Concept:
Timber joints are used to connect wooden members in construction.
Lengthening joints are specifically used to increase the length of timber members by joining two pieces end-to-end.
Common lengthening joints include:
• Lapped joints
• Fished joints
• Scarf joints
Step 1: Analyze Cogged joint.
Cogged joints are mainly used for connecting beams and joists at right angles.
Hence, statement A is incorrect.
Step 2: Analyze Lapped joint.
Lapped joints are used to join timber pieces for extending length.
Hence, statement B is correct.
Step 3: Analyze Fished joint.
Fished joints use side plates (fish plates) to strengthen and lengthen timber members.
Hence, statement C is correct.
Step 4: Analyze Dove tailed joint.
Dovetail joints are mainly used in furniture and corner joints.
Hence, statement D is incorrect.
Step 5: Analyze Mitred joint.
Mitred joints are corner joints generally used for frames and finishing work.
Hence, statement E is incorrect.
Step 6: Choose the correct option.
The lengthening joints are:
\[
\text{Lapped joint and Fished joint}
\]
Therefore, the correct answer is:
\[
{\text{(B) B and C}}
\]