Skip to main content
Yukti Vault

Algebra

Sets, Relations and Function: JEE Main & Advanced PYQs

214 previous year questions on Sets, Relations and Function from JEE Main and JEE Advanced papers, each with its exam and year, an answer and a solution.

Practice this chapter

Questions 101-150 of 214

  1. Let $\triangle,\nabla\in\{\wedge,\vee\}$ be such that $(p\to q)\,\triangle\,(p\,\nabla\,q)$ is a tautology. Then :
  2. For two statements $p$ and $q$, the logical statement $(p\to q)\wedge(q\to\sim p)$ is equivalent to
  3. If $q$ is false and $p\wedge q\leftrightarrow r$ is true, then which one of the following statements is a tautology ?
  4. In a class of $140$ students numbered $1$ to $140$, all even numbered students opted Mathematics course, those whose number is divisible by $3$ opted Physics course and …
  5. Consider the statement: "$P(n):n^{2}-n+41$ is prime". Then which one of the following is true?
  6. The number of functions $f:\{1,2,3,4\}\to\{a\in\mathbb Z:|a|\le8\}$ satisfying $f(n)+\frac1nf(n+1)=1$, $\forall n\in\{1,2,3\}$ is :
  7. The statement $B\Rightarrow\left((\sim A)\vee B\right)$ is not equivalent to :
  8. If $p\Rightarrow(q\vee r)$ is False, then the truth values of $p$, $q$, $r$ are respectively, (where $T$ is True and $F$ is False)
  9. Let $N$ be the set of natural numbers and two functions $f$ and $g$ be defined as $f,g:N\to N$ such that …
  10. For any two statements $p$ and $q$, the negation of the expression $p\vee(\sim p\wedge q)$ is
  11. The Boolean expression $\sim(p\vee q)\vee(\sim p\wedge q)$ is equivalent to
  12. If $A$, $B$ and $C$ are three sets such that $A\cap B=A\cap C$ and $A\cup B=A\cup C$, then :
  13. The contrapositive of the statement "if I am not feeling well, then I will go to the doctor" is
  14. Which one of the following statements is not a tautology?
  15. If $(p\wedge\sim q)\wedge(p\wedge r)\to\sim p\vee q$ is false, then the truth values of $p$, $q$ and $r$ are respectively
  16. The statement $(p\wedge(\sim q))\Rightarrow(p\Rightarrow(\sim q))$ is
  17. The Boolean expression $(p\wedge\sim q)\Rightarrow(q\vee\sim p)$ is equivalent to :
  18. 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 …
  19. The Boolean expression $(p\wedge\sim q)\vee q\vee(\sim p\wedge q)$ is equivalent to
  20. 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 :
  21. Let $R=\{(3,3),(5,5),(9,9),(12,12),(5,12),(3,9),(3,12),(3,5)\}$ be a relation on the set $A=\{3,5,9,12\}$. Then, $R$ is :
  22. Contrapositive of the statement "If two numbers are not equal, then their squares are not equal". is :
  23. The contrapositive of the statement "If you are born in India, then you are a citizen of India", is
  24. A relation on the set $A=\{x:|x|<3,\ x\in Z\}$, where $Z$ is the set of integers, is defined by $R=\{(x,y):y=|x|,\ x\neq-1\}$. Then the number of elements in the power …
  25. Let $A=\{1,2,3,4\}$ and $R:A\to A$ be the relation defined by $R=\{(1,1),(2,3),(3,4),(4,2)\}$. The correct statement is :
  26. The function $f:\mathbb R\to\left[-\frac12,\frac12\right]$ defined as $f(x)=\frac{x}{1+x^2}$, is :
