No, the production function does not exhibit diminishing marginal returns. As the amount of labour hired increases, the marginal product of labour is constant. This violates the law of diminishing marginal returns.

The law of variable proportion shows that as we increase the quantity of only one input, keeping other inputs fixed, the total product increases at an increasing rate in the beginning, then increases at diminishing rate and after a level of output ultimately falls. The behaviour of Total product according to this law is as under:
(I) TP increases continuously from points O to A.
(iI) It increases at an increasing rate (convex shape) from O to P and at a diminishing rate (concave shape) from P to A.
(iii) TP is maximum at A and remains so upto point B.
(iv) After Point B, Total Product falls.

The behaviour of TP in different cases will be:
(i) TP increases at increasing rate.
(ii) TP increases at diminishing rate.
(iii) TP is at its maximum and constant.
(iv) TP decreases.

(i) Average Product increases as long as Marginal Product (MP)> Average Product  (AP). Alternatively, when MP > AP, AP rises.
(ii) Average Product is maximum and constant when AverageProduct (AP) = Marginal Product (MP). Alternatively, when AP = MP, AP is maximum.
(iii) average product falls when Marginal Product < Average product.
(iv) Marginal Product can be zero and negative but Average product is never zero.

Q = 5L + 2K (Given)
Q = 5 x 0 + 2 x 10
Q = 0 + 20 = 20 units.
So, the maximum possible output (Q) = 20 units