Which of the following pairs is mismatched?

If Rolle's theorem holds for the function $f(x) = 2x^3 + bx^2 + cx$ on the interval $x \in [-1, 1]$ at the point $x = \frac{1}{2}$,then $(2b + c)$ is equal to:

$A$ $TV$ transmitting antenna is $128 \ m$ tall. If the receiving antenna is at the ground level,the maximum distance between them for satisfactory communication in line-of-sight mode is (radius of the earth $R_e = 6.4 \times 10^6 \ m$):

An electron is projected along the axis of a circular conductor carrying current $I$. The electron will experience:

An alloy of gold and copper crystallizes in a cubic lattice in which the gold atoms occupy the lattice points at the corners of the cube and copper atoms occupy the centers of each of the cube faces. Determine the formula of this compound.

Let $A, B$ and $C$ be three points in a plane. The locus of a point $P$ moving such that $PA^2 + PB^2 = 2PC^2$ is a