In the following combination of logic gates, the output $Y$ can be written in the terms of inputs $A$ and B as

If a black body at 400 K surrounded by atmosphere at 300 K has rate of cooling ' $\mathrm{R}_0$ ', the same body at 900 K , surrounded by same atmosphere, will have rate of cooling nearly

The electric field intensity on the surface of a solid charged sphere of radius $\mathbf{r}$ and volume charge density $\sigma$ is ( $\varepsilon_0=$ permittivity of free space)

Two strings ' X ' and ' Y ' of a guitar produces a beat frequency of 6 Hz . When the tension of the string ' Y ' is increased, the beat frequency is found to be 4 Hz . If the frequency of string ' X ' is 300 Hz , then the original frequency of string ' Y ' is