The equation of the tangent at the point p (t), where t is any parameter, to the parabola y2 = 4ax is:
yt = x + at2
y = xt + at2
y = tx
y = tx + a/t
If u = x2y + y2z + z2x then ux + uy + uz =
x + y + z
2 (x + y + z)
3(x2y + y2z + z2x)
(x + y + z)2
The radius of a spherical soap bubble is increasing at the rate of 0.3 cms-1.When r = 8 cm the rate of change of its surface area is
17.2 π cm2 s -1
19. 2π cm2 s -1
20 π cm3 s -1
91.2 π cm2 s -1
The rate of change of the area of a circle w.r.t its radius r when r = 3 is
3 π cm2/sec
6 π cm2 sec
π cm2 sec
-6 π cm2/sec
The slope of the tangent of the curve x = t2 + 3t - 8, y = 2t2 - 2t -5 at the point ( 2, -1 ) is:
22/7
6/7
-6
None of these
A man is walking at the rate of 8 kmph towards the foot of a tower 60 metres high.The rate at which he is approaching the top when he is 80 metres from the foot of the tower is.
6.4 kmph
32/3 kmph
6 kmph
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
The length of the sub-tangent to the curve √x + √y = 3 are the point ( 4, 1 ) is
2
1/2
-3
4
The tangent to the curve y = e2x at the point ( 0,1 ) meets the x axis at
(0,a )
(2, 0 )
( -1/2, 0 )
The tangent of the curve x2 + y2 – 2x -3 = 0 is parallel to axis at the point:
(2, ± √3)
(1, ± 2)
( ± 1, 2 )
( ± 3, 0 )
