Class 12 Mathematics Chapter 6: Application of Derivatives — Important Questions & Mock Tests
Practice Application of Derivatives topic-wise important questions, MCQs and 1, 2, 3 and 5 mark questions for CBSE revision.
300 Questions 75 Topics MCQs: 100 1 Mark: 50 2 Mark: 50 3 Mark: 50 5 Mark: 50
Topic-wise important and practice questions
Review question distribution across chapter topics for MCQs, 1 Mark questions, 2 Mark questions, 3 Mark questions, 5 Mark questions.
| Topic | MCQ | 1 Mark | 2 Mark | 3 Mark | 5 Mark | Total |
|---|---|---|---|---|---|---|
| Absolute Extrema on a Closed Interval | 5 | 0 | 5 | 0 | 5 | 15 |
| Local Extrema by the Second Derivative Test | 0 | 0 | 5 | 5 | 0 | 10 |
| Optimization of Product with Fixed Sum | 5 | 0 | 0 | 0 | 5 | 10 |
| Second Derivative Test | 5 | 5 | 0 | 0 | 0 | 10 |
| Absolute and Local Extrema from a Closed-Interval Graph | 5 | 0 | 0 | 0 | 0 | 5 |
| Absolute Minimum on a Closed Interval | 0 | 5 | 0 | 0 | 0 | 5 |
| Assertion-Reason on Applications of Derivatives | 5 | 0 | 0 | 0 | 0 | 5 |
| Complete First-Derivative Analysis | 0 | 0 | 0 | 0 | 5 | 5 |
| Critical Point Without a Local Extremum | 5 | 0 | 0 | 0 | 0 | 5 |
| Critical Points | 5 | 0 | 0 | 0 | 0 | 5 |
| Critical Points of a Differentiable Function | 0 | 5 | 0 | 0 | 0 | 5 |
| Decreasing Interval from the Sign of f′ | 0 | 5 | 0 | 0 | 0 | 5 |
| First Derivative Interpretation | 5 | 0 | 0 | 0 | 0 | 5 |
| First Derivative Test | 0 | 5 | 0 | 0 | 0 | 5 |
| First Derivative Test for Local Extrema | 5 | 0 | 0 | 0 | 0 | 5 |
| Geometry Model for an Open-Top Box | 0 | 5 | 0 | 0 | 0 | 5 |
| Graph Interpretation in Applications of Derivatives | 0 | 5 | 0 | 0 | 0 | 5 |
| Graphical Analysis of Local and Absolute Extrema | 0 | 0 | 0 | 0 | 5 | 5 |
| Graphical Identification of Local Extrema | 5 | 0 | 0 | 0 | 0 | 5 |
| Higher-Order Product Optimization | 0 | 0 | 0 | 0 | 5 | 5 |
| Increasing and Decreasing Intervals of a Cubic Polynomial | 0 | 0 | 5 | 0 | 0 | 5 |
| Increasing and Decreasing Trigonometric Functions | 5 | 0 | 0 | 0 | 0 | 5 |
| Interpreting a First-Derivative Graph | 5 | 0 | 0 | 0 | 0 | 5 |
| Intervals of Increase from the First Derivative | 5 | 0 | 0 | 0 | 0 | 5 |
| Local and Absolute Extrema | 5 | 0 | 0 | 0 | 0 | 5 |
| Local Extrema by the First Derivative Test | 0 | 0 | 5 | 0 | 0 | 5 |
| Local Extrema from a First-Derivative Graph | 0 | 0 | 0 | 5 | 0 | 5 |
| Marginal Cost | 0 | 0 | 5 | 0 | 0 | 5 |
| Marginal Revenue | 0 | 5 | 0 | 0 | 0 | 5 |
| Maximum Profit by the Second Derivative Test | 0 | 0 | 0 | 0 | 5 | 5 |
| Meaning of Derivative as a Rate of Change | 0 | 5 | 0 | 0 | 0 | 5 |
| Minimum Surface Area of a Closed Cylinder with Fixed Volume | 0 | 0 | 0 | 0 | 5 | 5 |
| Monotonicity and Local Extrema from the First Derivative | 0 | 0 | 0 | 5 | 0 | 5 |
