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Class 12 Mathematics: Application of Derivatives
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MCQs on derivative application, quantities rate change, derivative applications for error determination, increasing and decreasing functions, tangents, normals, approximations, maxima and minima.

Class 12 Mathematics: Application of Derivatives
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25 Questions

1. What is the mathematical expression for monotonically decreasing function?
2. 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?
3. What will be the differential function of √(x2 + 2)?
4. Find the approximate value of (82)1/4.
5. 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?
6. Find the approximate value of \(\sqrt{49.1}\).
7. What will be the estimate error made in calculating the area of the triangle ABC in which the sides a and b are measured accurately as 25 cm and 16 cm, while the angle C is measured as 60° but (1/2)° in error?
8. What is the relation between f(x) and ℓ when the minimum value or least value function f is defined on a set A and ℓ ∈ f(A)?
9. Find the approximate change in the volume of cube of side xm caused by increasing the side by 6%.
10. The rate of change of area of a square is 40 cm2/s. What will be the rate of change of side if the side is 10 cm.
11. What will be the value of the co-ordinate whose position of a particle moving along the parabola y2 = 4x at which the rate at of increase of the abscissa is twice the rate of increase of the ordinate?
12. If 1° = 0.01745 then, what is the value of cos62°?
13. The length of the rectangle is changing at a rate of 4 cm/s and the area is changing at the rate of 8 cm/s. What will be the rate of change of width if the length is 4cm and the width is 1 cm.
14. Find the approximate value of \(\sqrt{64.3}\).
15. If log103 = 0.4771 and log10e = 0.4343, then what is the value of log1030.5?
16. If the circumference of the circle is changing at the rate of 5 cm/s then what will be rate of change of area of the circle if the radius is 6cm.
17. What is the mathematical expression for a function to be strictly decreasing on (a,b)?
18. The length of a side of a cube is 10cm; if an error of 0.05cm is made in measuring the side, then what is the value of approximate error in calculating its volume?
19. Find the tangent to the curve y=5x4-3x2+2x-1 at x=1.
20. What is the condition for a function f to be decreasing if f be continuous and differentiable on (a,b)?
21. Find the approximate value of f(4.04), where f(x)=7x3+6x2-4x+3.
22. The volume of a cube of edge x is increasing at a rate of 12 cm/s. Find the rate of change of edge of the cube when the edge is 6 cm.
23. Find the tangent to the curve y=3x2+x+4 at x=3.
24. The total cost N(x) in rupees, associated with the production of x units of an item is given by N(x)=0.06x3-0.01x2+10x-43. Find the marginal cost when 5 units are produced.
25. A particle moving in a straight line covers a distance of x cm in t second, where x = t3 + 6t2 – 15t + 18. What will be the acceleration of the particle at the end of 2 seconds?

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