As per the Coal Mines Regulations (CMR), the minimum quantity of air required for ventilation in a coal mine panel is determined based on the number of persons employed in the largest shift and the production of the panel. CMR typically requires a minimum of 2.5 m$^3$/minute per person in the largest shift, plus an additional 2.5 m$^3$/minute per tonne of daily coal production. The largest shift has 130 persons, so the air required for personnel is $130 \times 2.5 = 325$ m$^3$/minute. The panel produces 400 tonnes per day, so the air required for production is $400 \times 2.5 = 1000$ m$^3$/minute. However, CMR also sets a minimum baseline for air quantity, often around 1000 m$^3$/minute for such panels, regardless of the calculated value. Here, the production-based requirement (1000 m$^3$/minute) dominates, and considering standard CMR guidelines for a panel of this size, 1000 m$^3$/minute is the minimum required.
Thus, the correct answer is 1000.