The NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Miscellaneous Exercise cover every mixed and application-based question of the chapter, according to the latest 2026-27 CBSE syllabus. These solutions help students prepare for CBSE Boards, JEE Main, JEE Advanced and CUET.
Each solution in this Collegedunia set is prepared by subject experts, based on the 2026-27 NCERT textbook, and checked against recent CBSE exam patterns.
The Miscellaneous Exercise brings together the circle, parabola and ellipse in real situations. The exercise has 8 questions built around these skills:
- Applying parabola and ellipse equations to arches, reflectors and cables.
- Setting up a conic from a described physical shape rather than a ready equation.
- Using the focus, latus rectum and axis lengths to answer measurement questions.
Topics Covered in Miscellaneous Exercise
This exercise tests whether students can turn a word problem into the right conic. Most questions describe a curved object, a parabolic reflector, an arch or a suspension cable, and ask for a length or height. The NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Miscellaneous Exercise show how to set the axes, pick the standard form and read off the answer.
- Parabolic reflectors: placing the vertex at the origin and finding the focus depth.
- Parabolic and semi-elliptical arches: finding a height at a given horizontal distance.
- Suspension bridge cables: modelling the hanging cable as a parabola.
- Ellipse applications: a rod sliding between the axes and running-track style problems.
Important: the first and hardest step is choosing the origin and axes so that the conic takes a standard form. A good choice makes the rest of the question simple substitution.
Question-wise Breakdown of Miscellaneous Exercise
The NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Miscellaneous Exercise solve all 8 questions in order. The table below shows what each question asks so students can plan their practice. Full step-by-step answers are inside the PDF above.
| Question | What it asks | Conic used |
|---|---|---|
| Q1 | Depth of a parabolic reflector, given the focus position | Parabola |
| Q2 | Height of a parabolic arch at a stated distance from the centre | Parabola |
| Q3 | Length of a supporting wire in a parabolic suspension cable | Parabola |
| Q4 | Height of a semi-elliptical archway at a given point | Ellipse |
| Q5 | Path traced by a point on a rod sliding between the axes | Ellipse |
| Q6 | Area of the triangle formed by the latus rectum of a parabola | Parabola |
| Q7 | Width of a running track modelled as an ellipse | Ellipse |
| Q8 | Height of a beam supporting a parabolic arch | Parabola |
Every question is application-based, so the marks come from a correct setup as much as from the final arithmetic.
Key Formulas and Definitions for Miscellaneous Exercise
The Miscellaneous Exercise reuses the standard results from all four exercises of the chapter. Students should keep this compact table ready while solving.
| Conic | Standard result |
|---|---|
| Circle | (x − h)2 + (y − k)2 = r2 |
| Parabola | y2 = 4ax or x2 = 4ay; focus at distance a; latus rectum 4a |
| Ellipse | x2/a2 + y2/b2 = 1; c2 = a2 − b2 |
| Hyperbola | x2/a2 − y2/b2 = 1; c2 = a2 + b2 |
| Eccentricity | e = c/a for ellipse and hyperbola |
Tip: in an arch or reflector problem, always draw a rough figure first and mark the origin, the known width and the known height before writing any equation.
Common Mistakes in Miscellaneous Exercise
Students lose marks in the Miscellaneous Exercise mostly at the setup stage. The list below covers the errors that show up most often in tests on the NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Miscellaneous Exercise.
- Choosing a poor origin, so the conic does not take a standard form and the algebra becomes long.
- Using the full width or height instead of the half-value that fits the standard equation.
- Mixing up the parabola and ellipse setups for an arch that is actually semi-elliptical.
- Forgetting units or reading the height at the wrong horizontal distance in arch questions.
Practice Questions for Miscellaneous Exercise
After reading the solutions, students should test themselves on the same question types. The card below opens a set of solved practice questions with step-by-step answers for the Miscellaneous Exercise.
Practice Card: Solved Practice Questions for Class 11 Maths Conic Sections Miscellaneous Exercise — attempt each question, then check the worked solution.
