Question

The distance between the origin and the normal to the curve

y = e2x + x2 at x = 0 is

Solution

Correct option is

 

  

So, slope of normal = –1/2   

   

SIMILAR QUESTIONS

Q1

Two variable curves C1 : y2 = 4a (x – b1) and C2 : x2 = 4a (y – b2) where ‘a’ is a given positive real no. and b1 and b2 are variable such that C1 and C2 are tangents to each other at point of contact then locus of point of contact is:

Q2

f : R âŸ¶ R be a differentiable function  x Ïµ R. If tangent drawn to the curve at any point x Ïµ (ab) always lie below the curve then

Q3

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

 

Q4

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

Q5

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

Q6

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

Q7

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 

Q8

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 

Q9

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

Q10

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