In a wire of cross-section radius $r,$ free electrons travel with drift velocity $v$ when a current $I$ flows through the wire. What is the current in another wire of half the radius and of the same material when the drift velocity is $2v$?

Nylon $2-$ Nylon $6$ is

The coefficient of $t^{50}$ in $(1 + t^2)^{25} (1 + t^{25}) (1 + t^{40}) (1 + t^{45}) (1 + t^{47})$ is

$A$ ray of light is incident normally on a glass slab of thickness $5 ~cm$ and refractive index $1.6$. The time taken by a ray to travel from the source to the surface of the slab is the same as the time taken to travel through the glass slab. The distance of the source from the surface is (in $~cm$)

$\begin{aligned} & f(x, y)=2(x-y)^2-x^4-y^4 \\ & \left|\left(f_{x x} f_{y y}-f_{x y}^2\right)\right|_{(0,0)} \end{aligned}$

The effect due to a uniform magnetic field on a freely suspended magnetic needle is as follows: