When is an object said to be in equilibrium?

$A$ $1 \,kg$ mass is suspended from the ceiling by a rope. $A$ horizontal force $F$ is applied at the midpoint of the rope so that the upper part of the rope makes an angle of $45^{\circ}$ with respect to the vertical axis as shown in the figure. The magnitude of $F$ is:

What will be the tension produced in the string $PQ$ for the given system?

Consider the following statements about the blocks shown in the diagram that are being pushed by a constant force $F$ on a frictionless table:
$A.$ All blocks move with the same acceleration.
$B.$ The net force on each block is the same.
Which of these statements is/are correct?

Two persons are holding a rope of negligible weight tightly at its ends so that it is horizontal. $A$ $15\, kg$ weight is attached to the rope at the mid-point,which now no longer remains horizontal. The minimum tension required to completely straighten the rope is

$A$ mass $M \text{ kg}$ is suspended by a weightless string. The horizontal force required to hold the mass at $60^{\circ}$ with the vertical is