Solution:The production function is 
(A) The degree of homogeneity is 1: This statement is incorrect. The degree of homogeneity is α+ß. While it may be equal to 1 (if α+ẞ=1), it is not necessarily true for any given Cobb-Douglas function unless specified.
(B) α is the output elasticity with respect to capital: This statement is correct. For a Cobb-Douglas function, the exponent of a factor (here, a for capital K) directly gives the output elasticity of that factor.
(C) It exhibits constant returns to scale: This statement is incorrect. The function exhibits constant returns to scale only if α+ẞ=1. The question does not provide this information.
(D) Marginal product of a factor = Average product of the factor: This statement is incorrect as a general principle.