Bird flu is caused by

On closing an open organ pipe from one end,it is noticed that the frequency of the third harmonic is $50 ~Hz$ more than the fundamental frequency of vibration in the open organ pipe. The fundamental frequency of the open organ pipe is (in $~Hz$)

If the straight line $y=mx+c$ is parallel to the axis of the parabola $y^2=lx$ and intersects the parabola at $\left(\frac{c^2}{8}, c\right)$,then the length of the latus rectum is

If $b+c=3a$,then $\cot \frac{B}{2} \cot \frac{C}{2}$ is equal to :

The principal value of ${\sin ^{ - 1}}\left( { - \frac{1}{2}} \right)$ is

$A$ spherical surface of radius of curvature $R$ separates air (refractive index $1.0$) from glass (refractive index $1.5$). The centre of curvature is in the glass. $A$ point object $P$ placed in air is found to have a real image $Q$ in the glass. The line $PQ$ cuts the surface at the point $O$,and $PO = OQ$. The distance $PO$ is equal to: (in $,R$)