$A$ piece of copper and another of germanium are cooled from room temperature to $80\, K$. The resistance of :

Which part of the human ear plays no role in hearing as such but is otherwise very much required?

As shown in the figure,charges $+q$ and $-q$ are placed at the vertices $B$ and $C$ of an isosceles triangle. The potential at the vertex $A$ is

When the temperature of a body increases from $T$ to $T+\Delta T$,its moment of inertia increases from $I$ to $I+\Delta I$. If $\alpha$ is the coefficient of linear expansion of the material of the body,then $\frac{\Delta I}{I}$ is (neglect higher orders of $\alpha$ ).

$\frac{d}{d x} \sin ^{-1}\left(3 x-4 x^3\right)$ is equal to

The number of solutions of the system of equations $2x + y - z = 7$,$x - 3y + 2z = 1$,and $x + 4y - 3z = 5$ is