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Class 12 Maths Practice Test - Application of Derivatives
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Class 12 Maths Practice Test - Application of Derivatives
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15 Questions

1. A particle moving in a straight line covers a distance of x cm in t second, where x = t3 + 6t2 – 15t + 18. When does the particle stop?
2. What will be the average rate of change of the function [y = 16 – x2] at x = 4?
3. What will be the differential function of √(x2 + 2)?
4. The time rate of change of the radius of a sphere is 1/2π. When it’s radius is 5cm, what will be the rate of change of the surface of the sphere with time?
5. Water is flowing into a right circular conical vessel, 45 cm deep and 27 cm in diameter at the rate of 11 cc per minute. How fast is the water level rising when the water is 30 cm deep?
6. What will be the differential function of log(x2 + 4)?
7. What will be the average rate of change of the function [y = 16 – x2] between x = 3 and x = 4?
8. A ladder 20 ft long leans against a vertical wall. If the top end slides downwards at the rate of 2ft per second, what will be the rate at which the slope of the ladder changes?
9. A ladder 20 ft long leans against a vertical wall. If the top end slides downwards at the rate of 2ft per second, what will be the rate at which the slope of the ladder changes?
10. A 5 ft long man walks away from the foot of a 12(½) ft high lamp post at the rate of 3 mph. What will be the rate at which the shadow increases?
11. What is the slope of the tangent to the curve y = 2x/(x2 + 1) at (0, 0)?
12. A solid cube changes its volume such that its shape remains unchanged. For such a cube of unit volume, what will be the value of rate of change of volume?
13. What will be the differential function of √(x2 + 2)?
14. The value of f’(x) is -1 at the point P on a continuous curve y = f(x). What is the angle which the tangent to the curve at P makes with the positive direction of x axis?
15. What will be the average rate of change of the function [y = 16 – x2] between x = 3 and x = 4?

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