If a particle moving along a line follows the law then the acceleration is proportional to
Square of the velocity
Cube of the displacement
Cube of the velocity
Constant
The point on the curve y = 12 x - x3 , the tangent at which are parallel to x-axis are
(2,16) and (-2,-16)
(2,16) and (-2,16)
(-2,16) and (2,-16)
None of these
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
The slope of the tangent to the curve y = 16 - x2 at x = 0 is
0
-2
2
16
A point moving on a line so that its velocity at time t is proportional to the square of the distance covered.Then its acceleration at time t varies as
Cube of the distance
The distance
The total area of a page is 150 square inches. The combined width of the margin at the top and bottom is 3" and the side is 2". The dimensions of the page in order that the area of the printed matter is maximum are
15, 10
25, 6
30, 5
If tangent to the curve x = at2, y = 2at is perpendicular to x axis, then its point of contact is:
(a, a)
( 0, a )
( a,0 )
( 0, 0 )
f ( x ) = 1 + 2 sin x + 2 cos 2 x, 0 ≤ x ≤ π/2 is maximum and minimum respectively at x =
π/6, π/2
π/2, π/6
π/3, π/3
π/3, π/2
Coordinates of the point P on the curve y2 = 2x3, where the tangent is perpendicular to the line 4x - 3y + 2 = 0 are given by:
(2, 4 )
(0, 0 )
( 1/8, 1/16)
The equation of the tangent to the curve y = 2 x2 - 3x - 1 at the point (1,-2) is
x - y - 3 = 0
x - y + 3 = 0
x + y - 3 = 0
x + y + 3 = 0
