Mathematical Reasoning & Induction · JEE Main previous year questions

2021 10 questions

1. Q182021 · 26 Aug 2021 · Shift 2

   Consider the two statements : (S1) : $(p\to q)\vee (\sim q\to p)$ is a tautology . (S2) : $(p\wedge \sim q)\wedge (\sim p\vee q)$ is a fallacy. Then :

   1. A.only (S1) is true.
   2. B.both (S1) and (S2) are false.
   3. C.both (S1) and (S2) are true.
   4. D.only (S2) is true.
   Show answer

   Answer: C

2. Q182021 · 27 Jul 2021 · Shift 2

   Which of the following is the negation of the statement "for all M > 0, there exists $x\in S$ such that $x\ge M$" ?

   1. A.there exists M > 0, such that x < M for all $x\in S$
   2. B.there exists M > 0, there exists $x\in S$ such that $x\ge M$
   3. C.there exists M > 0, there exists $x\in S$ such that x < M
   4. D.there exists M > 0, such that $x\ge M$ for all $x\in S$
   Show answer

   Answer: A

3. Q92021 · 25 Jul 2021 · Shift 1

   Let g : N $\to$ N be defined as g(3n + 1) = 3n + 2, g(3n + 2) = 3n + 3, g(3n + 3) = 3n + 1, for all $n\ge 0$. Then which of the following statements is true?

   1. A.There exists an onto function f : N $\to$ N such that fog = f
   2. B.There exists a one-one function f : N $\to$ N such that fog = f
   3. C.gogog = g
   4. D.There exists a function f : N $\to$ N such that gof = f
   Show answer

   Answer: A

4. Q172021 · 25 Jul 2021 · Shift 1

   The Boolean expression $(p\Rightarrow q)\wedge (q\Rightarrow \sim p)$ is equivalent to :

   1. A.$\sim q$
   2. B.q
   3. C.p
   4. D.$\sim p$
   Show answer

   Answer: D

5. Q182021 · 25 Jul 2021 · Shift 2

   Consider the statement "The match will be played only if the weather is good and ground is not wet". Select the correct negation from the following :

   1. A.The match will not be played and weather is not good and ground is wet.
   2. B.If the match will not be played, then either weather is not good or ground is wet.
   3. C.The match will be played and weather is not good or ground is wet.
   4. D.The match will not be played or weather is good and ground is not wet.
   Show answer

   Answer: C

6. Q182021 · 22 Jul 2021 · Shift 2

   Which of the following Boolean expressions is not a tautology?

   1. A.$(p\Rightarrow q)\vee (\sim q\Rightarrow p)$
   2. B.$(q\Rightarrow p)\vee (\sim q\Rightarrow p)$
   3. C.$(p\Rightarrow \sim q)\vee (\sim q\Rightarrow p)$
   4. D.$(\sim p\Rightarrow q)\vee (\sim q\Rightarrow p)$
   Show answer

   Answer: D

7. Q162021 · 20 Jul 2021 · Shift 1

   The Boolean expression $(p\wedge \sim q)\Rightarrow (q\vee \sim p)$ is equivalent to :

   1. A.$q\Rightarrow p$
   2. B.$p\Rightarrow q$
   3. C.$\sim q\Rightarrow p$
   4. D.$p\Rightarrow \sim q$
   Show answer

   Answer: B

8. Q192021 · 18 Mar 2021 · Shift 2

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

   1. A.$((\mathrm{P}\Rightarrow \mathrm{Q})\wedge \sim \mathrm{Q})\Rightarrow (\mathrm{P}\wedge \mathrm{Q})$
   2. B.$((\mathrm{P}\Rightarrow \mathrm{Q})\wedge \sim \mathrm{Q})\Rightarrow \mathrm{Q}$
   3. C.$((\mathrm{P}\Rightarrow \mathrm{Q})\wedge \sim \mathrm{Q})\Rightarrow \mathrm{P}$
   4. D.$((\mathrm{P}\Rightarrow \mathrm{Q})\wedge \sim \mathrm{Q})\Rightarrow \sim \mathrm{P}$
   Show answer

   Answer: D

9. Q152021 · 16 Mar 2021 · Shift 1

   Which of the following Boolean expression is a tautology?

   1. A.$(p\wedge q)\vee (p\to q)$
   2. B.$(p\wedge q)\vee (p\vee q)$
   3. C.$(p\wedge q)\to (p\to q)$
   4. D.$(p\wedge q)\wedge (p\to q)$
   Show answer

   Answer: C

10. Q172021 · 25 Feb 2021 · Shift 2

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

    1. A.If you will not earn money, you will not work
    2. B.If you will earn money, you will work
    3. C.You will earn money, if you will not work
    4. D.To earn money, you need to work
    Show answer

    Answer: A