The equation of motion of a particle is given by $s = 2t^3 - 9t^2 + 12t + 1$,where $s$ and $t$ are measured in $cm$ and $sec$. The time when the particle stops momentarily is

$A$ particle is in motion along a curve $12 y = x^{3}$. The rate of change of its ordinate exceeds that of its abscissa when:

The radius of a circle is increasing at a rate of $0.7 \text{ cm/s}$. The rate at which the circumference of the circle is increasing is . . . . . . .

The radius of a right circular cylinder increases at a constant rate. Its altitude is a linear function of the radius and increases three times as fast as the radius. When the radius is $1 \, cm$,the altitude is $6 \, cm$. When the radius is $6 \, cm$,the volume is increasing at the rate of $1 \, cm^3/sec$. When the radius is $36 \, cm$,the volume is increasing at a rate of $n \, cm^3/sec$. The value of $n$ is equal to:

If the sides of a triangle vary slightly in such a way that its circumradius remains constant,then $\frac{da}{\cos A} + \frac{db}{\cos B} + \frac{dc}{\cos C}$ is equal to

Air is discharging from a large spherical balloon at the rate of $4 \,m^3 / min$. The rate at which the surface area is shrinking when the radius of the balloon is $8 \,m$, is