The angle of incidence at which reflected light is totally polarized for reflection from air to glass (refractive index $n$) is

The driver of a car travelling with speed $30 \,m/s$ towards a hill sounds a horn of frequency $600 \,Hz$. If the velocity of sound in air is $330 \,m/s$,the frequency of reflected sound as heard by the driver is ........ $Hz$.

The binding energy of deuteron is $2.2\,MeV$ and that of $_2^4He$ is $28\,MeV$. If two deuterons are fused to form one $_2^4He$ nucleus, then the energy released is ......... $MeV$.

Two stones of masses $m$ and $3m$ are whirled in horizontal circles,the heavier one in a radius $\left(\frac{r}{3}\right)$ and the lighter one in a radius $r$. The tangential speed of the lighter stone is '$n$' times the value of the heavier stone. When the magnitude of the centripetal force becomes equal,the value of $n$ is:

$x = \log \left( \frac{1}{y} + \sqrt{1 + \frac{1}{y^2}} \right) \Rightarrow y$ is equal to

Let $O$ be the vertex and $Q$ be any point on the parabola $x^2 = 8y$. If the point $P$ divides the line segment $OQ$ internally in the ratio $1:3$,then the locus of $P$ is: