State whether the following statement is true or false:
The rate of doing work is called power.

$A$ girl is carrying a school bag of $3 \, kg$ mass on her back and moves $200 \, m$ on a levelled road. The work done against the gravitational force will be $(g = 10 \, m \, s^{-2})$.

$(i)$ An object thrown at a certain angle to the ground moves in a curved path and falls back to the ground. The initial and the final points of the path of the object lie on the same horizontal line. What is the total work done against the force of gravity and by the force of gravity on the object? Explain with proper mathematical expression.
$(ii)$ $A$ certain force acting on a $20 \, kg$ mass changes its velocity from $5 \, m s^{-1}$ to $2 \, m s^{-1}$. Calculate the work done by the force.

Calculate the electricity bill amount for the month of April if $4$ bulbs of $40 \, W$ for $5 \, hrs$, $4$ tube lights of $60 \, W$ for $5 \, hrs$, a $TV$ of $100 \, W$ for $6 \, hrs$, and a washing machine of $400 \, W$ for $3 \, hrs$ are used per day. The cost per unit is ₹ $1.80$.

$A$ girl of mass $40\, kg$ climbs a rope $6\, m$ long at a constant speed in $15$ seconds. What power does she expend during the climb (in $W$)?

How much work is done by a weight lifter when he holds a weight of $80 \,kg$ on his shoulders for two minutes?