
(a) iii, (b) i, (c) ii, (d) iv
To solve the problem, we need to match the traits of the Big Five personality theories (List - I) with their corresponding characteristics (List - II).
1. Understanding the Big Five Traits:
The Big Five personality traits are:
2. Matching the Traits:
We analyze each trait in List - I and match it with the correct description in List - II:
3. Verifying the Matches:
The correct matching is:
Final Answer:
The correct matching is: $\boxed{(a)-(iii), (b)-(i), (c)-(ii), (d)-(iv)}$.
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 \(P,O,Q\).