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Mathematical Reasoning: JEE Main & Advanced PYQs

95 previous year questions on Mathematical Reasoning from JEE Main and JEE Advanced papers, each with its exam and year, an answer and a solution.

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Questions 1-50 of 95

  1. If $P$ and $Q$ are two statements, then which of the following compound statement is a tautology ?
  2. The Boolean expression $(p\wedge q)\Rightarrow((r\wedge q)\wedge p)$ is equivalent to :
  3. The statement among the following that is a tautology is :
  4. Which of the following Boolean expressions is not a tautology ?
  5. If $\square,\lozenge\in\{\wedge,\vee\}$ such that $(\sim q\wedge p)\ \square\ (q\ \lozenge\ \sim p)$ is a tautology, then
  6. Negation of $(p\Rightarrow q)\Rightarrow(q\Rightarrow p)$ is
  7. Let $F_1(A,B,C)=(A\wedge\sim B)\vee[\sim C\wedge(A\vee B)]\vee\sim A$ and $F_2(A,B)=(A\vee B)\vee(B\to\sim A)$ be two logical expressions. Then :
  8. If the Boolean expression $(p\Rightarrow q)\Leftrightarrow(q*(\sim p))$ is a tautology, then the Boolean expression $p*(\sim q)$ is equivalent to :
  9. If $r\in\{p,q,\sim p,\sim q\}$ such that the Boolean expression $(\sim(p\vee q))\vee(p\wedge r)$ is equivalent to $r$, then $r$ is equal to
  10. 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 :
  11. Among the statements : (S1) : $(p\Rightarrow q)\vee((\sim p)\wedge q)$ is a tautology (S2) : $(q\Rightarrow p)\Rightarrow((\sim p)\wedge q)$ is a contradiction
  12. The contrapositive of the statement "If you will work, you will earn money" is :
  13. The negation of the statement $\sim p\wedge(p\vee q)$ is :
  14. For the statements $p$ and $q$, consider the following compound statements : (a) $(\sim q\wedge(p\to q))\to\sim p$ (b) $((p\vee q)\wedge\sim p)\to q$ Then which of the …
  15. The negation of $(p\wedge(\sim q))\vee(\sim p)$ is equivalent to
  16. If the truth value of the Boolean expression $((p\vee q)\wedge(q\to r)\wedge(\sim r))\to(p\wedge q)$ is false, then the truth values of the statements $p,q,r$ …
  17. Among the two statements (S1) : $(p\Rightarrow q)\wedge(p\wedge(\sim q))$ is a contradiction and (S2) …
  18. If the Boolean expression $(p\wedge q)\circledast(p\otimes q)$ is a tautology, then $\circledast$ and $\otimes$ are respectively given by :
  19. The statement $(p\wedge(p\to q)\wedge(q\to r))\to r$ is :
  20. The negation of the statement $(p\vee q)\wedge(q\vee(\sim r))$ is
  21. The statement $\sim[p\vee(\sim(p\wedge q))]$ is equivalent to
  22. The statement $\sim(p\leftrightarrow\sim q)$ is equivalent to
  23. Let $*,\square\in\{\wedge,\vee\}$ be such that the Boolean expression $(p*\sim q)\Rightarrow(p\ \square\ q)$ is a tautology. Then :
  24. The statement $A\to(B\to A)$ is equivalent to :
  25. The Boolean expression $(p\Rightarrow q)\wedge(q\Rightarrow\sim p)$ is equivalent to :
  26. 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 :
  27. Negation of the statement $(p\vee r)\Rightarrow(q\vee r)$ is :
  28. Statement $(P\Rightarrow Q)\wedge(R\Rightarrow Q)$ is logically equivalent to
  29. Let $r\in\{p,q,\sim p,\sim q\}$ be such that the logical statement $r\vee(\sim p)\Rightarrow(p\wedge q)\vee r$ is a tautology. Then $r$ is equal to :
  30. Negation of the Boolean statement $(p\vee q)\Rightarrow((\sim r)\vee p)$ is equivalent to
  31. The conditional statement $((p\wedge q)\to((\sim p)\vee r))\vee(((\sim p)\vee r)\to(p\wedge q))$ is :
  32. Let $\Delta\in\{\wedge,\vee,\Rightarrow,\Leftrightarrow\}$ be such that $(p\wedge q)\ \Delta\ ((p\vee q)\Rightarrow q)$ is a tautology. Then $\Delta$ is equal to :
  33. The number of choices for $\Delta\in\{\wedge,\vee,\Rightarrow,\Leftrightarrow\}$, such that $(p\Delta q)\Rightarrow((p\Delta\sim q)\vee((\sim p)\Delta q))$ is a …
  34. The statement $(p\wedge(\sim q))\vee((\sim p)\wedge q)\vee((\sim p)\wedge(\sim q))$ is equivalent to
  35. The maximum number of compound propositions, out of $p\vee r\vee s$, $p\vee r\vee\sim s$, $p\vee\sim q\vee s$, $\sim p\vee\sim r\vee s$, $\sim p\vee\sim r\vee\sim s$ …
  36. Consider the following two propositions : $P1:\sim(p\to\sim q)$ $P2:(p\wedge\sim q)\wedge((\sim p)\vee q)$ If the proposition $p\to((\sim p)\vee q)$ is evaluated as …
  37. The negation of the Boolean expression $((\sim q)\wedge p)\Rightarrow((\sim p)\vee q)$ is logically equivalent to :
  38. Negation of $p\wedge(q\wedge\sim(p\wedge q))$ is
  39. The negation of the statement $(((A\wedge(B\vee C))\Rightarrow(A\vee B))\Rightarrow A)$ is
  40. Let $\Delta,\nabla\in\{\wedge,\vee\}$ be such that $p\nabla q\Rightarrow((p\Delta q)\nabla r)$ is a tautology. Then $(p\nabla q)\Delta r$ is logically equivalent to :
  41. The boolean expression $(\sim(p\wedge q))\vee q$ is equivalent to :
  42. The number of ordered triplets of the truth values of $p,q$ and $r$ such that the truth value of the statement $(p\vee q)\wedge(p\vee r)\Rightarrow(q\vee r)$ is True, is …
  43. Which of the following statement is a tautology ?
  44. Consider the following statements: $A$: Rishi is a judge. $B$: Rishi is honest. $C$: Rishi is not arrogant. The negation of the statement "if Rishi is a judge and he is …
  45. Let $p,q,r$ be three logical statements. Consider the compound statements $S_1:((\sim p)\vee q)\vee((\sim p)\vee r)$ and $S_2:p\to(q\vee r)$ Then, which of the following …
  46. Consider the following statements : $P$ : Ramu is intelligent. $Q$ : Ramu is rich. $R$ : Ramu is not honest. The negation of the statement ``Ramu is intelligent and …
  47. The statement $(p\wedge q)\Rightarrow(p\wedge r)$ is equivalent to :
  48. Which of the following is a contradiction?
  49. Let $p,q,r$ be three statements such that the truth value of $(p\wedge q)\to(\sim q\vee r)$ is $F$. Then the truth values of $p,q,r$ are respectively :
  50. $(p\wedge r)\Leftrightarrow(p\wedge(\sim q))$ is equivalent to $(\sim p)$ when $r$ is

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