1.In a new system of units, speed of light $c$, gravitational constant $G$, and Planck's constant $h$ are taken as fundamental units. Find dimensions of Mass, Length, and Time in this system.
2.A physical quantity $P = \frac{a^3 b^2}{\sqrt{c} d}$. If relative errors in $a, b, c, d$ are $1\%, 3\%, 4\%, 2\%$, find maximum percentage error in $P$.
3.The main scale of a Vernier Calliper has $1\text{ mm}$ divisions. $10$ divisions of Vernier scale coincide with $9$ main scale divisions. Find its least count.
4.A screw gauge has pitch $0.5\text{ mm}$ and $50$ circular divisions. Find least count. If zero mark lies 2 divisions below main line, find zero error.
