$A$ ray of light along $x+\sqrt{3}y=\sqrt{3}$ gets reflected upon reaching the $x$-axis. The equation of the reflected ray is:

$A$ whistle revolves in a circle with an angular speed of $20\, rad/s$ using a string of length $50\, cm$. If the frequency of sound from the whistle is $385\, Hz$,then what is the minimum frequency heard by an observer,who is far away from the centre in the same plane? (Speed of sound is $340\, m/s$)

The radiation emitted by a star $A$ is $10000$ times that of the sun. If the surface temperatures of the sun and the star $A$ are $6000 \ K$ and $2000 \ K$ respectively,the ratio of the radii of the star $A$ and the sun is : (in $: 1$)

The distance of the point $(1, 1, 9)$ from the point of intersection of the line $\frac{x-3}{1} = \frac{y-4}{2} = \frac{z-5}{2}$ and the plane $x+y+z=17$ is

For a ray of light,the critical angle is minimum when it travels from

With a standard rectangular bar magnet,the time period of a vibration magnetometer is $4 ~s$. The bar magnet is cut parallel to its length into four equal pieces. The time period of the vibration magnetometer when one piece is used (in seconds) (bar magnet breadth is small) is