| Monotonicity from a Graph of f′ | 0 | 0 | 5 | 0 | 0 | 5 |
| Monotonicity of Transcendental Functions | 0 | 0 | 0 | 5 | 0 | 5 |
| Monotonicity of Trigonometric or Log-Trigonometric Functions | 0 | 0 | 5 | 0 | 0 | 5 |
| Monotonicity with a Parameter | 0 | 0 | 5 | 0 | 0 | 5 |
| Multiple Local Extrema of a Quartic | 0 | 0 | 0 | 5 | 0 | 5 |
| Open-Top Box Maximum-Volume Optimization | 0 | 0 | 0 | 0 | 5 | 5 |
| Open-Top Box Optimization Model | 5 | 0 | 0 | 0 | 0 | 5 |
| Open-Top Box Optimization Setup | 0 | 0 | 0 | 5 | 0 | 5 |
| Optimization of a Product with Powers | 0 | 0 | 0 | 5 | 0 | 5 |
| Optimization with a Fixed Sum | 0 | 0 | 5 | 0 | 0 | 5 |
| Optimization: Minimum Sum of Squares | 0 | 0 | 0 | 5 | 0 | 5 |
| Parameter Condition for Monotonicity on an Interval | 5 | 0 | 0 | 0 | 0 | 5 |
| Profit Maximization Using Derivatives | 5 | 0 | 0 | 0 | 0 | 5 |
| Rate of Change of Circle Area with Radius | 0 | 5 | 0 | 0 | 0 | 5 |
| Second Derivative Test with First-Derivative Verification | 0 | 0 | 0 | 0 | 5 | 5 |
| Working Rule for Absolute Extrema | 0 | 0 | 0 | 5 | 0 | 5 |
| Marginal Cost as a Rate of Change | 3 | 0 | 0 | 0 | 0 | 3 |
| Marginal Revenue as a Rate of Change | 2 | 0 | 0 | 0 | 0 | 2 |
| Related Rates Using Similar Triangles | 1 | 0 | 1 | 0 | 0 | 2 |
| Extended Related-Rate Model for a Sand Cone | 0 | 0 | 0 | 0 | 1 | 1 |
| Extended Sliding-Ladder Related Rates | 0 | 0 | 0 | 0 | 1 | 1 |
| Ladder Related Rate and Area Change | 0 | 0 | 0 | 1 | 0 | 1 |
| Linked Rates for Sphere Volume and Surface Area | 0 | 0 | 0 | 1 | 0 | 1 |
| Multiple Related Rates in a Conical Tank | 0 | 0 | 0 | 0 | 1 | 1 |
| Rate of Change of Area of a Circle | 1 | 0 | 0 | 0 | 0 | 1 |
| Rate of Change of Circumference | 1 | 0 | 0 | 0 | 0 | 1 |
| Rate of Change of Volume of a Cube | 1 | 0 | 0 | 0 | 0 | 1 |
| Rate of Change of Volume of a Sphere | 1 | 0 | 0 | 0 | 0 | 1 |
| Related Rate of Circular Area | 0 | 0 | 1 | 0 | 0 | 1 |
| Related Rate of Sphere Volume | 0 | 0 | 1 | 0 | 0 | 1 |
| Related Rates for a Cube | 0 | 0 | 1 | 0 | 0 | 1 |
| Related Rates for a Growing Cone | 0 | 0 | 0 | 1 | 0 | 1 |
| Related Rates for a Sliding Ladder | 1 | 0 | 0 | 0 | 0 | 1 |
| Related Rates for a Spherical Balloon | 0 | 0 | 0 | 0 | 1 | 1 |
| Related Rates for an Inflating Sphere | 1 | 0 | 0 | 0 | 0 | 1 |
| Related Rates for Area of a Rectangle | 1 | 0 | 0 | 0 | 0 | 1 |
| Related Rates for Cube Volume and Surface Area | 1 | 0 | 0 | 0 | 0 | 1 |
| Related Rates in a Conical Tank | 1 | 0 | 0 | 0 | 0 | 1 |
| Related Rates in a Similar Conical Tank | 0 | 0 | 0 | 1 | 0 | 1 |
| Shadow Related Rates Using Similar Triangles | 0 | 0 | 0 | 0 | 1 | 1 |
| Simultaneous Related Rates for a Rectangle | 0 | 0 | 0 | 1 | 0 | 1 |
| Sliding Ladder Related Rate | 0 | 0 | 1 | 0 | 0 | 1 |