At what point the slope of the tangent to the curve x2 + y2 - 2x - 3 = 0 is zero
( 3, 0 ), ( -1, 0 )
( 3, 0 ), ( 1, 2 )
( -1, 0 ), ( 1, 2 )
( 1, 2 ), ( 1, -2 )
The interval in which x2 + 2x - 5 is strictly increasing is
(1, 0 )
( 0,1 )
f (x ) = √3 sin x + 3 cos x is max at x =
π/3
π/2
π/6
2π/3
Two towns A and B are 60 km a part A school is to be built to serve 150 students.If the total distance to be traveled by all 200 students is to be as small as possible, then the school should be built at:
Town B
45 km from town A
Town A
45 km from town B
If f (x ) = a ( x + sin x ) + a is increasing, then the value of a is
a >0
a < 0
a = -1
a = -2
The equation to the normal of the curve y = sin x at ( 0,0) is:
x = 0
y = 0
x + y = 0
x - y = 0
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 length x of a rectangle is decreasing at the rate of 3cm /min and width y is increasing at the rate of 2 cm/ min. When x = 10 cm and y = 6cm, the rate of change of the perimeter is
2
-2
1
-1
If the parametric equation of a curve is given by x = et cost, y =et sin t, then tangent to the curve at the point t = π/4 makes the angle with the axis of x.
0
π/4
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
None of these
