Monocyclic compounds $\text{P , Q , R}$ and $S$ are the major products formed in the reaction sequences given below.
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The product having the highest number of unsaturated carbon atom$(s)$ is-

The displacements of two particles of same mass executing $SHM$ are represented by the equations $x_1 = 4 \sin \left(10 t + \frac{\pi}{6}\right)$ and $x_2 = 5 \cos (\omega t)$. The value of $\omega$ for which the energies of both the particles remain same is (in $\text{ unit}$)

$\sum_{n=1}^{\infty} \frac{2n^2+n+1}{n!}$ is equal to

Find the oxidation state of sodium in $Na_{2}O_{2}$.

Cycas leaflets are

What is the correct order of solubility in water for $He, Ne, Ar, Kr, Xe$?