If the rate of change of volume of a sphere is equal to the rate of change of its radius then its radius is
1
√2π
0
1/√2π
The dimension of the rectangle of perimeter 36 cm. Which will Sweep out a volume as large as possible when revolved about one of its sides, are
10, 8
11, 7
12, 6
A stone is thrown vertically up and the height s reached in time t is given by s = 80t - 16t2.The stone reaches the maximum height in time t =
2
2.5
3
3.5
The length of the subnormal to the parabola y2 = 4dx at any point is equal to:
√2 a
2√2 a
a/√2
2a
If the percentage increase in the edge of cube is k,then percentage increase in the volume is
k
2k
3k
k3
If a particle moves according to the law s = t3/3 - 3t2 + 8t then the distance covered before it first comes to rest is
16/3
8
10/3
20/3
A box is constructed from a rectangular metal sheet of 21 cm by 16 cm, by cutting equal squares of sides x from the corners of the sheet and then turning up the projected portions. The value of x so that volume of the box is maximum is
Tangents to curve y = x3 at x = -1 and x = 1 are
Parallel
Intersecting obliquely
Perpendicular to each other
None of these
The tangent of the curve y = x2 + 3x will pass through the point ( 0, -9 ) if it is drawn at the point.
( -3, 0 )
( -4, 4 )
The equation of the tangent to the curve y = 2sinx + sin2x at x = π/3 is equal to:
2y = 3√3
y = 3√3
2y + 3 √3 = 0
y + 3 √3 = 0