  27. Consider the following three statements: $P$ : $5$ is a prime number $Q$ : $7$ is a factor of $192$ $R$ : LCM of $5$ and $7$ is $35$ Then the truth value of which one of …
  28. Two sets $A$ and $B$ are as under: $A=\{(a,b)\in R\times R:|a-5|<1 \text{ and } |b-5|<1\}$; $B=\{(a,b)\in R\times R:4(a-6)^2+9(b-5)^2\le36\}$. Then :
  29. The contrapositive of the following statement, "If the side of a square doubles, then its area increases four times", is
  30. Let $R$ be a relation defined on $\mathbb N$ as $a\,R\,b$ is $2a+3b$ is a multiple of $5$, $a,b\in\mathbb N$. Then $R$ is
  31. The contrapositive of the statement 'If two numbers are not equal, then their squares are not equal', is :
  32. Let $A=\{\theta:\sin\theta=\tan\theta\}$ and $B=\{\theta:\cos\theta=1\}$ be two sets. Then :
  33. Let $R=\{(1,3),(4,2),(2,4),(2,3),(3,1)\}$ be a relation on the set $A=\{1,2,3,4\}$. The relation $R$ is :
  34. The contrapositive of the statement "If it is raining, then I will not come", is
  35. If the Boolean expression $(p\oplus q)\wedge(\sim p\odot q)$ is equivalent to $p\wedge q$, where $\oplus,\odot\in\{\wedge,\vee\}$, then the ordered pair $(\oplus,\odot)$ …
  36. The statement $(p\to q)\to\left((\sim p\to q)\to q\right)$ is :
  37. The number of values of $r\in\{p,q,{\sim}p,{\sim}q\}$ for which $\left((p\wedge q)\Rightarrow(r\vee q)\right)\wedge\left((p\wedge r)\Rightarrow q\right)$ is a tautology …
  38. Consider: S1: $(p\Rightarrow q)\vee(p\wedge\sim q)$ is a tautology. S2: $(\sim p\Rightarrow\sim q)\wedge(\sim p\vee q)$ is a contradiction. Then
  39. Let $S=\mathbb N\cup\{0\}$. Define a relation $R$ from $S$ to $\mathbb R$ by : $R=\left\{(x,y):\log_ey=x\log_e\left(\frac25\right),x\in S,y\in\mathbb R\right\}$. Then …
  40. Let $S=\{a+b\sqrt{2}: a,b\in\mathbb{Z}\}$, $T_1=\{(-1+\sqrt{2})^n: n\in\mathbb{N}\}$, and $T_2=\{(1+\sqrt{2})^n: n\in\mathbb{N}\}$. Then which of the following …
  41. 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 …
  42. Let $p$ and $q$ be two statements. Then ${\sim}\left(p\wedge(p\to{\sim}q)\right)$ is equivalent to
  43. The minimum number of elements that must be added to the relation $R=\{(a,b),(b,c),(b,d)\}$ on the set $\{a,b,c,d\}$ so that it is an equivalence relation is
  44. The relation $R=\{(a,b): \gcd(a,b)=1,\ 2a\neq b,\ a,b\in\mathbb Z\}$ is:
  45. Let $S=\{1,2,3,4,5,6\}$. Then the number of one-one functions $f:S\to P(S)$, where $P(S)$ denotes the power set of $S$, such that $f(n)\subset f(m)$ where $n<m$ is …
  46. Let $R$ be a relation on $\mathbb N\times\mathbb N$ defined by $(a,b)R(c,d)$ if and only if $ad(b-c)=bc(a-d)$. Then $R$ is
  47. Let $S=\left\{\alpha:\log_2\left(9^{2\alpha-4}+13\right)-\log_2\left(\frac52\cdot3^{2\alpha-4}+1\right)=2\right\}$. Then the maximum value of $\beta$ for which the …
  48. The Boolean expression $((p\wedge q)\vee(p\vee\sim q))\wedge(\sim p\wedge\sim q)$ is equivalent to
  49. Let $S=\{1,2,3,\dots,10\}$. Consider the set $$X=\{R: R\text{ is an equivalence relation on the set }S\text{ such that }R\text{ has exactly }42\text{ elements}\}.$$ Then …
  50. The logical statement $\left[\sim(\sim p\vee q)\vee(p\wedge r)\right]\wedge(\sim q\wedge r)$ is equivalent to :

Other chapters