A stone is dropped into a quiet pond and waves move in circles outward from the place where it strikes, at a speed of 30 cm per second. At the instant when the radius of the wave ring is 50mt, the rate of increase in the area of the wave ring is

f(x) = |x| has

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