$A$ thin uniform rod of length $l$ and mass $m$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega$. Its centre of mass rises to a maximum height of:

Among $Ni(CO)_4$,$[Ni(CN)_4]^{2-}$ and $[NiCl_4]^{2-}$,which of the following statements is correct regarding their magnetic properties?

$A$ parallel plate capacitor of capacity $C_0$ is charged to a potential $V_0$. $(i)$ The energy stored in the capacitor when the battery is disconnected and the plate separation is doubled is $E_1$. (ii) The energy stored in the capacitor when the charging battery is kept connected and the separation between the capacitor plates is doubled is $E_2$. Then,the value of $E_1 / E_2$ is:

When ethanol is reacted with $PCl_5$,it gives $A$,$POCl_3$,and $HCl$. The reaction of $A$ with silver nitrite $(AgNO_2)$ gives the major product $(B)$ and $AgCl$. What are $A$ and $B$ respectively?

When a tuning fork of frequency $341 \ Hz$ is sounded with another tuning fork,six beats per second are heard. When the second tuning fork is loaded with wax and sounded with the first tuning fork,the number of beats is two per second. The natural frequency of the second tuning fork is (in $Hz$)

Which of the following elements shows polymorphism?