Light ray incident along a vector $\overrightarrow{A O}(\overrightarrow{A O}=2 \hat{i}-3 \hat{j})$ emerges out along vector $\overrightarrow{O B}(\overrightarrow{O B}=C \hat{i}-4 \hat{j})$ as shown in the figure below. The value of $C$ is $\_\_\_\_$ .

$K_1$ and $K_2$ be the maximum kinetic energies of photoelectrons emitted from a surface of a given material for the light of wavelength $\lambda_1$ and $\lambda_2$, respectively. If $\lambda_1=2 \lambda_2$ then the work function of material is given by :

Two radioactive substances A and B of mass numbers 200 and 212 respectively, shows spontaneous $\alpha$-decay with same $Q$ value of 1 MeV . The ratio of energies of $\alpha$-rays produced by A and B is $\_\_\_\_$ .

$$ \text { The output } Y \text { for the given inputs } A \text { and } B \text { to the circuit is : } $$