The characteristic of a couple, is :

ANS:E - all the above.

1. Algebraic sum of forces constituting a couple is zero": This statement is incorrect. A couple consists of two parallel forces with equal magnitudes and opposite directions. The algebraic sum of these forces is indeed zero, but it's not a defining characteristic of a couple. Instead, it's the moments of these forces that create the couple.
2. "Algebraic sum of moments of forces constituting a couple, about any point, is the same": This statement correctly describes a fundamental characteristic of a couple. Regardless of the point chosen for calculating the moments, the algebraic sum of the moments of the forces constituting a couple is the same. This property defines a couple and distinguishes it from other force systems.
3. "A couple can be balanced only by a couple but of opposite sense": This statement is true. To balance a couple, you need another couple with equal magnitude but opposite sense (opposite direction and parallel). This is because the effect of a couple cannot be canceled out by a single force; it requires an equal and opposite couple.
4. "A couple can be never balanced by a single force": This statement is also true. A single force cannot balance a couple because a couple creates a rotational effect, and a single force cannot counteract this rotational effect. Only an equal and opposite couple can balance out the effects of a couple.

• "Algebraic sum of moments of forces constituting a couple, about any point, is the same."
• "A couple can be balanced only by a couple but of opposite sense."
• "A couple can never be balanced by a single force."