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

The total revenue in Rupees received from the sale of $x$ units of a product is given by $R(x) = 3x^2 + 36x + 5$. The marginal revenue,when $x = 15$ is . . . . . . .

If a man of height $1.8 \ m$ is walking away from the foot of a light pole of height $6 \ m$ with a speed of $7 \ km/h$ on a straight horizontal road,then the rate of change of the length of his shadow is (in $km/h$):

$A$ ladder of $5 \ m$ long rests against a vertical wall with the lower end on the horizontal ground. The lower end of the ladder is pulled along the ground away from the wall at the rate of $3 \ m/sec$. The height of the upper end (in meters) while it is descending at the rate of $4 \ m/sec$,is

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...

$A$ particle moving from a fixed point on a straight line travels a distance $S$ metres in $t$ seconds. If $S = t^3 - t^2 - t + 3$,then the distance (in metres) travelled by the particle when it comes to rest is: