Compound $\mathbf{I}$ undergoes hydroboration-oxidation reaction with $\left(\mathrm{BH}_3\right)_2$ followed by treatment with $\mathrm{H}_2 \mathrm{O}_2$ and aqueous NaOH to produce another compound II, which upon oxidation with $\mathrm{CrO}_3$ gives 2,3-dimethyl-cyclohexanone as the product. What is the structure of $\mathbf{I}$ ?

The work done when one mole of an ideal gas expands at constant temperature $T$ from volume $V$ to $2 V$ (in two equal steps of volume in a linear fashion) is $\frac{7}{12} R T$. How much more work would be done by the gas if it expands in three equal steps?

[ $R$ is the universal gas constant]

At a particular temperature, the magnitude of the rate constant of a reaction is $5 \times 10^{-5}$ and the unit of the pre-exponential factor of the Arrhenius equation for this reaction is $\mathrm{mol} \mathrm{L}^{-1} \mathrm{~min}^{-1}$. Which of the following plots is correct for this reaction?

$\left[\right.$ Note: $[\mathrm{R}]_0$ is the initial concentration and $t_{1 / 2}$ is the half-life of the reaction $]$

What is the time period of revolution of an electron in the fourth Bohr orbit of $\mathrm{He}^{+}$?

[Bohr radius $=52.9$ picometers, mass of an electron $=9.11 \times 10^{-31} \mathrm{~kg}$, Planck's constant $=6.626 \times 10^{-34} \mathrm{Js}$ ]