Can error be completely eliminated?

The percentage error in the measurement of a physical quantity $m$ given by $m = \pi \tan \theta$ is minimum when $\theta = \dots \dots \dots \dots \dots ^\circ$ (Assume that the error in $\theta$ remains constant).

The relative error in the determination of the surface area of a sphere is $\alpha$. Then the relative error in the determination of its volume is

The resistance $R = \frac{V}{I}$ where $V = (100 \pm 5) \text{ V}$ and $I = (10 \pm 0.2) \text{ A}$. The percentage error in $R$ is: (in $\%$)

$A$ person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is $\delta T = 0.01 \ s$ and he measures the depth of the well to be $L = 20 \ m$. Take the acceleration due to gravity $g = 10 \ ms^{-2}$ and the velocity of sound $v = 300 \ ms^{-1}$. Then the fractional error in the measurement,$\delta L / L$,is closest to: (in $\%$)

The dimensions of a cone are measured using a scale with a least count of $2 \text{ mm}$. The diameter of the base and the height are both measured to be $20.0 \text{ cm}$. The maximum percentage error in the determination of the volume is. . . . .