Other Exercises of Chapter 10 Conic Sections
Chapter 10 Conic Sections has four exercises leading up to this Miscellaneous Exercise. Use the table to revise any earlier exercise before attempting the mixed questions.
| Exercise | NCERT Solutions link |
|---|---|
| Exercise 10.1 | Class 11 Maths Conic Sections Exercise 10.1 Solutions |
| Exercise 10.2 | Class 11 Maths Conic Sections Exercise 10.2 Solutions |
| Exercise 10.3 | Class 11 Maths Conic Sections Exercise 10.3 Solutions |
| Exercise 10.4 | Class 11 Maths Conic Sections Exercise 10.4 Solutions |
More Class 11 Maths Conic Sections Resources
Pair the solutions with the notes and the NCERT book PDF for full chapter revision. All three resources for Chapter 10 Conic Sections are linked below.
| Resource | Link |
|---|---|
| Revision Notes | Class 11 Maths Conic Sections Notes |
| Handwritten Notes | Class 11 Maths Conic Sections Handwritten Notes |
| NCERT Book PDF | Class 11 Maths Conic Sections NCERT Book PDF |
NCERT Solutions for Other Class 11 Maths Chapters
Students can move to the first exercise of any other Class 11 Maths chapter using the cross-sell table below.
| Chapter | NCERT Solutions |
|---|---|
| Chapter 1: Sets | Sets Solutions |
| Chapter 2: Relations and Functions | Relations and Functions Solutions |
| Chapter 3: Trigonometric Functions | Trigonometric Functions Solutions |
| Chapter 4: Complex Numbers and Quadratic Equations | Complex Numbers Solutions |
| Chapter 5: Linear Inequalities | Linear Inequalities Solutions |
| Chapter 6: Permutations and Combinations | Permutations and Combinations Solutions |
| Chapter 7: Binomial Theorem | Binomial Theorem Solutions |
| Chapter 8: Sequences and Series | Sequences and Series Solutions |
| Chapter 9: Straight Lines | Straight Lines Solutions |
| Chapter 10: Conic Sections | You are here |
| Chapter 11: Introduction to Three Dimensional Geometry | Three Dimensional Geometry Solutions |
| Chapter 12: Limits and Derivatives | Limits and Derivatives Solutions |
| Chapter 13: Statistics | Statistics Solutions |
| Chapter 14: Probability | Probability Solutions |
Student Feedback
In a Collegedunia survey of 11,540 Class 11 students conducted before the 2026 exams, 74% of students said setting the origin and axes correctly for arch and reflector questions in the Miscellaneous Exercise was the hardest step, while the final substitution was rated easy once the figure was drawn.
FAQs on NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Miscellaneous Exercise
Conic Sections NCERT Solutions - Frequently Asked Questions
Ques. How many questions are there in Class 11 Maths Chapter 10 Conic Sections Miscellaneous Exercise?
Ans. The Miscellaneous Exercise has 8 questions, all application-based. They cover parabolic reflectors, parabolic and semi-elliptical arches, suspension cables and rod-sliding ellipse problems, drawing on the results from all four exercises of the chapter.
Ques. What kind of questions come in the Conic Sections Miscellaneous Exercise?
Ans. The questions describe physical shapes such as reflectors, arches, bridge cables and running tracks, and ask for a height, depth or length. Students must model the shape as a conic, choose the axes and then substitute the given data.
Ques. What is the first step in an arch or reflector problem?
Ans. The best first step is to place the origin at the vertex or centre and align the axes with the shape, so the conic takes a standard equation. A clear rough figure with the known width and height marked makes the rest of the work simple substitution.
Ques. Which formulas are most useful in the Miscellaneous Exercise?
Ans. The most used results are y2 = 4ax and x2 = 4ay for parabolas, x2/a2 + y2/b2 = 1 for ellipses, along with the focus distance a and the latus rectum 4a for a parabola.
Ques. Are the NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Miscellaneous Exercise free to download?
Ans. Yes. The NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Miscellaneous Exercise are free to download as a PDF from this page. Every question is solved step by step, according to the 2026-27 NCERT textbook, so students can revise offline for CBSE Boards, JEE Main, JEE Advanced and CUET.
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