Synapsis occurs between

The solution of $\frac{dy}{dx} = (\frac{x}{y})^{-1/3}$ is

An air column in a tube $32 ~cm$ long,closed at one end,is in resonance with a tuning fork. The air column in another tube,open at both ends,of length $66 ~cm$ is in resonance with another tuning fork. When these two tuning forks are sounded together,they produce $8$ beats per second. Then the frequencies of the two tuning forks are (Consider fundamental frequencies only):

Chemical $A$ is used for water softening to remove temporary hardness. $A$ reacts with sodium carbonate to generate caustic soda. When $CO_2$ is bubbled through a solution of $A$,it turns cloudy. What is the chemical formula of $A$?

The number of radial nodes of $3s$ and $2p$ orbitals respectively are

The four distinct points $(0,0), (2,0), (0,-2)$ and $(k,-2)$ are concyclic,if $k$ is equal to