Given: Total cost = ₹ 15,000
Direct material = ₹ 5,000
Factory overhead is 150% of direct labour cost.
Let direct labour cost be ₹ X.
Then, factory overhead = 150% of X = 1.5X.
Total cost = Direct Material + Direct Labour + Factory Overhead
So, ₹ 15,000 = ₹ 5,000 + X + 1.5X
Combine terms: ₹ 15,000 = ₹ 5,000 + 2.5X
So, 2.5X = ₹ 10,000
Therefore, X = ₹ 4,000
Oops! But this suggests ₹ 4,000 — wait! Let’s double-check:
₹ 5,000 (Material) + X (Labour) + 1.5X (Overhead) = 15,000
So: 5,000 + 2.5X = 15,000 → 2.5X = 10,000 → X = 4,000
So the amount of direct labour charged is ₹ 4,000 — therefore the correct answer is (B) ₹ 4,000.
(Note: The original options show ₹ 4,000 as (B), so we choose that.)
Correct Answer: (B) ₹ 4,000
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 \(P,O,Q\).