If in a $\triangle ABC$,$r_1 < r_2 < r_3$,then:

$A$ $\xrightarrow{\Delta} B + C_{(gas)}$ $\xrightarrow{Ca(OH)_2} D_{(milky)} + H_2O$ $\xrightarrow{C_{(gas)}} E$. Then the incorrect statement is:

Which of the following transitions in a hydrogen atom emits a photon of the highest frequency?

Work done to increase the temperature of one mole of an ideal gas by $30^{\circ} C$,if it is expanding under the condition $V \propto T^{2/3}$ is,$(R = 8.314 \ J/mol \cdot K)$ (in $J$)

The balancing length for a cell is $560 \, cm$ in a potentiometer experiment. When an external resistance of $10 \, \Omega$ is connected in parallel to the cell, the balancing length changes by $60 \, cm$. The internal resistance of the cell in ohms is:

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by $f(x)=x-[x]$ and $g(x)=[x]$ for $x \in R$,where $[x]$ is the greatest integer not exceeding $x$,then for every $x \in R, f(g(x))$ is equal to