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RD Sharma Solutions

RD Sharma Class 12 Maths Solutions Chapter 16 - Tangents and Normals

RD Sharma Class 12 Maths Solutions Chapter 16 - Tangents and Normals

Q: 4. Why is the derivative dy/dx fundamental to finding the slope of the tangent?

The derivative dy/dx represents the instantaneous rate of change of y with respect to x. Geometrically, this rate of change at a specific point is the slope of the line that just touches the curve at that point, which is the tangent. The RD Sharma solutions build upon this core concept of Applications of Derivatives, using it as the foundation for every problem involving tangents.

RD Sharma Solutions for Class 12 Maths Chapter 16 - Tangents and Normals - Free PDF Download

Tangents are lines that only meet a given curve and at the point of contact, their normal is a line perpendicular to it. One explanation of why tangents are so important is that they give slopes of the straight lines. Normal lines are also important when dealing with orientation questions, especially in higher dimensions. The RD Sharma Class 12 Chapter 16 Solutions will give a basic understanding of Tangents and Normals along with the important questions asked in board exams.

Vedantu provides an excellent and free PDF of RD Sharma Class 12 Tangents and Normals Solutions according to the NCERT curriculum so that students can score good marks in their board exams.

These RD Sharma Solutions For Class 12 Maths Chapter 16 are prepared by experts who have vast experience in the subject. The experts have done a lot of research to provide unique and step-by-step solutions to all-important questions of Tangents and Normals so that students can understand the concepts easily and ace their exams with good marks.

Benefits of solving Class 12 RD Sharma Textbook

RD Sharma is one of the most popular books for CBSE boards Class 12. Teachers often recommend students to solve this book if they want a book that will improve their scores in board exams. The questions here are of good level and are based on NCERT which makes it a perfect choice for students who are done with their NCERT textbook and want to practice more questions.

The secret to excelling in Maths in boards exams is practice. The more questions students practice, the more confident they become about the topics. They learn better time management skills. Solving questions makes students more familiar with the board question pattern and the marking scheme. They are able to know which topics are important from the examination point of view and which they can overlook. This ensures easy revision during examinations.

Thus, we can conclude by saying that there are several benefits of solving the Class 12 RD Sharma Textbook.

We have all the solutions to the Class 12 RD Sharma Textbook on our website. Students can easily download them for free in PDF format by registering on our website.

Let us look into a Few of the Important Topics from RD Sharma Class 12 Tangents and Normals Solutions.

Some of the topics which have been elaborated in the RD Sharma Class 12 Tangents and Normals Solutions are:

The slope of a line
Slopes of Tangent and Normal
Finding the slopes of the tangent and the normal at a given point
Finding the point on a given curve at which tangent is parallel or perpendicular to a given line
Equations of tangents and normal
Finding the equations of tangent and normal to a curve at a given point
Finding tangent and normal parallel or perpendicular to a given line
Finding tangent or normal passing through a given point
Miscellaneous applications of tangents and normals
Finding the equations of tangent and normal
Finding the equation of the curve
The angle of intersection of two curves
Orthogonal curves

Tips to Prepare for Exam using RD Sharma Solutions for Class 12 Maths Chapter 16

These tips will help students to secure good marks in their board exams from the Tangents and Normals Chapter.

Understand the basic concepts of lines, types of lines, and their properties before attempting Tangent and Normal questions.
Understand the concepts of Tangents and Normal lines clearly and also remember the basic formulas which are used to define Tangents and Normals.
Students are advised to download the free PDF of RD Sharma Solutions For Class 12 Maths Chapter 16 available on the Vedantu platform which provides solutions in an easy and understandable way.

Exercises in RD Sharma Solutions For Class 12 Maths Chapter 16

There are three exercises:

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Vedantu gives you the extra edge that you need to excel in your examinations. Whether you are preparing for CBSE, ICSE, NEET, JEE or International examinations, Vedantu is there to help make your preparation journey a smooth one.

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Conclusion

The RD Sharma Class 12 Tangents and Normals Solutions are prepared according to the CBSE syllabus with respect to the NCERT curriculum. All the solutions PDFs are free to download. So these solutions are very useful for Class 12 students to prepare for their board exams which also have a lot of practice problems for students to improve their subject knowledge.

FAQs on RD Sharma Class 12 Maths Solutions Chapter 16 - Tangents and Normals

1. How do Vedantu's solutions for RD Sharma Class 12 Chapter 16 help in solving problems on tangents and normals?

Vedantu's solutions for RD Sharma Class 12 Chapter 16 provide detailed, step-by-step methods for every problem. They break down complex questions into simple, understandable steps, ensuring students can follow the correct procedure for finding the equations of tangents and normals, angles between curves, and other related concepts as per the 2025-26 CBSE syllabus.

2. What is the first step to find the equation of a tangent to a curve y = f(x) at a given point (x₁, y₁)?

The first and most crucial step, as demonstrated in the RD Sharma solutions, is to find the derivative of the function, which is dy/dx or f'(x). This derivative represents the formula for the slope of the tangent at any point on the curve. You then substitute the given point (x₁, y₁) into the derivative to find the specific slope at that point.

3. How do you determine the equation of a normal to a curve at a specific point?

To find the equation of the normal, you follow these steps, which are clearly outlined in the RD Sharma solutions for Chapter 16:

First, calculate the slope of the tangent (m_t) at the given point by finding dy/dx.
Next, find the slope of the normal (m_n) using the relation m_n = -1 / m_t.
Finally, use the point-slope form, y - y₁ = m_n(x - x₁), to get the final equation of the normal.

4. Why is the derivative dy/dx fundamental to finding the slope of the tangent?

The derivative dy/dx represents the instantaneous rate of change of y with respect to x. Geometrically, this rate of change at a specific point is the slope of the line that just touches the curve at that point, which is the tangent. The RD Sharma solutions build upon this core concept of Applications of Derivatives, using it as the foundation for every problem involving tangents.

5. What is a common mistake when finding the slope of the normal, and how do the solutions help prevent it?

A common mistake is forgetting that the slope of the normal is the negative reciprocal of the tangent's slope. Students often incorrectly use the same slope as the tangent or just change its sign. The RD Sharma solutions reinforce the correct formula, m_normal = -1 / m_tangent, in every relevant problem, helping students avoid this critical error and understand the perpendicular relationship between the two lines.

6. How do the RD Sharma solutions handle problems where the tangent is parallel to the x-axis or y-axis?

The solutions provide a clear method for these special cases:

If a tangent is parallel to the x-axis, its slope is 0. So, we set dy/dx = 0 and solve for the coordinates of the point.
If a tangent is parallel to the y-axis (or perpendicular to the x-axis), its slope is undefined. This occurs when the denominator of dy/dx is zero. We solve for the point where dx/dy = 0.

7. Why is it beneficial to practice from RD Sharma for Tangents and Normals after completing NCERT?

While NCERT builds the foundation, RD Sharma provides a wider variety of problems, including more complex and Higher Order Thinking Skills (HOTS) questions. Practising with RD Sharma Solutions for Chapter 16 helps students master different problem formats, handle tricky calculations, and build the speed and confidence needed for the CBSE Class 12 board exams.

8. How is the concept of tangents used to find the angle of intersection between two curves?

The angle of intersection between two curves at a point is defined as the angle between their tangents at that point. The RD Sharma solutions show that to find this angle (θ), you must:

Find the slopes of the tangents for both curves at the intersection point (let's call them m₁ and m₂).
Use the formula tan(θ) = |(m₁ - m₂)/(1 + m₁m₂)|.
This method effectively applies the core concept of tangents to a more complex problem scenario.