If $x = at + bt^2$,where $x$ is the distance travelled by the body in kilometres while $t$ is the time in seconds,then the units of $b$ are

If the unit of force is $100\,N$,unit of length is $10\,m$ and unit of time is $100\,s$,what is the unit of mass in this system of units?

The equation of a stationary wave is $y = 2A \sin \left(\frac{2 \pi ct}{\lambda}\right) \cos \left(\frac{2 \pi x}{\lambda}\right)$. Which of the following statements is wrong?

$A$ dimensionless quantity is constructed in terms of electronic charge $e$,permittivity of free space $\varepsilon_0$,Planck's constant $h$,and speed of light $c$. If the dimensionless quantity is written as $e^\alpha \varepsilon_0^\beta h^\gamma c^\delta$ and $n$ is a non-zero integer,then $(\alpha, \beta, \gamma, \delta)$ is given by

Velocities $(V)$ and accelerations $(a)$ in two systems of units $1$ and $2$ are related as $V_2 = \frac{n}{m^2} V_1$ and $a_2 = \frac{a_1}{mn}$ respectively. Here $m$ and $n$ are constants. Dimensionally, the relations between distances ($S_1$ and $S_2$) and times ($t_1$ and $t_2$) in the two systems are respectively:

$E, m, l$ and $G$ denote energy,mass,angular momentum,and gravitational constant respectively. Then the dimensions of $\frac{El^2}{m^5G^2}$ are: