Embibe Experts Solutions for Chapter: Physical World and Measurement, Exercise 11: Exercise (Assertion & Reason)

Dimensional formula of $∆\mathrm{Q}$ heat supplied to the system is given by:

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

Dimensional formula of angular momentum is :

Planck's constant $\left(h\right)$, speed of light in vacuum $\left(c\right)$ and Newton's gravitational constant $\left(G\right)$ are three fundamental constants. Which of the following combinations of these has the dimension of length? 

Suppose the refractive index $\text{'}\mathrm{\mu }\text{'}$ is given as :$\mathrm{\mu }=\mathrm{A}+\frac{\mathrm{B}}{{\mathrm{\lambda }}^2}$, where$\mathrm{A}$ and $\mathrm{B}$ are constants and $\mathrm{\lambda }$ is wavelength, then dimensions of $\mathrm{B}$ are same as that of :

If $\mathrm{E}, \mathrm{M}, \mathrm{L}$ and $\mathrm{G}$ denote energy, mass, angular momentum and Gravitational constant respectively, then quantity ${\mathrm{E}}^2{\mathrm{L}}^2/{\mathrm{M}}^5{\mathrm{G}}^2$ has dimensions of :

In a vernier callipers, one main scale division is $x cm$ and $n$ divisions of the vernier scale coincide with $(n-1)$ divisions of the main scale. The least count $(in cm)$ of the callipers is 

Which of the following units denotes the dimensions$\left[\raisebox{1ex}{$M{L}^2$}\!\left/ \!\raisebox{-1ex}{$Q^2$}\right.\right]$ , where $Q$ denotes the electric charge?