A

To find the heat developed in an electric wire, we use the formula:
Q = I^2 R t
where:
Q = heat developed (in Joules)
I = current (in Amperes)
R = resistance (in Ohms)
t = time (in seconds)

If we want to express the heat in calories, we can convert Joules to calories using the conversion factor:
1 cal = 4.18 J
Thus:
Q (in cal) = \frac{I^2 R t}{4.18}

However, matching this to the options provided, we need to account for the given constant in the options, which appears to be a multiplicative factor of 4.2 instead of 4.18. Hence:
Q = \frac{I^2 R t}{4.2} cal
Based on this, option (a) \frac{I^2 R t}{4.2} is the correct one.
Therefore, A.