If the error committed in measuring the radius of the circle is $0.05 \%$,then the corresponding error in calculating the area is (in $\%$)

Find the rate of change of the area of a circle with respect to its radius $r$ when $r=5 \text{ cm}$.

The edge of a cube is decreasing at the rate of $0.04 \ cm/sec$. If the edge of the cube is $10 \ cm$,then the rate of decrease of the surface area of the cube is...

$A$ kind of bacteria grows by $t^3$ in $t \ s$. The time taken for the rate of growth of the bacteria to become $1200 \ \text{per } s$ is: (in $s$)

$A$ ladder of length $17 \,m$ rests with one end against a vertical wall and the other on the level ground. If the lower end slips away at the rate of $1 \,m/sec$, then when it is $8 \,m$ away from the wall, its upper end is coming down at the rate of

The radius of a circular plate is increasing at the rate of $0.01 \text{ cm/s}$ when the radius is $12 \text{ cm}$. Then,the rate at which the area increases,is