When 81.0 g of aluminium is allowed to react with 128.0 g of oxygen gas, the mass of aluminium oxide produced in grams is ________ . (Nearest integer)

Given :

Molar mass of Al is $27.0 \mathrm{~g} \mathrm{~mol}^{-1}$

Molar mass of O is $16.0 \mathrm{~g} \mathrm{~mol}^{-1}$

Consider the following sequence of reactions.

Total number of $\mathrm{sp}^3$ hybridised carbon atoms in the major product C formed is _________.

A compound ' $\mathrm{X}^{\prime}$ absorbs 2 moles of hydrogen and ' X ' upon oxidation with $\mathrm{KMnO}_4 \mid \mathrm{H}^{+}$ gives

The total number of $\sigma$ bonds present in the compound ' $X^{\prime}$ ' is __________.

If $\mathrm{I}=\int_0^{\frac{\pi}{2}} \frac{\sin ^{\frac{3}{2}} x}{\sin ^{\frac{3}{2}} x+\cos ^{\frac{3}{2}} x} \mathrm{~d} x$, then $\int_0^{2I} \frac{x \sin x \cos x}{\sin ^4 x+\cos ^4 x} \mathrm{~d} x$ equals :