$A$ biological catalyst is essentially

$A$ lens having focal length $f$ and aperture of diameter $d$ forms an image of intensity $I$. If the central region of the lens with diameter $\frac{d}{2}$ is covered by black paper,what will be the new focal length and intensity of the image?

The negation of the statement pattern $\sim p \vee (q \rightarrow \sim r)$ is

$A$ source of sound of frequency $640 ~Hz$ is moving at a velocity of $\frac{100}{3} ~m/s$ along a road,and is at an instant $30 ~m$ away from a point $A$ on the road (as shown in figure). $A$ person standing at $O$,$40 ~m$ away from the road,hears sound of apparent frequency $v^{\prime}$. The value of $v^{\prime}$ is (velocity of sound $= 340 ~m/s$). (in $~Hz$)

$A$ pipe closed at one end has a length of $0.8 ~m$. At its open end,a $0.5 ~m$ long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is $50 ~N$ and the speed of sound is $320 ~m/s$,the mass of the string used is: (in $~g$)

If the equilibrium constant for the reaction,$H_{2(g)} + I_{2(g)} \rightleftharpoons 2 HI_{(g)}$ is $K$,what is the equilibrium constant of $HI_{(g)} \rightleftharpoons \frac{1}{2} H_{2(g)} + \frac{1}{2} I_{2(g)}$?