If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing, is
a constant
proportional to the radius
inversely proportional to the radius
inversely proportional to the surface area
If y = x + x2 + x3 + ... to where , then for , is equal to :
y + y2 + y3 + ... to
1 - y + y2 - y3 + ... to
1 - 2y + 3y2 - ... to
1 + 2y + 3y2 + ... to
Twenty two metres are available to fence a flower bed in the form of a circular sector. If the flower bed should have the greatest possible surface area, the radius of the circle must be :
4 m
3 m
6 m
5 m
Given f(0) = 0 and f(x) = for . Then only one of the following statements on f (x) is true. That is f(x), is :
continuous at x = 0
not continuous at x = 0
both continuous and differentiable at x = 0
not defined at x = 0
The value of x for which the polynomial 2x3 - 9x2 + 12x + 4 is a decreasing function of x, is :
- 1 < x < 1
0 < x < 2
x > 3
1 < x < 2
The range of the function :
[- 1, 1]
[1, - 1]
{0}
{1}
D.
{1}
Let f : R R : f(x) = x2 and g : R R : g(x) = x + 5, then gof is :
(x + 5)
(x + 52)
(x2 + 52)
(x2 + 5)