The curve y = x3 + x + 1, 2y = x3 + 5x at ( 1, 3 ) are:
Touching each other
Intersecting orthogonally
Not intersecting
None of these
If u = f(x2 + y2) then ∂u/∂x:∂u/∂y is
x2:y2
1/x2:1/y2
x:y
If u = x2y + y2z + z2x then ux + uy + uz =
If tangent to the curve x = at2, y = 2at is perpendicular to x axis, then its point of contact is:
(a, a)
( 0, a )
( a,0 )
( 0, 0 )
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 tangent of the curve y = x2 + 3x will pass through the point ( 0, -9 ) if it is drawn at the point.
( -3, 0 )
( -4, 4 )
On the intervals [0, 1 ] the function x25 ( 1 - x ) 75 takes its maximum value at the point:
1/4
1/2
