Which of the following relations can be derived using dimensional analysis?

If $C$ (the velocity of light), $h$ (Planck's constant), and $G$ (gravitational constant) are taken as fundamental quantities, then the dimensional formula of mass 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 $c$.

Consider the efficiency of Carnot's engine is given by $\eta = \frac{\alpha \beta}{\sin \theta} \log_{e} \frac{\beta x}{k T}$,where $\alpha$ and $\beta$ are constants. If $T$ is temperature,$k$ is Boltzmann constant,$\theta$ is angular displacement and $x$ has the dimensions of length. Then,choose the incorrect option.

If the dimensional formula of $(\text{Energy} \times \text{speed})$ is $[M^{a} L^{b} T^{c}]$,then $a, b,$ and $c$ are:

If $10 \ g \ cm \ s^{-1} = x \ N \ s$,then the number $x$ is