List of top Mathematics Questions on cartesian products of sets

Let $S =\{1,2,3,5,7,10,11\}$ The number of non-empty subsets of $S$ that have the sum of all elements a multiple of 3 , is _____
The Cartesian form of the curve given by \( x = \frac{a}{2}\left(t + \frac{1}{t}\right) \), \( y = \frac{a}{2}\left(t - \frac{1}{t}\right) \), where \( t \) is a parameter, is:
If the equations \( x = t^2 + t + 1, \quad y = t^2 - t + 1 \) represent a curve \( C \) with parameter \( t \), then the Cartesian equation of \( C \) is:

Let \(S ={  (\begin{matrix}   -1 & 0 \\   a & b \end{matrix}), a,b, ∈(1,2,3,.....100)}\) and 
let \(T_n = {A ∈ S : A^{n(n + 1)} = I}. \)
Then the number of elements in \(\bigcap_{n=1}^{100}\) \(T_n \) is

If \( A = \{1, 2, 5, 6\} \) and \( B = \{1, 2, 3\} \), then \( A \times B \cap B \times A \) is equal to:
If the function $f: R \rightarrow R$ is defined by $f(x)=|x|(x-\sin x)$, then which of the following statements is TRUE?
What is the least value of k such that the function x$^2$ + kx + 1 is strictly increasing on (1,2)
Let $A=\{1,2,3,5,8,9\}$ Then the number of possible functions $f: A \rightarrow A$ such that $f(m \cdot n)=f(m) \cdot f(n)$ for every $m, n \in A$ with $m \cdot n \in A$ is equal to______
The cardinality of the set P(P(P($\phi$))) is [P(A) represents power set of the set A]