A man 6 feet height walks at a uniform of 20 above the floor. An object falls freely under gravity, starting from rest at the same height as the lamp, put at a horizontal distance of 5 ft from it. The speed of the shadow of the object on the floor when it has fallen through 15 ft is

A ladder 20 feet  long  whose top is resting against  a vertical wall on a level plane beginning to slide outward. When the foot and top of the ladder are sliding at the same rate, the distance of the foot from the wall is

A person of height 180 cm starts from a lamp post of height 450 cm and walks at the constant rate of 4 km per hour. The rate at which his shadow increases is

A particle is moving in a straight line with the relation between the time and the distance in such a way that s=t³-9t²+24t-18. The value of its velocity when the acceleration is zero is

The approximate value of  cos 61⁰, given that 1⁰=0.1745 radian is

If there is a possible error of 0.01 cm in the measurement of side of a cube, the possible error in its surface area when the side is 10 cm is

If θ is the angle between the curves y²=4ax, ay=2x² at (a, 2a) then tan θ=

The set of all values of a for which the function f(x)=(a²-3a+2)(cos²x/4-sin²x/4)+(a-1)x+sin 1 does not possess critical points is

The least value of (x-a) (x-b) occurs at x=

F(x)= tan^-1 x is