C

Step 1: The specific heat capacity is given by the formula \( C = AT \).
Step 2: To find the mean specific heat from 27ºC to 127ºC, we first find the average temperature in degrees Kelvin:
\( T_{avg} = \frac{T_1 + T_2}{2} = \frac{(27 + 273) + (127 + 273)}{2} = \frac{300 + 400}{2} = 350 K\).
The mean specific heat over this range is then calculated as:
\( C_{mean} = A \cdot T_{avg} = 350A \).
This matches with option B.
Step 3: The actual specific heat at 127ºC corresponds to temperature of 400 K:
\( C_{actual} = A \cdot (127 + 273) = A \cdot 400\).
This matches with option A.
Step 4: The graph of specific heat versus temperature is a straight line, starting at the origin and rising linearly; this corresponds to the shape shown in the provided images for option C.
Step 5: The graph of heat transferred versus temperature is quadratic, reflecting the nature of energy absorption at varying temperatures; this corresponds to option D.
Therefore, the correct match is (i) 350A, (ii) 400A, (iii) C for the graph of specific heat, and (iv) D for the graph of heat transferred.