List of top Mathematics Questions on cartesian products of sets asked in KEAM

Let \(A\) be the set of odd integers in \([0,10]\) and let \(B\) be the set of prime numbers in \([0,10]\). If \[ R=\{(a,b)\in A\times B:\ a+b \text{ is odd}\}, \] then \(n(R)\) is equal to:

Let $A$ and $B$ be two sets of having 3 and 2 elements respectively. Then the number of subsets of $A \times B$ having at least three elements is

Let $X = \{a,b,c,d,e,f\}$ and $Y = \{7,8,9,10,11\}$ be two sets. Which one of the following is true?

Let $A=\{1,2,3,4\}$ and $B=\{7,8,3,4\}$. Then the number of elements common to both $A \times B$ and $B \times A$ is ________.

If two sets A and B are having 11 elements in common, then the number of elements common to $A\times B$ and $B\times A$ is:

Let \( A, B, C \) be any three finite sets. If \( n(A \times B) = 160\), \( n(B \times C) = 80 \) and \( n(C \times A) = 200\), then \( n(A) = \)