The point of intersection of the tangents drawn to the curve x2y = 1 – y at the points where it is meet by the curve xy = 1 – y is given by


Correct option is

(0, 1)

             x2y = 1 – yxy –1– y   



           x2y = 1– y    



At (0, 1), (y – 1) = 0    ⇒ y = 1  

So point of intersection is (0, 1). 



A lamp of negliligible height is placed on the ground ‘l1’ m away from a wall. A man ‘l2’ m tall is walking at a speed of  m/sec from the lamp to the nearest point on the well. When he is midway between the lamp and the wall, the rate of change in the length of his shadow on the wall is



Consider the parabola y2 = 4xA = (4, –4) and B = (9, 6) be two fixed points on the parabola. Let ‘C’ be moving point on the parabola between A and B such that the area of triangle ABC is maximum, then coordinate of ‘C’ is


If the rate of change of volume of a sphere is the same as rate of change of its radius, then radius, is equal to


A spherical balloon is pumped at the constant rate of 3 m3/min. The rate of increase of its surface area as certain instant is found to be 5 m2/min. At this instant it’s radius is equal to


The third derivative of a function f’’(x) vanishes for all x. If f (0) = 1, f’ (1) = 2 and f’’ = –1, then f (x) is equal to 


The chord joining the points where x = p and x = q on the curve ax2 + bx + c is parallel to the tangent at the point on the curve whose abscissa is 


If the tangent at (1, 1) on y2 = x (2 – x)2 meets the curve again at P, then is


The distance between the origin and the normal to the curve

y = e2x + x2 at x = 0 is


If the line ax + by + c = 0 is a normal to the curve xy = 1 then


The slope of the normal at the point with abscissa x = –2 of the graph of the function f (x) = | x2 – x | is