When concentrated ${H_2SO_4}$ reacts with $X$ at a temperature of $160-170 \, ^\circ C$,ethylene is obtained. What is $X$?

For the reaction $N_{2(g)} + O_{2(g)} \rightleftharpoons 2NO_{(g)}$,the equilibrium constant $(K_c)$ at temperature $T$ is $4 \times 10^{-4}$. What is the value of $K_c$ for the reaction $NO_{(g)} \rightleftharpoons 1/2 N_{2(g)} + 1/2 O_{2(g)}$ at the same temperature?

The central fringe of the interference pattern produced by light of wavelength $6000 \, \mathring{A}$ is found to shift to the position of the $4^{th}$ bright fringe after a glass plate of refractive index $1.5$ is introduced. The thickness of the glass plate would be ........ $\mu m$.

Two objects of masses $200 \text{ g}$ and $500 \text{ g}$ possess velocities $10 \hat{i} \text{ m/s}$ and $(3 \hat{i} + 5 \hat{j}) \text{ m/s}$ respectively. The velocity of their centre of mass in $\text{m/s}$ is:

$A$ uniform rope of length $L$ and mass $m_1$ hangs vertically from a rigid support. $A$ block of mass $m_2$ is attached to the free end of the rope. $A$ transverse pulse of wavelength $\lambda_1$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is $\lambda_2$. The ratio $\lambda_2/\lambda_1$ is

The solubility of barium iodate in an aqueous solution prepared by mixing $200 \ mL$ of $0.010 \ M$ barium nitrate with $100 \ mL$ of $0.10 M$ sodium iodate is $X \times 10^{-6} mol dm ^{-3}$. The value of $X$ is $.....$
Use: Solubility product constant $\left(K_{ sp }\right)$ of barium iodate $=1.58 \times 10^{-9}$