JEE Main
Mathematics
Sets and Relations
Previous Years Questions

Let $$P(S)$$ denote the power set of $$S=\{1,2,3, \ldots ., 10\}$$. Define the relations $$R_{1}$$ and $$R_{2}$$ on $$P(S)$$ as $$\mathrm{AR}_{1} \mat... Let$$R$$be a relation on$$1\mathbb{R}$$, given by$$R=\{(a, b): 3 a-3 b+\sqrt{7}$$is an irrational number$$\}$$. Then$$R$$is Among the relations \mathrm{S}=\left\{(\mathrm{a}, \mathrm{b}): \mathrm{a}, \mathrm{b} \in \mathbb{R}-\{0\}, 2+\frac{\mathrm{a}}{\mathrm{b}}>0\right... Let$$\mathrm{R}$$be a relation on$$\mathrm{N} \times \mathbb{N}$$defined by$$(a, b) ~\mathrm{R}~(c, d)$$if and only if$$a d(b-c)=b c(a-d)$$. Th... The minimum number of elements that must be added to the relation$$\quad \mathrm{R}=\{(\mathrm{a}, \mathrm{b}),(\mathrm{b}, \mathrm{c})\}$$on the se... Let R be a relation defined on$$\mathbb{N}$$as$$a\mathrm{R}b$$if$$2a+3b$$is a multiple of$$5,a,b\in \mathbb{N}$$. Then R is The relation$$\mathrm{R = \{ (a,b):\gcd (a,b) = 1,2a \ne b,a,b \in \mathbb{Z}\}}$$is : Let R be a relation from the set$$\{1,2,3, \ldots, 60\}$$to itself such that$$R=\{(a, b): b=p q$$, where$$p, q \geqslant 3$$are prime numbers}. T...$$ \text { Let } S=\left\{x \in[-6,3]-\{-2,2\}: \frac{|x+3|-1}{|x|-2} \geq 0\right\} \text { and } T=\left\{x \in \mathbb{Z}: x^{2}-7|x|+9 \leq 0\...
For $$\alpha \in \mathbf{N}$$, consider a relation $$\mathrm{R}$$ on $$\mathbf{N}$$ given by $$\mathrm{R}=\{(x, y): 3 x+\alpha y$$ is a multiple of 7\$...
Let $$R_{1}$$ and $$R_{2}$$ be two relations defined on $$\mathbb{R}$$ by $$a \,R_{1} \,b \Leftrightarrow a b \geq 0$$ and $$a \,R_{2} \,b \Leftrighta... Let a set A = A1$$\cup$$A2$$\cup$$.....$$\cup$$Ak, where Ai$$\cap$$Aj =$$\phi$$for i$$\ne$$j, 1$$\le$$j, j$$\le$$k. Define the relatio... Let R1 = {(a, b)$$\in$$N$$\times$$N : |a$$-$$b|$$\le$$13} and R2 = {(a, b)$$\in$$N$$\times$$N : |a$$-$$b|$$\ne$$13}. Then on N :... Let$$A = \{ x \in R:|x + 1|
Let A, B and C be sets such that $$\phi$$ $$\ne$$ A $$\cap$$ B $$\subseteq$$ C. Then which of the following statements is not true ?
Two newspapers A and B are published in a city. It is known that 25% of the city populations reads A and 20% reads B while 8% reads both A and B. Furt...
Let Z be the set of integers. If A = {x $$\in$$ Z : 2(x + 2) (x2 $$-$$ 5x + 6) = 1} and B = {x $$\in$$ Z : $$-$$ 3 < 2x $$-$$ 1 < 9}, t...
Let S = {1, 2, 3, … , 100}. The number of non-empty subsets A of S such that the product of elements in A is even is :
The number of functions f from {1, 2, 3, ...., 20} onto {1, 2, 3, ...., 20} such that f(k) is a multiple of 3, whenever k is a multiple of 4, is :
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 ...
Two sets A and B are as under : A = {($$a$$, b) $$\in$$ R $$\times$$ R : |$$a$$ - 5| < 1 and |b - 5| < 1}; B = {($$a$$, b) $$\in$$ R $$\t... Let A and B be two sets containing four and two elements respectively. Then, the number of subsets of the set A \times B , each having atleast three... Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can be formed such that Y$$ \subseteq $$X, Z$$ \subseteq $$X and Y$$ \...

## Numerical

Let S = {1, 2, 3, 5, 7, 10, 11}. The smaller of non-empty subsets of S that have the sum of all elements a multiple of 3, is _____________.
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 re...
Let $$S=\{4,6,9\}$$ and $$T=\{9,10,11, \ldots, 1000\}$$. If $$A=\left\{a_{1}+a_{2}+\ldots+a_{k}: k \in \mathbf{N}, a_{1}, a_{2}, a_{3}, \ldots, a_{k}\... Let$$A=\{1,2,3,4,5,6,7\}$$and$$B=\{3,6,7,9\}$$. Then the number of elements in the set$$\{C \subseteq A: C \cap B \neq \phi\}$$is ___________.... Let$$A=\{1,2,3,4,5,6,7\}$$. Define$$B=\{T \subseteq A$$: either$$1 \notin T$$or$$2 \in T\}$$and$$C=\{T \subseteq A: T$$the sum of all the ele... Let S = {1, 2, 3, 4}. Then the number of elements in the set { f : S$$\times$$S$$\to$$S : f is onto and f (a, b) = f (b, a)$$\ge$$a$$\forall$$... Let R1 and R2 be relations on the set {1, 2, ......., 50} such that R1 = {(p, pn) : p is a prime and n$$\ge$$0 is an integer} and R2 = {(p, pn) : p ... Let A = {1, a1, a2 ....... a18, 77} be a set of integers with 1 1 2 18 1 + a2 + ...... + a18 is equal to _____________.... Let A = {n$$\in$$N : H.C.F. (n, 45) = 1} and Let B = {2k : k$$\in$${1, 2, ......., 100}}. Then the sum of all the elements of A$$\cap$$B is ____... The sum of all the elements of the set$$\{ \alpha \in \{ 1,2,.....,100\} :HCF(\alpha ,24) = 1\} $$is __________. Let A = {n$$ \in $$N: n is a 3-digit number} B = {9k + 2: k$$ \in $$N} and C = {9k +$$l$$: k$$ \in...
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