Let f(x) = 2x3 - 9ax2 + 12a2x + 1, where a > 0. The minimum of f is attained at a point q and the maximum is attained at a point p. If p = q, then a is equal to
1
3
2
0
The difference between the maximum and minimum value of of the function on [2, 3] is
39/6
49/6
59/6
69/6
If a and b are the non-zero distinct roots of x2 + ax + b = 0, then the minimum value of x2 + ax + b is
2/3
9/4
- 9/4
- 2/3
The equation of the tangent to the curve (1 + x2)y = 2 - x where it crosses the x-axis, is :
x + 5y = 2
x - 5y = 2
5x - y = 2
5x + y - 2 = 0
A.
x + 5y = 2
The given equation of curve is (1 + x2)y = 2 - x, it meets x-axis at (2, 0)
It can be rewritten as y =
On differentiating w.r.t. x, we get
The sides of an equilateral triangle are increasing at the rate of 2 cm/s. The rate at which the area increases, when the side is 10 cm, is:
10 sq cm/s
If PQ and PR are the two sides of a triangle, then the angle between them which gives maximum area of the triangle, is :
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