A circular sector of perimeter 60 m with maximum area is to be constructed. The radius of the circular arc in metre must be :
20
5
15
10
The tangent and the normal drawn to the curve y = x2 - x + 4at P(1, 4) cut the x-axis at A and B respectively. If the length of the subtangent drawn to the curve at P is equal to the length of the subnormal, then the area of the triangle PAB in sq unit is :
4
32
8
16
Which one of the following is not true always?
If f(x) is not continuous at x = a, then it is not differentiable at x = a
If f(x) is continuous at x = a, then it is differentiable at x = a
If f(x) and g(x) are differentiable at x = a, then f(x) + g(x) is also differentiable at x = a
If a function f(x) is continuous at x = a, then f(x) exists
If y = :
x2y2
D.
If f(x) is a function such that f''(x) + f(x) = 0 and g(x) = [f(x)]2 + [f'(x)]2 and (3) = 3 then g(8) is equal to :
5
0
3
8