Ultraviolet radiations of different frequencies v₁ and v₂ are incident on two photosensitive materials having work functions W₁ and W₂ (W₁ > W₂) respectively. The kinetic energy of the emitted electrons is same in both the cases. Which one of the two radiations will be of higher frequency? 

Given, the kinetic energy of the emitted electrons is same in both cases.

Kinetic energy is given by, 
                           $\mathrm{K}.\mathrm{E}. = \mathrm{hv}-\mathrm{\varphi }$

$\mathrm{\nu }$ is the frequency of radiation and $\mathrm{\varphi }$ is the work function of materials.
Therefore, as per given, 

$$\begin{gathered} \mathrm{K}.\mathrm{E}. = {\mathrm{hv}}_1-{\mathrm{W}}_1 \\ \Rightarrow {\mathrm{hv}}_1 = \mathrm{K}.\mathrm{E}. + {\mathrm{W}}_1 \end{gathered}$$

and,
$$\begin{gathered} \mathrm{K}.\mathrm{E}. = {\mathrm{hv}}_2-{\mathrm{W}}_2 \\ \Rightarrow {\mathrm{hv}}_2 = \mathrm{K}.\mathrm{E}.+{\mathrm{W}}_2 \end{gathered}$$

 $G\mathrm{iven} \mathrm{that}, {\mathrm{W}}_1 > {\mathrm{W}}_2$ 
Thus,    ${\mathrm{v}}_1 > {\mathrm{v}}_2.$