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

The equation of state of some gases can be expressed as $(P + \frac{a}{V^2}) = \frac{b\theta}{l}$,where $P$ is the pressure,$V$ is the volume,$\theta$ is the absolute temperature,and $a$ and $b$ are constants. The dimensional formula of $a$ is

In the equation $x = a + bt + ct^2$,where $x$ is in meters and $t$ is in seconds,find the units of $a, b,$ and $c$.

If the velocity of light $(c)$,gravitational constant $(G)$,and Planck's constant $(h)$ are chosen as fundamental units,then the dimensions of mass in this new system are:

An expression of energy density is given by $u = \frac{\alpha}{\beta} \sin \left(\frac{\alpha x}{k t}\right)$,where $\alpha, \beta$ are constants,$x$ is displacement,$k$ is Boltzmann constant,and $t$ is the temperature. The dimensions of $\beta$ will be.

In a nuclear power plant,the energy released depends on the mass of the uranium sample $(m)$,the length of the oscillator $(\ell)$,and the frequency $(f)$ of oscillation as $E = m^{x} \ell^{y} f^{z}$. Then,what is the value of $x + y + z$?