NIMCET 2024 Paper

Assume $4\mathit{x}=\mathit{\theta }$, then the equation becomes $\mathit{s}\mathit{i}\mathit{n}\mathit{\theta }=\frac{1}{2}$ and
We can shift the interval to
In the interval $\left(0,2\mathit{\pi }\right),\mathit{s}\mathit{i}\mathit{n}\mathit{\theta }=\frac{1}{2}$ has two solutions, hence in the interval , there will be 48 solutions. Hence the cardinality of the set $\mathit{C}=48$.