The equation of the parabola with the focus $(3,0)$ and the directrix $x+3=0$ is:

$3.65 \ g$ of $HCl$ is dissolved in $16.2 \ g$ of water. The mole fraction of $HCl$ in the resulting solution is

The dispersive powers of the materials of two lenses forming an achromatic combination are in the ratio of $4: 3$. If the effective focal length of the two lenses is $+60 ~cm$,then the focal lengths of the lenses should be:

$A$ $1 ~N$ pendulum bob is held at an angle $\theta$ from the vertical by a $2 ~N$ horizontal force $F$ as shown in the figure. The tension in the string supporting the pendulum bob (in newton) is

If $x^2+y^2+z^2 \neq 0, \quad x=c y+b z, \quad y=a z+c x$ and $z=b x+a y$,then $a^2+b^2+c^2+2 a b c$ is equal to

$A$ ray of light refracts from medium $1$ into a thin layer of medium $2$,crosses the layer,and is incident at the critical angle on the interface between medium $2$ and $3$ as shown in the figure. If the angle of incidence of the ray is $\theta$,the value of $\theta$ is