CHAPTER-4, APPLICATIONS OF DERIVATIVES 1. The angle of intersection of the two curves xy = a^{2} and x^{2} + y^{2} = 2 a^{2} is π / 4 π / 6 π / 3 none of these 2. If the rate of change of volume of a sphere is equal to the rate of change of its radius then its radius = 1 √2π 1/√2π 1/2. 1/√π 3. Tangents to curve y = x^{3} at x = – 1 and x = 1 are intersecting obliquely parallel perpendicular to each other none of these 4. For the curve x = 3 cos θ, y = 3 sin θ, 0 ≤ θ ≤ π, the tangent is parallel to x-axis when θ = 0 θ = π / 3 θ = π / 2 θ = π 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 ω^{2} s s^{2} / ω^{2} ω^{2} – ω^{2} s 6. The equation of the normal at the point ‘t’ to the curve x = at^{2}, y = 2 at is tx + y = 2 at tr + y = at^{3} tx + y = 2at + at^{3} none of these 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 2/√3 ak √3 ak √3/2 ak none of these 8. The angle at which the circle x^{2} + y^{2} = 16 can be seen from the point (8, 0) is π / 3 π / 4 π / 2 π / 6 9. The points on the curve y = 12 x – x^{3}, the tangent at which are parallel to x-axis are (2, 16) and ( – 2, – 16) (2, 16) and (- 2, 16) ( – 2, 16) and (2, – 16) none of these 10. The normal at the point (1, 1) on the curve 2y = 3 – x^{2} is x + y =0 x + y + 1 = 0 x – y + 1 =0 x – y = 0 Loading … Question 1 of 10