If the present units of length,time,and mass $(m, s, kg)$ are changed to $100 \; m, 100 \; s, 0.1 \; kg$,then:

In an experiment,four quantities $a, b, c,$ and $d$ are measured with percentage errors of $1\%, 2\%, 3\%,$ and $4\%$ respectively. The quantity $P$ is calculated as $P = \frac{a^3 b^2}{cd}$. The percentage error in $P$ is ........ $\%$

$A$ great physicist of this century ($P.A.M.$ Dirac) loved playing with numerical values of fundamental constants of nature. This led him to an interesting observation. Dirac found that from the basic constants of atomic physics ($c, e,$ mass of electron, mass of proton) and the gravitational constant $G$, he could arrive at a number with the dimension of time. Further, it was a very large number, its magnitude being close to the present estimate on the age of the universe ($\approx 15$ billion years). From the table of fundamental constants in this book, try to see if you too can construct this number. If its coincidence with the age of the universe were significant, what would this imply for the constancy of fundamental constants?

The number of particles crossing a unit area perpendicular to the $X$-axis in unit time is given by $n = -D \frac{n_2 - n_1}{x_2 - x_1}$,where $n_1$ and $n_2$ are the number of particles per unit volume at positions $x_1$ and $x_2$ respectively. Find the dimensions of $D$,which is known as the diffusion constant.

If $y$ represents pressure and $x$ represents velocity gradient,then the dimensions of $\frac{d^2 y}{d x^2}$ are

Given the pressure formula $P = FK$,where $F$ is force,find the dimensional formula of $K$.