Sets JEE Main PYQs, 2020 to 2025

Let $A=\{1,2,3, \ldots, 10\}$ and $B=\left\{\frac{m}{n}: m, n \in A, m< n\right.$ and $\left.\operatorname{gcd}(m, n)=1\right\}$. Then $n(B)$ is equal to :

Let $A=\{n \in[100,700] \cap \mathrm{N}: n$ is neither a multiple of 3 nor a multiple of 4$\}$. Then the number of elements in $A$ is

Let $A$ and $B$ be two finite sets with $m$ and $n$ elements respectively. The total number of subsets of the set $A$ is 56 more than the total number of subsets of $B$. Then the distance of the point $P(m, n)$ from the point $Q(-2,-3)$ is :

Let $A = \{ x \in R:[x + 3] + [x + 4] \le 3\} ,$

$$B = \left\{ {x \in R:{3^x}{{\left( {\sum\limits_{r = 1}^\infty {{3 \over {{{10}^r}}}} } \right)}^{x - 3}} < {3^{ - 3x}}} \right\},$$ where [t] denotes greatest integer function. Then,