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Explanation:

Since cumulative time spent per year on research and teaching activities is the same for all professors, we’ll directly take the percentages for calculations.

Research efficiency of Prof. Arithmetic = (2 + 3 + 3)/(70 + 50 + 60) = 2/45

Research efficiency of Prof. Algebra = (3 + 2 + 3)/(35 + 25 + 40) = 2/25

Research efficiency of Prof. Geometry = (3 + 1 + 4)/(75 + 25 + 20) = 2/30
 
Research efficiency of Prof. Calculus = (3 + 3 + 2)/(55 + 55 + 40) = 2/37.5

∴ The least efficient is Prof. Arithmetic.

Hence, option (a).

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