If the percentage error in the radius of a circle is $3\%$,then the percentage error in its area is:

Find the approximate value of $f(3.02),$ where $f(x)=3x^{2}+5x+3$.

The approximate value of $\tan ^{-1}(0.999)$ (up to $4$ decimal places) is

There is a possible error of $0.02 \ cm$ in measuring the base diameter of a right circular cone as $14 \ cm$. If the semi-vertical angle of the cone is $45^{\circ}$,then the approximate error in its volume is (in $cm^3$)

Electric current $(I)$ is measured by a galvanometer,where the current is proportional to the tangent of the angle $( \theta)$ of deflection. If the deflection is read as $45^{\circ}$ and an error of $1\%$ is made in reading the angle,the percentage error in the current is:

The time period $T$ of a simple pendulum of length $l$ is given by $T=2 \pi \sqrt{\frac{l}{g}}$,where $g$ denotes the acceleration due to gravity. If the length of the pendulum is increased by $1 \%$,then the approximate change in its time period is (in $\%$)