$
3. C.If $A \subseteq C$ , then $B \subset A$ or $D \subset B$
4. D.If $A ⊈ C$ , then $A \subseteq B$ and $B \subseteq D$
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Answer: A