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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 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.
2. 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 percentage error in calculating its volume?
3. Find the equation of all the lines having slope 0 which are tangent to the curve y=6x2-7x.
4. At what rate will the lateral surface area of the cylinder increase if the radius is increasing at the rate of 2 cm/s when the radius is 5 cm and height is 10 cm?
5. Find the equation of the tangent of the tangent to the curve 2x2+3y2=3 at the point(3,4).
6. Find the slope of the tangent to the curve x=4 cos3⁡3θ and y=5 sin3⁡⁡3θ at θ=π/4.
7. Find the points on the curve y=3x4+2x3-1 at which the tangents is parallel to the x-axis.
8. Find the approximate value of \(\sqrt{11}\).
9. What is the mathematical expression for a function to be strictly decreasing on (a,b)?
10. Find the interval in which function f(x) = sinx+cosx, 0 ≤ x ≤ 2π is decreasing.
11. Find the approximate value of (82)1/4.
12. What is a monotonically increasing function?
13. 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?
14. 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?
15. Find the tangent to the curve y=3x2+x+4 at x=3.
16. 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?
17. Find the intervals in which f(x) = 2x2 – 3x is increasing.
18. Find the interval in which function f(x) = x2 – 4x + 5 is increasing.
19. Find the approximate value of f(5.03), where f(x)=4x2-7x+2.
20. What will be the increment of the differentiable function f(x) = 2x2 – 3x + 2 when x changes from 3.02 to 3?
21. 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?
22. 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?
23. If the rate of change of radius of a circle is 6 cm/s then find the rate of change of area of the circle when r=2 cm.
24. 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.
25. What will be the differential function of √(x2 + 2)?

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