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
None of these
If a particle moving along a line follows the law t = as2 + bs + c , then the retardation of the particle is proportional to
Square of the velocity
Cube of the displacement
Cube of the velocity
Square of the displacement
If y = a log | x | + bx2 + x has its extreme value at x = -1 and x = 2 then:
a = 2, b = -1
a = 2, b = -1/2
a = -2, b = 1/2
f (x ) = √3 sin x + 3 cos x is max at x =
π/3
π/2
π/6
2π/3
The tangent to the parabola x2 = 2 y at the point (1,1/2) makes with x - axis at an angle.
0o
45o
30o
60o
From a variable point of an ellipse normal is drawn to the ellipse.The maximum distance of the normal from the centre of the ellipse is
a + b
a - b
a - 2b
2a - b
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 minimum radius vector of the curve is of length
a + 2b
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
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