In a certain system of units,one unit of mass is $50 \ g$,one unit of length is $10 \ cm$,and one unit of time is $5 \ s$. Then,in this system,$1$ unit of pressure equals to :-

$1$ joule of energy is to be converted into a new system of units in which length is measured in $10 \,m$,mass in $10 \,kg$,and time in $1 \,minute$. The numerical value of $1 \,J$ in the new system is:

If energy $(E)$,velocity $(V)$,and time $(T)$ are chosen as the fundamental quantities,the dimensional formula of surface tension will be

If velocity of light $c$,Planck's constant $h$,and gravitational constant $G$ are taken as fundamental quantities,then express time in terms of dimensions of these quantities.

The efficiency of an engine is given by $\eta = \frac{\alpha \beta}{\sin \theta} \cdot \log_{e} \frac{\beta x}{kT}$,where $\alpha$ and $\beta$ are constants. If $T$ is the absolute temperature,$k$ is the Boltzmann constant,$\theta$ is angular displacement,and $x$ is distance,then the incorrect statement is:

The equation of a stationary wave is given by $y = 2a \sin \left( \frac{2 \pi nt}{\lambda} \right) \cos \left( \frac{2 \pi x}{\lambda} \right)$. Which of the following statements is $NOT$ correct?