ICAR AIEEA PG Agri-Business Management 14 July 2023 (Shift 1) Paper

Area and dimension calculation:

• Area of one carpet = $6\text{ m} \times 4\text{ m} = 24\text{ m}^2$.
  Total floor area covered by 34 carpets = $34 \times 24 = 816\text{ m}^2$.
• Let breadth of the hall be $B\text{ m}$, then length $L = (B + 10)\text{ m}$.
  $B(B + 10) = 816$
  $B^2 + 10B - 816 = 0$
  $(B + 34)(B - 24) = 0$
  Since breadth must be positive, $B = 24\text{ m}$.
• Length $L = 24 + 10 = 34\text{ m}$.

Perimeter (circumference) of a circle is given by $C = 2\pi r$.
Given $C = 40\text{ m}$:
$2 \times \pi \times r = 40$
$r = \frac{40}{2\pi} = \frac{20}{\pi} = \frac{20}{3.14159} \approx 6.366\text{ m} \approx 6.36\text{ m}$.

Option analysis:

• 6.23 m: Inaccurate approximation.
• 6.20 m: Inaccurate approximation.
• 6.28 m: Value of $2\pi$, not the radius.
• 6.36 m: Correct radius.

The average of the first $n$ natural numbers ($1, 2, 3, \dots, n$) is given by:
$\text{Average} = \frac{n + 1}{2}$
For $n = 100$:
$\text{Average} = \frac{100 + 1}{2} = \frac{101}{2} = 50.5$.

Option analysis:

• 50: Ignores the $+1$ term in median calculation.
• 50.5: Correct average of numbers 1 to 100.
• 51: Calculation error.
• 49.5: Average of numbers 0 to 99.