CHAPTER-4, APPLICATIONS OF DERIVATIVES

1. The angle of intersection of the two curves xy = a2 and x2 + y2 = 2 a2 is

 
 
 
 

2. If the rate of change of volume of a sphere is equal to the rate of change of its radius then its radius =

 
 
 
 

3. Tangents to curve y = x3 at x = – 1 and x = 1 are

 
 
 
 

4. For the curve x = 3 cos θ, y = 3 sin θ, 0 ≤ θ ≤ π, the tangent is parallel to x-axis when

 
 
 
 

5. The displacement s of a particle at time ‘t’ is given by s = a cos ω t + b sin ω t. Acceleration at time ‘f’ is

 
 
 
 

6. The equation of the normal at the point ‘t’ to the curve x = at2, y = 2 at is

 
 
 
 

7. The side of an equilateral triangle is ‘a’ units and is increasing at the rate of k units/sec. Rate of increase of its area is

 
 
 
 

8. The angle at which the circle x2 + y2 = 16 can be seen from the point (8, 0) is

 
 
 
 

9. The points on the curve y = 12 x – x3, the tangent at which are parallel to x-axis are

 
 
 
 

10. The normal at the point (1, 1) on the curve 2y = 3 – x2 is

 
 
 
 

Question 1 of 10