JEE Math Practice Question

Let S = {($$\lambda $$, $$\mu $$) $$ \in $$ R $$ \times $$ R : f(t) = (|$$\lambda $$| e|t| $$-$$ $$\mu $$). sin (2|t|), t $$ \in $$ R, is a differentiable function}. Then S is a subset of :

1. A.R $$ \times $$ [0, $$\infty $$)
2. B.[0, $$\infty $$) $$ \times $$ R
3. C.R $$ \times $$ ($$-$$ $$\infty $$, 0)
4. D.($$-$$ $$\infty $$, 0) $$ \times $$ R