There is a possible error of 0.03 cm in a scale of length 1 foot with which the height of a closed right circular cylinder and the diameter of a sphere are measured as 3.5 feet each. If the radii of both cylinder and sphere are same, then the approximate error in the sum of the surface areas of both cylinder and sphere is (in square feet)

If the point $P\left(x_1, y_1\right)$ lying on the curve $y=x^2-x+1$ is the closest point to the line $y=x-3$, then the perpendicular distance from $P$ to the line $3 x+4 y-2=0$ is

If the normal drawn at the point $P$ on the curve $y^2=x^3-x+1$ makes equal intercepts on the coordinate axes, then the equation of the tangent drawn to the curve at $P$ is

If a balloon lying at an altitude of 30 m from an observed at a particular instant is moving horizontally. At the rate of $1 \mathrm{~m} / \mathrm{s}$ away from him, then the rate at which the balloon is moving away directly from the observer at the 40 th second is (in m/s) .