

Step 1: Understanding the Effect of Alkyl Groups on Basicity The basicity of amines in aqueous solutions increases with the number of alkyl groups attached to the nitrogen atom. Alkyl groups are electron-donating groups, and they increase the electron density on nitrogen, making the lone pair more available to accept a proton.
Trimethylamine \((CH_3)_3N\) has three methyl groups attached to nitrogen, making it highly electron-donating and thus the most basic.
Dimethylamine \((CH_3)_2\)NH has two methyl groups, so it is also basic, but not as basic as trimethylamine.
Methylamine \((CH_3NH_2)\) has one methyl group, which donates less electron density than two or three groups.
Ammonia \((NH_3)\) has no alkyl groups, so it is the least basic.
Step 2: Arranging in Order of Basicity The increasing order of basicity is:
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).