The side of a cube is equal to the diameter of a sphere.If the side and radius increase at the same rate then the ratio of the increase of their surfaces is
π : 6
2π :3
3 : 2π
3 : π
None of these
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 u = x2y + y2z + z2x then ux + uy + uz =
x + y + z
3(x2y + y2z + z2x)
(x + y + z)2
The coordinates of the point of the curve y = x2 + 3x + 4 the tangent at which passes through the origin are:
( 2, 14 ), ( -2, 2 )
( 2, 14 ), ( -2, -2 )
( 2, 14 ), ( 2, 2 )
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 equation of the normal of the curve y = x (2 - x ) at the point ( 2, 0 ) is
x - 2y = 2
2x + y = 4
x - 2y + 2 = 0
Let p ( x ) = a0 + a1 x2 + a2 x4 + - - - - - - an x2n be a polynomial in real variable x with 0 < a0 < a1, < a2 - - - - - < an. The function P (x ) has
Only one minimum
Only one maximum
Neither a max nor min
The dimension of the rectangle of perimeter 36 cm. Which will Sweep out a volume as large as possible when revolved about one of its sides, are
10, 8
11, 7
12, 6
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)