JEE Main 2024 — Sets and Relations Questions with Solutions

The number of elements in the set S = x , y , z : x , y , z ∈ Z , x + 2 y + 3 z = 42 , x , y , z ≥ 0 equals ________

A group of 40 students appeared in an examination of 3 subjects - Mathematics, Physics & Chemistry. It was found that a…

Let A = 1 , 2 , 3 , 4 and R = ( 1 , 2 ) , ( 2 , 3 ) , ( 1 , 4 ) be a relation on A . Let S be the equivalence relation…

Let R be a relation on Z × Z defined by ( a , b ) R ( c , d ) if and only if a d - b c is divisible by 5 . Then R is

The number of symmetric relations defined on the set { 1 , 2 , 3 , 4 } which are not reflexive is _______.

Let a relation R on N × N be defined as: (x₁, y₁ ) R (x₂, y₂ ) if and only if x₁ ≤ x₂ or y₁ ≤ y₂. Consider the two stat…

Consider the relations R 1 and R 2 defined as a R 1 b ⇔ a 2 + b 2 = 1 for all a , b , ∈ R and a , b R 2 c , d ⇔ a + d =…

Let the set S=\2,4,8,16, …, 512\ be partitioned into 3 sets A, B, C with equal number of elements such that A B C=S and…

In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130 students studi…

Let A=\2,3,6,8,9,11\ and B=\1,4,5,10,15\. Let R be a relation on A × B defined by (a, b) R(c, d) if and only if 3 a d-7…