The function f(x) = is
differentiable at both x = 2 and x = 0
differentiable at x = 2 but not at x = 0
continuous at x = 2 but not at x = 0
continuous at both x = 2and x = 0
A wire of length 20 cm is bent in the form of a sector of a circle. The maximum area that can be enclosed by the wire is
20 sq cm
25 sq cm
10 sq cm
30 sq cm
B.
25 sq cm
Given that,
length of the wire P = 20cm
Then, P = diameter + arc length
20 = 2r + S
S = 20 - 2r
S = 2(10 - r) ...(i)
Also, know that area of semicircle
The condition for the line y = mx + c to be a normal to the parabola y2 = 4ax is
c = - 2am - am3
c = 2am + am3
P is the point of contact of the tangent form the origin to the curve y = loge(x). The length of the perpendicular drawn form the origin to the normal at P is
For the curve 4x5 = 5y4, the ratio of the cube of the subtangent at a point on the curve the square of the subnormal at the same point is
A space vector makes the angles 150° and 60° with the positive direction of x-and y-axes. The angle made by the vector with the positive direction z-axis is
90°
60°
180°
120°