If the rate of change of volume of a sphere is equal to the rate of change of its radius then its radius =
1
0
On the intervals [0, 1 ] the function x25 ( 1 - x ) 75 takes its maximum value at the point:
1/4
1/2
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
A box is constructed from a rectangular metal sheet of 21 cm by 16 cm, by cutting equal squares of sides x from the corners of the sheet and then turning up the projected portions. The value of x so that volume of the box is maximum is
Find ∂2y/∂y∂x for the function u = x/y2 - y/x2
2/y2 + 2/x2
2/y3 + 2/x3
-2/y3 + 2/x3
If u = x2y + y2z + z2x then ux + uy + uz =
x + y + z
3(x2y + y2z + z2x)
(x + y + z)2
The displacement s of a particle at time 't' is given by s = a cos ωt + b sin ωt.Acceleration at time 't' is.
ω2s
s2/ω2
ω2
-ω2s
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
Square of the velocity
None of these
The equation of the normal to the curve y (x - 2 ) (x - 3) 0 x + 7 = 0 at the point where it cuts the x axis is:
x - 20y = 7
20 x - y = 7
20x + y = 140
20x - y = 140
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
