H C Verma Solutions for Chapter: Introduction to Physics, Exercise 2: OBJECTIVE I

Which of the following sets cannot enter into the list of fundamental quantities in any system of units?

A physical quantity is measured and the result is expressed as $nu$, where $u$ is the unit used and $n$ is the numerical value. If the result is expressed in various units, then

Suppose a quantity, $x$ can be dimensionally represented in terms of $\mathrm{M}$, $\mathrm{L}$ and $\mathrm{T}$ that is, $\left[x\right]={\mathrm{M}}^{\mathrm{a}}{\mathrm{L}}^{\mathrm{b}}{\mathrm{T}}^{\mathrm{c}}$. The quantity mass

The dimensionless quantity

A unitless quantity

$\int \frac{dx}{\sqrt{2ax-x^2}}=a^{\mathrm{n}}{\sin }^{-1}\left[\frac{x}{a}-1\right]$

Find the value of $n$. (Solve using dimensional analysis)