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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. Find the tangent to the curve y=3x2+x+4 at x=3.
2. Find the tangent to the curve y=7x3-2x2 at the point x=2.
3. 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.
4. What will be the average rate of change of the function [y = 16 – x2] between x = 3 and x = 4?
5. What will be the increment of the differentiable function f(x) = 2x2 – 3x + 2 when x changes from 3.02 to 3?
6. Find the slope of the normal to the curve y=4x2-14x+5 at x=5.
7. Find the approximate value of \(\sqrt{64.3}\).
8. 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.
9. 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?
10. 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?
11. What will be the average rate of change of the function [y = 16 – x2] at x = 4?
12. Find the slope of the tangent to the curve x=4 cos3⁡3θ and y=5 sin3⁡⁡3θ at θ=π/4.
13. The edge of a cube is increasing at a rate of 7 cm/s. Find the rate of change of area of the cube when x=6 cm.
14. What is the relation between f(x) and ℓ when the maximum value or greatest value function f is defined on a set A and ℓ ∈ f(A)?
15. Find the approximate value of \(\sqrt{11}\).
16. 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?
17. Find the intervals in which f(x) = 2x2 – 3x is increasing.
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 relative error in calculating its volume?
19. What is the condition for a function f to be increasing if f be continuous and differentiable on (a,b)?
20. Find the approximate error in the volume of the sphere if the radius of the sphere is measured to be 6cm with an error of 0.07cm.
21. What will be the differential function of log(x2 + 4)?
22. What is the mathematical expression for monotonically decreasing function?
23. If 1° = 0.01745 then, what is the value of cos62°?
24. Find the equation of all the lines having slope 0 which are tangent to the curve y=6x2-7x.
25. Find the equation of the normal to the curve x=12 cosec⁡θ and y=2 sec⁡θ at x=π/4 .

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