The equation of motion of a damped oscillator is given by $m \frac{d^2 x}{d t^2}+b \frac{d x}{d t}+k x=0$. The dimensional formula of $\frac{b}{\sqrt{k m}}$ is

A physical quantity $X$ is given by $X=\frac{2 k^3 l^2}{m \sqrt{n}}$. The percentage errors in the measurements of $k, l, m$ and $n$ are $1 \%, 2 \%, 3 \%$ and $4 \%$ respectively. The value of $X$ is uncertain by

The number of significant figures in the measurement of a length 0.079000 m is

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