Let $f$ be a differentiable function satisfying $f(x) = 1 - 2x + \int\limits_0^x e^{(x-t)} f(t)\,dt$, $x \in \mathbb{R}$ and let

$g(x) = \int\limits_0^x (f(t) + 2)^{15} (t - 4)^6 (t + 12)^{17}\,dt$, $x \in \mathbb{R}$.

If $p$ and $q$ are respectively the points of local minima and local maxima of $g$, then the value of $|p+q|$ is equal to ________.

Which one of the following is not a measurable quantity?

The mean free path of a molecule of diameter $5 \times 10^{-10}$ m at the temperature $41^{\circ}$C and pressure $1.38 \times 10^5$ Pa, is given as ________ m. (Given $k_B = 1.38 \times 10^{-23}$ J/K).

The time period of a simple harmonic oscillator is $T = 2\pi \sqrt{\frac{k}{m}}$. Measured value of mass $(m)$ of the object is 10 g with an accuracy of 10 mg and time for 50 oscillations of the spring is found to be 60 s using a watch of 2 s resolution. Percentage error in determination of spring constant $(k)$ is ________%.