The correct increasing order of C - H(A), C - 0 (B), C = O(C) and C = N (D) bonds in terms of covalent bond length is :

The covalent bond length depends mainly on two factors:
  • bond order (greater bond order → shorter bond)
  • size of the atoms involved (bond with a smaller atom is shorter).

Typical experimental bond lengths (in Å) are frequently quoted as

$$\begin{aligned} \text{C-H (single)} & : 1.09 \; \text{Å} \\[2pt] \text{C}\equiv\text{N (triple)} & : 1.16 \; \text{Å} \\[2pt] \text{C}=\text{O (double)} & : 1.21 \; \text{Å} \\[2pt] \text{C-O (single)} & : 1.43 \; \text{Å} \end{aligned}$$

Arranging these values from the shortest bond (smallest length) to the longest bond (largest length):

$$\text{C-H} \lt \text{C}\equiv\text{N} \lt \text{C}=\text{O} \lt \text{C-O}$$

Using the labels given in the question:
  A = C-H, D = C≡N, C = C=O, B = C-O

The increasing order of covalent bond length is therefore
$$A \lt D \lt C \lt B$$

Hence the correct option is Option A.